+++ /dev/null
-BOO007-2
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 77
- additive_id2 is 76
- additive_identity is 82
- additive_inverse1 is 84
- additive_inverse2 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- distributivity3 is 88
- distributivity4 is 87
- inverse is 86
- multiplicative_id1 is 79
- multiplicative_id2 is 78
- multiplicative_identity is 85
- multiplicative_inverse1 is 81
- multiplicative_inverse2 is 80
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
- Id : 14, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
- Id : 16, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
- Id : 18, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
- Id : 20, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
- Id : 22, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
- Id : 24, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
- Id : 26, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
- Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
- Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 6.095314s
-BOO007-4
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 87
- additive_identity is 88
- additive_inverse1 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- inverse is 84
- multiplicative_id1 is 85
- multiplicative_identity is 86
- multiplicative_inverse1 is 82
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
- Id : 14, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
- Id : 16, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
- Id : 18, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Timeout !
-FAILURE in 625 iterations
-BOO031-1
-Order
- == is 100
- _ is 99
- a is 98
- add is 95
- additive_inverse is 83
- associativity_of_add is 80
- associativity_of_multiply is 79
- b is 97
- c is 96
- distributivity is 92
- inverse is 89
- l1 is 91
- l2 is 87
- l3 is 90
- l4 is 86
- multiplicative_inverse is 81
- multiply is 94
- n0 is 82
- n1 is 84
- property3 is 88
- property3_dual is 85
- prove_multiply_add_property is 93
-Facts
- Id : 4, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
- Id : 6, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
- Id : 8, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
- Id : 10, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
- Id : 12, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
- Id : 14, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
- Id : 16, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
- Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
- Id : 20, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
- Id : 22, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
- Id : 24, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Goal
- Id : 2, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-Timeout !
-FAILURE in 413 iterations
-BOO034-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- b is 96
- c is 94
- d is 93
- e is 92
- f is 91
- g is 90
- inverse is 97
- left_inverse is 85
- multiply is 95
- prove_single_axiom is 89
- right_inverse is 84
- ternary_multiply_1 is 87
- ternary_multiply_2 is 86
-Facts
- Id : 4, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
- Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
- Id : 8, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
- Id : 10, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
- Id : 12, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-Goal
- Id : 2, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-Timeout !
-FAILURE in 424 iterations
-BOO072-1
-Order
- == is 100
- _ is 99
- a is 97
- add is 96
- b is 98
- dn1 is 93
- huntinton_1 is 95
- inverse is 94
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-Found proof, 0.440809s
-BOO073-1
-Order
- == is 100
- _ is 99
- a is 98
- add is 96
- b is 97
- c is 95
- dn1 is 92
- huntinton_2 is 94
- inverse is 93
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-Found proof, 95.580028s
-BOO076-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- nand is 95
- prove_meredith_2_basis_2 is 94
- sh_1 is 93
-Facts
- Id : 4, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-Timeout !
-FAILURE in 277 iterations
-COL003-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 1120 iterations
-COL003-12
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 1252 iterations
-COL003-20
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 1223 iterations
-COL006-6
-Order
- == is 100
- _ is 99
- apply is 96
- fixed_pt is 97
- k is 92
- k_definition is 91
- prove_strong_fixed_point is 95
- s is 94
- s_definition is 93
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
- Id : 6, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 1708 iterations
-COL011-1
-Order
- == is 100
- _ is 99
- apply is 97
- combinator is 98
- o is 95
- o_definition is 94
- prove_fixed_point is 96
- q1 is 93
- q1_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
- Id : 6, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-Goal
- Id : 2, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 1839 iterations
-COL037-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 944 iterations
-COL038-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 93
- m_definition is 92
- prove_fixed_point is 96
- v is 91
- v_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
- Id : 8, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 1682 iterations
-COL043-3
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- h is 92
- h_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 1406 iterations
-COL044-8
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- n is 92
- n_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 1249 iterations
-COL046-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- m is 91
- m_definition is 90
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 1258 iterations
-COL049-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 91
- m_definition is 90
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
- Id : 8, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 1565 iterations
-COL057-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- i is 89
- i_definition is 88
- prove_strong_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
- Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 1505 iterations
-COL060-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-Found proof, 0.103279s
-COL061-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q1_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-Found proof, 0.116546s
-COL063-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_f_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-Found proof, 1.828433s
-COL064-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_v_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-Found proof, 13.759082s
-COL065-1
-Order
- == is 100
- _ is 99
- apply is 97
- b is 92
- b_definition is 91
- f is 98
- g is 96
- h is 95
- i is 94
- prove_g_combinator is 93
- t is 90
- t_definition is 89
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-Found proof, 68.133820s
-GRP014-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- group_axiom is 92
- inverse is 93
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse
- (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5)
- (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 3.453474s
-GRP024-5
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_commutator is 86
- b is 97
- c is 96
- commutator is 95
- identity is 92
- inverse is 90
- left_identity is 91
- left_inverse is 89
- multiply is 94
- name is 87
- prove_center is 93
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
- Id : 12, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-Goal
- Id : 2, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-Timeout !
-FAILURE in 602 iterations
-GRP114-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- identity is 93
- intersection is 85
- intersection_associative is 79
- intersection_commutative is 81
- intersection_idempotent is 84
- intersection_union_absorbtion is 76
- inverse is 91
- inverse_involution is 87
- inverse_of_identity is 88
- inverse_product_lemma is 86
- left_identity is 92
- left_inverse is 90
- multiply is 95
- multiply_intersection1 is 74
- multiply_intersection2 is 72
- multiply_union1 is 75
- multiply_union2 is 73
- negative_part is 96
- positive_part is 97
- prove_product is 94
- union is 83
- union_associative is 78
- union_commutative is 80
- union_idempotent is 82
- union_intersection_absorbtion is 77
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
- Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
- Id : 14, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
- Id : 16, {_}:
- intersection ?16 ?16 =>= ?16
- [16] by intersection_idempotent ?16
- Id : 18, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
- Id : 20, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
- Id : 22, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
- Id : 24, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
- Id : 26, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
- Id : 28, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
- Id : 30, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
- Id : 32, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
- Id : 34, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
- Id : 36, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
- Id : 38, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
- Id : 40, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
- Id : 42, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-Goal
- Id : 2, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-Timeout !
-FAILURE in 1190 iterations
-GRP164-2
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 87
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 89
- least_upper_bound is 95
- left_identity is 90
- left_inverse is 88
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 91
- prove_distrun is 93
- symmetry_of_glb is 86
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-Timeout !
-FAILURE in 1400 iterations
-GRP167-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 84
- associativity_of_lub is 83
- glb_absorbtion is 79
- greatest_lower_bound is 88
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 93
- inverse is 91
- lat4_1 is 74
- lat4_2 is 73
- lat4_3 is 72
- lat4_4 is 71
- least_upper_bound is 86
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- negative_part is 96
- positive_part is 97
- prove_lat4 is 94
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
- Id : 36, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
- Id : 38, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
- Id : 40, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-Goal
- Id : 2, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-Timeout !
-FAILURE in 1375 iterations
-GRP178-2
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 90
- least_upper_bound is 86
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- p09b_1 is 74
- p09b_2 is 73
- p09b_3 is 72
- p09b_4 is 71
- prove_p09b is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
- Id : 36, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
- Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
- Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-Timeout !
-FAILURE in 2472 iterations
-GRP181-4
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- c is 72
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 94
- p12x_1 is 75
- p12x_2 is 74
- p12x_3 is 73
- p12x_4 is 71
- p12x_5 is 70
- p12x_6 is 69
- p12x_7 is 68
- prove_p12x is 96
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p12x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
- Id : 40, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
- Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
- Id : 44, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
- Id : 46, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-Goal
- Id : 2, {_}: a =>= b [] by prove_p12x
-Timeout !
-FAILURE in 1207 iterations
-GRP183-4
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 94
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 95
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 92
- p20x_1 is 76
- p20x_3 is 75
- prove_20x is 93
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p20x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-Timeout !
-FAILURE in 933 iterations
-GRP184-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21 is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-Timeout !
-FAILURE in 1398 iterations
-GRP184-3
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21x is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-Timeout !
-FAILURE in 1398 iterations
-GRP185-2
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 88
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 91
- least_upper_bound is 94
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p22a_1 is 75
- p22a_2 is 74
- p22a_3 is 73
- prove_p22a is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p22a_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-Timeout !
-FAILURE in 944 iterations
-GRP185-3
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 93
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 90
- least_upper_bound is 94
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p22b is 92
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-Timeout !
-FAILURE in 1232 iterations
-GRP186-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Timeout !
-FAILURE in 1205 iterations
-GRP186-2
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p23_1 is 75
- p23_2 is 74
- p23_3 is 73
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p23_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Timeout !
-FAILURE in 964 iterations
-GRP187-1
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 94
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p33_1 is 75
- prove_p33 is 95
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}:
- least_upper_bound ?24 ?24 =>= ?24
- [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_p33
-Timeout !
-FAILURE in 1541 iterations
-GRP200-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 95
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang1 is 82
- multiply is 96
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang2 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-Timeout !
-FAILURE in 712 iterations
-GRP202-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang3 is 82
- multiply is 95
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang1 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-Timeout !
-FAILURE in 674 iterations
-GRP404-1
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Timeout !
-FAILURE in 342 iterations
-GRP405-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 234.971871s
-GRP422-1
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 14.541466s
-GRP423-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 12.056212s
-GRP444-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 21.164993s
-GRP452-1
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- divide is 93
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 0.549585s
-GRP453-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 91
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 0.716819s
-GRP471-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 115.504740s
-GRP477-1
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 11.020022s
-GRP506-1
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Timeout !
-FAILURE in 184 iterations
-GRP508-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- inverse is 94
- multiply is 96
- prove_these_axioms_4 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-Timeout !
-FAILURE in 183 iterations
-LAT080-1
-Order
- == is 100
- _ is 99
- a is 98
- join is 95
- meet is 97
- prove_normal_axioms_1 is 96
- single_axiom is 94
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-Found proof, 13.776911s
-LAT087-1
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- join is 95
- meet is 96
- prove_normal_axioms_8 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-Found proof, 13.866156s
-LAT093-1
-Order
- == is 100
- _ is 99
- a is 97
- b is 98
- join is 94
- meet is 96
- prove_wal_axioms_2 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-Found proof, 13.533964s
-LAT138-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H7 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 250 iterations
-LAT140-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H2 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-Timeout !
-FAILURE in 250 iterations
-LAT146-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H34 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H28 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-Timeout !
-FAILURE in 250 iterations
-LAT148-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H34 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Timeout !
-FAILURE in 250 iterations
-LAT152-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H40 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 249 iterations
-LAT156-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 249 iterations
-LAT159-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H50 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Timeout !
-FAILURE in 250 iterations
-LAT164-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H76 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 250 iterations
-LAT165-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H77 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-Timeout !
-FAILURE in 269 iterations
-LAT166-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H77 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H78 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-Timeout !
-FAILURE in 269 iterations
-LAT169-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Timeout !
-FAILURE in 268 iterations
-LAT170-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Timeout !
-FAILURE in 269 iterations
-LAT173-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H40 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-Timeout !
-FAILURE in 269 iterations
-LAT175-1
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H79_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H32 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-Timeout !
-FAILURE in 250 iterations
-RNG009-7
-Fatal error: exception Assert_failure("tptp_cnf.ml", 4, 25)
-RNG019-6
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Timeout !
-FAILURE in 393 iterations
-RNG019-7
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- distributivity_of_difference1 is 71
- distributivity_of_difference2 is 70
- distributivity_of_difference3 is 69
- distributivity_of_difference4 is 68
- inverse_product1 is 73
- inverse_product2 is 72
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- product_of_inverses is 74
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Timeout !
-FAILURE in 546 iterations
-RNG020-6
-Order
- == is 100
- _ is 99
- add is 95
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form2 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 97
- v is 96
- x is 98
- y is 94
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-Timeout !
-FAILURE in 398 iterations
-RNG026-6
-Order
- == is 100
- _ is 99
- a is 98
- add is 92
- additive_identity is 90
- additive_inverse is 91
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- b is 97
- c is 95
- commutativity_for_addition is 79
- commutator is 75
- d is 94
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 88
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 86
- multiply is 96
- prove_teichmuller_identity is 89
- right_additive_identity is 87
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 85
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-Timeout !
-FAILURE in 406 iterations
-RNG027-7
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- cx is 97
- cy is 96
- cz is 98
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 95
- product_of_inverses is 75
- prove_right_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-Timeout !
-FAILURE in 538 iterations
-RNG028-9
-Order
- == is 100
- _ is 99
- add is 91
- additive_identity is 92
- additive_inverse is 86
- additive_inverse_additive_inverse is 83
- associativity_for_addition is 79
- associator is 94
- commutativity_for_addition is 80
- commutator is 76
- distribute1 is 82
- distribute2 is 81
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 90
- left_additive_inverse is 85
- left_alternative is 77
- left_multiplicative_zero is 88
- multiply is 96
- product_of_inverses is 75
- prove_left_moufang is 93
- right_additive_identity is 89
- right_additive_inverse is 84
- right_alternative is 78
- right_multiplicative_zero is 87
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-Timeout !
-FAILURE in 537 iterations
-RNG029-7
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 96
- product_of_inverses is 75
- prove_middle_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}:
- add additive_identity ?2 =>= ?2
- [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-Timeout !
-FAILURE in 537 iterations
-RNG035-7
-Fatal error: exception Assert_failure("tptp_cnf.ml", 4, 25)
-ROB006-1
-Order
- == is 100
- _ is 99
- a is 98
- absorbtion is 88
- add is 95
- associativity_of_add is 92
- b is 97
- c is 90
- commutativity_of_add is 93
- d is 89
- negate is 96
- prove_huntingtons_axiom is 94
- robbins_axiom is 91
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
- Id : 8, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}:
- add (negate (add a (negate b)))
- (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-Timeout !
-FAILURE in 163 iterations
-ROB006-2
-Order
- == is 100
- _ is 99
- absorbtion is 90
- add is 98
- associativity_of_add is 95
- c is 92
- commutativity_of_add is 96
- d is 91
- negate is 94
- prove_idempotence is 97
- robbins_axiom is 93
-Facts
- Id : 4, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
- Id : 6, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
- Id : 8, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-Timeout !
-FAILURE in 253 iterations
+++ /dev/null
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 77
- additive_id2 is 76
- additive_identity is 82
- additive_inverse1 is 84
- additive_inverse2 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- distributivity3 is 88
- distributivity4 is 87
- inverse is 86
- multiplicative_id1 is 79
- multiplicative_id2 is 78
- multiplicative_identity is 85
- multiplicative_inverse1 is 81
- multiplicative_inverse2 is 80
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
- Id : 14, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
- Id : 16, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
- Id : 18, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
- Id : 20, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
- Id : 22, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
- Id : 24, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
- Id : 26, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
- Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
- Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 50.092125s
-% SZS status Unsatisfiable for BOO007-2.p
-% SZS output start CNFRefutation for BOO007-2.p
-Id : 22, {_}: multiply (inverse ?30) ?30 =>= additive_identity [30] by multiplicative_inverse2 ?30
-Id : 24, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
-Id : 69, {_}: multiply (add ?160 ?161) ?162 =<= add (multiply ?160 ?162) (multiply ?161 ?162) [162, 161, 160] by distributivity3 ?160 ?161 ?162
-Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-Id : 16, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
-Id : 10, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 26, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
-Id : 18, {_}: add (inverse ?26) ?26 =>= multiplicative_identity [26] by additive_inverse2 ?26
-Id : 8, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 20, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
-Id : 14, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
-Id : 12, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
-Id : 6, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 151, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= add (multiply ?356 ?357) additive_identity [357, 356] by Super 14 with 20 at 2,3
-Id : 157, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= add additive_identity (multiply ?356 ?357) [357, 356] by Demod 151 with 4 at 3
-Id : 3270, {_}: multiply ?3107 (add ?3108 (inverse ?3107)) =>= multiply ?3107 ?3108 [3108, 3107] by Demod 157 with 30 at 3
-Id : 136, {_}: add (multiply (inverse ?335) ?336) ?335 =>= multiply multiplicative_identity (add ?336 ?335) [336, 335] by Super 8 with 18 at 1,3
-Id : 2697, {_}: add (multiply (inverse ?335) ?336) ?335 =>= add ?336 ?335 [336, 335] by Demod 136 with 26 at 3
-Id : 3279, {_}: multiply ?3129 (add ?3128 (inverse ?3129)) =<= multiply ?3129 (multiply (inverse (inverse ?3129)) ?3128) [3128, 3129] by Super 3270 with 2697 at 2,2
-Id : 3256, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= multiply ?356 ?357 [357, 356] by Demod 157 with 30 at 3
-Id : 3316, {_}: multiply ?3129 ?3128 =<= multiply ?3129 (multiply (inverse (inverse ?3129)) ?3128) [3128, 3129] by Demod 3279 with 3256 at 2
-Id : 135, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= multiply (add ?333 ?332) multiplicative_identity [332, 333] by Super 8 with 18 at 2,3
-Id : 141, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= multiply multiplicative_identity (add ?333 ?332) [332, 333] by Demod 135 with 6 at 3
-Id : 2790, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= add ?333 ?332 [332, 333] by Demod 141 with 26 at 3
-Id : 152, {_}: multiply ?359 (add (inverse ?359) ?360) =>= add additive_identity (multiply ?359 ?360) [360, 359] by Super 14 with 20 at 1,3
-Id : 2899, {_}: multiply ?2812 (add (inverse ?2812) ?2813) =>= multiply ?2812 ?2813 [2813, 2812] by Demod 152 with 30 at 3
-Id : 122, {_}: add ?311 (multiply (inverse ?311) ?312) =>= multiply multiplicative_identity (add ?311 ?312) [312, 311] by Super 10 with 16 at 1,3
-Id : 1484, {_}: add ?1608 (multiply (inverse ?1608) ?1609) =>= add ?1608 ?1609 [1609, 1608] by Demod 122 with 26 at 3
-Id : 1488, {_}: add ?1618 additive_identity =<= add ?1618 (inverse (inverse ?1618)) [1618] by Super 1484 with 20 at 2,2
-Id : 1524, {_}: ?1618 =<= add ?1618 (inverse (inverse ?1618)) [1618] by Demod 1488 with 28 at 2
-Id : 2914, {_}: multiply ?2849 (inverse ?2849) =<= multiply ?2849 (inverse (inverse (inverse ?2849))) [2849] by Super 2899 with 1524 at 2,2
-Id : 2987, {_}: additive_identity =<= multiply ?2849 (inverse (inverse (inverse ?2849))) [2849] by Demod 2914 with 20 at 2
-Id : 3172, {_}: add additive_identity (inverse (inverse ?3022)) =?= add ?3022 (inverse (inverse ?3022)) [3022] by Super 2790 with 2987 at 1,2
-Id : 3182, {_}: inverse (inverse ?3022) =<= add ?3022 (inverse (inverse ?3022)) [3022] by Demod 3172 with 30 at 2
-Id : 3183, {_}: inverse (inverse ?3022) =>= ?3022 [3022] by Demod 3182 with 1524 at 3
-Id : 3317, {_}: multiply ?3129 ?3128 =<= multiply ?3129 (multiply ?3129 ?3128) [3128, 3129] by Demod 3316 with 3183 at 1,2,3
-Id : 3479, {_}: multiply (multiply ?3373 ?3374) ?3373 =>= multiply ?3373 ?3374 [3374, 3373] by Super 6 with 3317 at 3
-Id : 3807, {_}: multiply (add ?3814 (multiply ?3812 ?3813)) ?3812 =>= add (multiply ?3814 ?3812) (multiply ?3812 ?3813) [3813, 3812, 3814] by Super 12 with 3479 at 2,3
-Id : 70, {_}: multiply (add ?164 ?165) ?166 =<= add (multiply ?164 ?166) (multiply ?166 ?165) [166, 165, 164] by Super 69 with 6 at 2,3
-Id : 27040, {_}: multiply (add ?32987 (multiply ?32988 ?32989)) ?32988 =>= multiply (add ?32987 ?32989) ?32988 [32989, 32988, 32987] by Demod 3807 with 70 at 3
-Id : 27129, {_}: multiply (multiply (add ?33340 ?33341) ?33342) ?33341 =?= multiply (add (multiply ?33340 ?33342) ?33342) ?33341 [33342, 33341, 33340] by Super 27040 with 12 at 1,2
-Id : 1722, {_}: add (multiply ?1843 ?1842) (inverse (inverse ?1842)) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1842, 1843] by Super 8 with 1524 at 2,3
-Id : 1739, {_}: add (inverse (inverse ?1842)) (multiply ?1843 ?1842) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1843, 1842] by Demod 1722 with 4 at 2
-Id : 6934, {_}: add ?1842 (multiply ?1843 ?1842) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1843, 1842] by Demod 1739 with 3183 at 1,2
-Id : 6935, {_}: add ?1842 (multiply ?1843 ?1842) =<= multiply (add ?1843 ?1842) ?1842 [1843, 1842] by Demod 6934 with 3183 at 2,1,3
-Id : 235, {_}: add (multiply ?485 additive_identity) ?484 =<= multiply (add ?485 ?484) ?484 [484, 485] by Super 8 with 30 at 2,3
-Id : 498, {_}: multiply ?740 (add ?739 ?740) =>= add (multiply ?739 additive_identity) ?740 [739, 740] by Super 6 with 235 at 3
-Id : 236, {_}: add (multiply additive_identity ?488) ?487 =<= multiply ?487 (add ?488 ?487) [487, 488] by Super 8 with 30 at 1,3
-Id : 968, {_}: add (multiply additive_identity ?739) ?740 =?= add (multiply ?739 additive_identity) ?740 [740, 739] by Demod 498 with 236 at 2
-Id : 450, {_}: add ?682 (multiply additive_identity ?683) =<= multiply ?682 (add ?682 ?683) [683, 682] by Super 10 with 28 at 1,3
-Id : 453, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= multiply (inverse ?690) multiplicative_identity [690] by Super 450 with 18 at 2,3
-Id : 478, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= multiply multiplicative_identity (inverse ?690) [690] by Demod 453 with 6 at 3
-Id : 479, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= inverse ?690 [690] by Demod 478 with 26 at 3
-Id : 2879, {_}: multiply ?359 (add (inverse ?359) ?360) =>= multiply ?359 ?360 [360, 359] by Demod 152 with 30 at 3
-Id : 2886, {_}: add (inverse (add (inverse additive_identity) ?2774)) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Super 479 with 2879 at 2,2
-Id : 221, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 18 with 28 at 2
-Id : 2945, {_}: add (inverse (add multiplicative_identity ?2774)) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2886 with 221 at 1,1,1,2
-Id : 1490, {_}: add ?1622 (inverse ?1622) =>= add ?1622 multiplicative_identity [1622] by Super 1484 with 24 at 2,2
-Id : 1526, {_}: multiplicative_identity =<= add ?1622 multiplicative_identity [1622] by Demod 1490 with 16 at 2
-Id : 1546, {_}: add multiplicative_identity ?1675 =>= multiplicative_identity [1675] by Super 4 with 1526 at 3
-Id : 2946, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2945 with 1546 at 1,1,2
-Id : 183, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 22 with 24 at 2
-Id : 2947, {_}: add additive_identity (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2946 with 183 at 1,2
-Id : 2948, {_}: multiply additive_identity ?2774 =<= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2947 with 30 at 2
-Id : 2949, {_}: multiply additive_identity ?2774 =<= inverse (add multiplicative_identity ?2774) [2774] by Demod 2948 with 221 at 1,1,3
-Id : 2950, {_}: multiply additive_identity ?2774 =>= inverse multiplicative_identity [2774] by Demod 2949 with 1546 at 1,3
-Id : 2951, {_}: multiply additive_identity ?2774 =>= additive_identity [2774] by Demod 2950 with 183 at 3
-Id : 3009, {_}: add additive_identity ?740 =<= add (multiply ?739 additive_identity) ?740 [739, 740] by Demod 968 with 2951 at 1,2
-Id : 3029, {_}: ?740 =<= add (multiply ?739 additive_identity) ?740 [739, 740] by Demod 3009 with 30 at 2
-Id : 3031, {_}: ?484 =<= multiply (add ?485 ?484) ?484 [485, 484] by Demod 235 with 3029 at 2
-Id : 6936, {_}: add ?1842 (multiply ?1843 ?1842) =>= ?1842 [1843, 1842] by Demod 6935 with 3031 at 3
-Id : 6956, {_}: add (multiply ?7059 ?7058) ?7058 =>= ?7058 [7058, 7059] by Super 4 with 6936 at 3
-Id : 52241, {_}: multiply (multiply (add ?83798 ?83799) ?83800) ?83799 =>= multiply ?83800 ?83799 [83800, 83799, 83798] by Demod 27129 with 6956 at 1,3
-Id : 52270, {_}: multiply (multiply ?83922 ?83923) (multiply ?83921 ?83922) =>= multiply ?83923 (multiply ?83921 ?83922) [83921, 83923, 83922] by Super 52241 with 6936 at 1,1,2
-Id : 3280, {_}: multiply ?3132 (add ?3131 (inverse ?3132)) =<= multiply ?3132 (multiply ?3131 (inverse (inverse ?3132))) [3131, 3132] by Super 3270 with 2790 at 2,2
-Id : 3318, {_}: multiply ?3132 ?3131 =<= multiply ?3132 (multiply ?3131 (inverse (inverse ?3132))) [3131, 3132] by Demod 3280 with 3256 at 2
-Id : 3319, {_}: multiply ?3132 ?3131 =<= multiply ?3132 (multiply ?3131 ?3132) [3131, 3132] by Demod 3318 with 3183 at 2,2,3
-Id : 3542, {_}: multiply ?3472 (add ?3474 (multiply ?3473 ?3472)) =>= add (multiply ?3472 ?3474) (multiply ?3472 ?3473) [3473, 3474, 3472] by Super 14 with 3319 at 2,3
-Id : 23927, {_}: multiply ?27205 (add ?27206 (multiply ?27207 ?27205)) =>= multiply ?27205 (add ?27206 ?27207) [27207, 27206, 27205] by Demod 3542 with 14 at 3
-Id : 24009, {_}: multiply ?27527 (multiply ?27528 (add ?27526 ?27527)) =?= multiply ?27527 (add (multiply ?27528 ?27526) ?27528) [27526, 27528, 27527] by Super 23927 with 14 at 2,2
-Id : 7091, {_}: add (multiply ?7292 ?7293) ?7293 =>= ?7293 [7293, 7292] by Super 4 with 6936 at 3
-Id : 7092, {_}: add (multiply ?7296 ?7295) ?7296 =>= ?7296 [7295, 7296] by Super 7091 with 6 at 1,2
-Id : 49144, {_}: multiply ?77879 (multiply ?77880 (add ?77881 ?77879)) =>= multiply ?77879 ?77880 [77881, 77880, 77879] by Demod 24009 with 7092 at 2,3
-Id : 6968, {_}: add ?7096 (multiply ?7097 ?7096) =>= ?7096 [7097, 7096] by Demod 6935 with 3031 at 3
-Id : 6969, {_}: add ?7099 (multiply ?7099 ?7100) =>= ?7099 [7100, 7099] by Super 6968 with 6 at 2,2
-Id : 49175, {_}: multiply (multiply ?78012 ?78010) (multiply ?78011 ?78012) =>= multiply (multiply ?78012 ?78010) ?78011 [78011, 78010, 78012] by Super 49144 with 6969 at 2,2,2
-Id : 77462, {_}: multiply (multiply ?134082 ?134083) ?134084 =?= multiply ?134083 (multiply ?134084 ?134082) [134084, 134083, 134082] by Demod 52270 with 49175 at 2
-Id : 77468, {_}: multiply (multiply (add (inverse ?134104) ?134102) ?134103) ?134104 =>= multiply ?134103 (multiply ?134104 ?134102) [134103, 134102, 134104] by Super 77462 with 2879 at 2,3
-Id : 3544, {_}: multiply (multiply ?3481 ?3480) ?3480 =>= multiply ?3480 ?3481 [3480, 3481] by Super 6 with 3319 at 3
-Id : 3902, {_}: multiply (add ?3943 (multiply ?3941 ?3942)) ?3942 =>= add (multiply ?3943 ?3942) (multiply ?3942 ?3941) [3942, 3941, 3943] by Super 12 with 3544 at 2,3
-Id : 27853, {_}: multiply (add ?34448 (multiply ?34449 ?34450)) ?34450 =>= multiply (add ?34448 ?34449) ?34450 [34450, 34449, 34448] by Demod 3902 with 70 at 3
-Id : 27945, {_}: multiply (multiply ?34816 (add ?34815 ?34817)) ?34817 =?= multiply (add (multiply ?34816 ?34815) ?34816) ?34817 [34817, 34815, 34816] by Super 27853 with 14 at 1,2
-Id : 53412, {_}: multiply (multiply ?86132 (add ?86133 ?86134)) ?86134 =>= multiply ?86132 ?86134 [86134, 86133, 86132] by Demod 27945 with 7092 at 1,3
-Id : 53441, {_}: multiply (multiply ?86256 ?86257) (multiply ?86255 ?86257) =>= multiply ?86256 (multiply ?86255 ?86257) [86255, 86257, 86256] by Super 53412 with 6936 at 2,1,2
-Id : 49173, {_}: multiply (multiply ?78002 ?78004) (multiply ?78003 ?78004) =>= multiply (multiply ?78002 ?78004) ?78003 [78003, 78004, 78002] by Super 49144 with 6936 at 2,2,2
-Id : 79216, {_}: multiply (multiply ?86256 ?86257) ?86255 =?= multiply ?86256 (multiply ?86255 ?86257) [86255, 86257, 86256] by Demod 53441 with 49173 at 2
-Id : 290220, {_}: multiply (add (inverse ?134104) ?134102) (multiply ?134104 ?134103) =>= multiply ?134103 (multiply ?134104 ?134102) [134103, 134102, 134104] by Demod 77468 with 79216 at 2
-Id : 148, {_}: multiply (add ?349 ?350) (inverse ?349) =>= add additive_identity (multiply ?350 (inverse ?349)) [350, 349] by Super 12 with 20 at 1,3
-Id : 160, {_}: multiply (inverse ?349) (add ?349 ?350) =>= add additive_identity (multiply ?350 (inverse ?349)) [350, 349] by Demod 148 with 6 at 2
-Id : 4141, {_}: multiply (inverse ?4194) (add ?4194 ?4195) =>= multiply ?4195 (inverse ?4194) [4195, 4194] by Demod 160 with 30 at 3
-Id : 3259, {_}: add (multiply (inverse ?3073) ?3072) ?3073 =<= add (add ?3072 (inverse (inverse ?3073))) ?3073 [3072, 3073] by Super 2697 with 3256 at 1,2
-Id : 3300, {_}: add ?3072 ?3073 =<= add (add ?3072 (inverse (inverse ?3073))) ?3073 [3073, 3072] by Demod 3259 with 2697 at 2
-Id : 3301, {_}: add ?3072 ?3073 =<= add (add ?3072 ?3073) ?3073 [3073, 3072] by Demod 3300 with 3183 at 2,1,3
-Id : 4158, {_}: multiply (inverse (add ?4240 ?4241)) (add ?4240 ?4241) =>= multiply ?4241 (inverse (add ?4240 ?4241)) [4241, 4240] by Super 4141 with 3301 at 2,2
-Id : 4229, {_}: additive_identity =<= multiply ?4241 (inverse (add ?4240 ?4241)) [4240, 4241] by Demod 4158 with 22 at 2
-Id : 5045, {_}: multiply (inverse (add ?4937 ?4936)) ?4936 =>= additive_identity [4936, 4937] by Super 6 with 4229 at 3
-Id : 7219, {_}: multiply (inverse ?7487) (multiply ?7487 ?7488) =>= additive_identity [7488, 7487] by Super 5045 with 6969 at 1,1,2
-Id : 7871, {_}: multiply (add (inverse ?8300) ?8302) (multiply ?8300 ?8301) =>= add additive_identity (multiply ?8302 (multiply ?8300 ?8301)) [8301, 8302, 8300] by Super 12 with 7219 at 1,3
-Id : 7967, {_}: multiply (add (inverse ?8300) ?8302) (multiply ?8300 ?8301) =>= multiply ?8302 (multiply ?8300 ?8301) [8301, 8302, 8300] by Demod 7871 with 30 at 3
-Id : 290221, {_}: multiply ?134102 (multiply ?134104 ?134103) =?= multiply ?134103 (multiply ?134104 ?134102) [134103, 134104, 134102] by Demod 290220 with 7967 at 2
-Id : 166, {_}: multiply (add (inverse ?383) ?384) ?383 =>= add additive_identity (multiply ?384 ?383) [384, 383] by Super 12 with 22 at 1,3
-Id : 4249, {_}: multiply (add (inverse ?383) ?384) ?383 =>= multiply ?384 ?383 [384, 383] by Demod 166 with 30 at 3
-Id : 77480, {_}: multiply (multiply ?134153 ?134154) (add (inverse ?134153) ?134152) =>= multiply ?134154 (multiply ?134152 ?134153) [134152, 134154, 134153] by Super 77462 with 4249 at 2,3
-Id : 77935, {_}: multiply (add (inverse ?134153) ?134152) (multiply ?134153 ?134154) =>= multiply ?134154 (multiply ?134152 ?134153) [134154, 134152, 134153] by Demod 77480 with 6 at 2
-Id : 295050, {_}: multiply ?134152 (multiply ?134153 ?134154) =?= multiply ?134154 (multiply ?134152 ?134153) [134154, 134153, 134152] by Demod 77935 with 7967 at 2
-Id : 3012, {_}: add additive_identity ?487 =<= multiply ?487 (add ?488 ?487) [488, 487] by Demod 236 with 2951 at 1,2
-Id : 3025, {_}: ?487 =<= multiply ?487 (add ?488 ?487) [488, 487] by Demod 3012 with 30 at 2
-Id : 6954, {_}: add ?7050 (multiply ?7052 (multiply ?7051 ?7050)) =>= multiply (add ?7050 ?7052) ?7050 [7051, 7052, 7050] by Super 10 with 6936 at 2,3
-Id : 219, {_}: add ?458 (multiply ?459 additive_identity) =<= multiply (add ?458 ?459) ?458 [459, 458] by Super 10 with 28 at 2,3
-Id : 310, {_}: multiply ?527 (add ?527 ?528) =>= add ?527 (multiply ?528 additive_identity) [528, 527] by Super 6 with 219 at 3
-Id : 220, {_}: add ?461 (multiply additive_identity ?462) =<= multiply ?461 (add ?461 ?462) [462, 461] by Super 10 with 28 at 1,3
-Id : 632, {_}: add ?527 (multiply additive_identity ?528) =?= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 310 with 220 at 2
-Id : 3013, {_}: add ?527 additive_identity =<= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 632 with 2951 at 2,2
-Id : 3021, {_}: ?527 =<= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 3013 with 28 at 2
-Id : 3024, {_}: ?458 =<= multiply (add ?458 ?459) ?458 [459, 458] by Demod 219 with 3021 at 2
-Id : 7015, {_}: add ?7050 (multiply ?7052 (multiply ?7051 ?7050)) =>= ?7050 [7051, 7052, 7050] by Demod 6954 with 3024 at 3
-Id : 54601, {_}: multiply ?88480 (multiply ?88481 ?88482) =<= multiply (multiply ?88480 (multiply ?88481 ?88482)) ?88482 [88482, 88481, 88480] by Super 3025 with 7015 at 2,3
-Id : 54602, {_}: multiply ?88484 (multiply ?88485 ?88486) =<= multiply (multiply ?88484 (multiply ?88486 ?88485)) ?88486 [88486, 88485, 88484] by Super 54601 with 6 at 2,1,3
-Id : 7204, {_}: add ?7439 (multiply ?7441 (multiply ?7439 ?7440)) =>= multiply (add ?7439 ?7441) ?7439 [7440, 7441, 7439] by Super 10 with 6969 at 2,3
-Id : 7269, {_}: add ?7439 (multiply ?7441 (multiply ?7439 ?7440)) =>= ?7439 [7440, 7441, 7439] by Demod 7204 with 3024 at 3
-Id : 30112, {_}: multiply ?38749 (multiply ?38748 ?38750) =<= multiply (multiply ?38749 (multiply ?38748 ?38750)) ?38748 [38750, 38748, 38749] by Super 3025 with 7269 at 2,3
-Id : 81336, {_}: multiply ?88484 (multiply ?88485 ?88486) =?= multiply ?88484 (multiply ?88486 ?88485) [88486, 88485, 88484] by Demod 54602 with 30112 at 3
-Id : 297313, {_}: multiply c (multiply b a) === multiply c (multiply b a) [] by Demod 297312 with 81336 at 2
-Id : 297312, {_}: multiply c (multiply a b) =>= multiply c (multiply b a) [] by Demod 292477 with 295050 at 2
-Id : 292477, {_}: multiply b (multiply c a) =>= multiply c (multiply b a) [] by Demod 255 with 290221 at 2
-Id : 255, {_}: multiply a (multiply c b) =>= multiply c (multiply b a) [] by Demod 254 with 6 at 2,3
-Id : 254, {_}: multiply a (multiply c b) =>= multiply c (multiply a b) [] by Demod 253 with 6 at 3
-Id : 253, {_}: multiply a (multiply c b) =<= multiply (multiply a b) c [] by Demod 2 with 6 at 2,2
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-2.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 87
- additive_identity is 88
- additive_inverse1 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- inverse is 84
- multiplicative_id1 is 85
- multiplicative_identity is 86
- multiplicative_inverse1 is 82
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
- Id : 14, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
- Id : 16, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
- Id : 18, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 74.913351s
-% SZS status Unsatisfiable for BOO007-4.p
-% SZS output start CNFRefutation for BOO007-4.p
-Id : 14, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
-Id : 16, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
-Id : 8, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 18, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
-Id : 10, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 6, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 81, {_}: multiply ?187 (add (inverse ?187) ?188) =>= add additive_identity (multiply ?187 ?188) [188, 187] by Super 10 with 18 at 1,3
-Id : 57, {_}: add additive_identity ?136 =>= ?136 [136] by Super 4 with 12 at 3
-Id : 2041, {_}: multiply ?187 (add (inverse ?187) ?188) =>= multiply ?187 ?188 [188, 187] by Demod 81 with 57 at 3
-Id : 2049, {_}: multiply (add (inverse ?1798) ?1799) ?1798 =>= multiply ?1798 ?1799 [1799, 1798] by Super 6 with 2041 at 3
-Id : 72, {_}: add ?169 (multiply (inverse ?169) ?170) =>= multiply multiplicative_identity (add ?169 ?170) [170, 169] by Super 8 with 16 at 1,3
-Id : 65, {_}: multiply multiplicative_identity ?154 =>= ?154 [154] by Super 6 with 14 at 3
-Id : 1065, {_}: add ?169 (multiply (inverse ?169) ?170) =>= add ?169 ?170 [170, 169] by Demod 72 with 65 at 3
-Id : 80, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= add (multiply ?184 ?185) additive_identity [185, 184] by Super 10 with 18 at 2,3
-Id : 88, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= add additive_identity (multiply ?184 ?185) [185, 184] by Demod 80 with 4 at 3
-Id : 2371, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= multiply ?184 ?185 [185, 184] by Demod 88 with 57 at 3
-Id : 2380, {_}: add ?2048 (multiply (inverse ?2048) ?2047) =<= add ?2048 (add ?2047 (inverse (inverse ?2048))) [2047, 2048] by Super 1065 with 2371 at 2,2
-Id : 2402, {_}: add ?2048 ?2047 =<= add ?2048 (add ?2047 (inverse (inverse ?2048))) [2047, 2048] by Demod 2380 with 1065 at 2
-Id : 71, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= multiply (add ?166 ?167) multiplicative_identity [167, 166] by Super 8 with 16 at 2,3
-Id : 79, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= multiply multiplicative_identity (add ?166 ?167) [167, 166] by Demod 71 with 6 at 3
-Id : 1969, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= add ?166 ?167 [167, 166] by Demod 79 with 65 at 3
-Id : 2056, {_}: multiply ?1815 (add (inverse ?1815) ?1816) =>= multiply ?1815 ?1816 [1816, 1815] by Demod 81 with 57 at 3
-Id : 1077, {_}: add ?1042 (multiply (inverse ?1042) ?1043) =>= add ?1042 ?1043 [1043, 1042] by Demod 72 with 65 at 3
-Id : 1082, {_}: add ?1054 additive_identity =<= add ?1054 (inverse (inverse ?1054)) [1054] by Super 1077 with 18 at 2,2
-Id : 1115, {_}: ?1054 =<= add ?1054 (inverse (inverse ?1054)) [1054] by Demod 1082 with 12 at 2
-Id : 2072, {_}: multiply ?1854 (inverse ?1854) =<= multiply ?1854 (inverse (inverse (inverse ?1854))) [1854] by Super 2056 with 1115 at 2,2
-Id : 2140, {_}: additive_identity =<= multiply ?1854 (inverse (inverse (inverse ?1854))) [1854] by Demod 2072 with 18 at 2
-Id : 2304, {_}: add (inverse (inverse ?1984)) additive_identity =?= add (inverse (inverse ?1984)) ?1984 [1984] by Super 1969 with 2140 at 2,2
-Id : 2314, {_}: add additive_identity (inverse (inverse ?1984)) =<= add (inverse (inverse ?1984)) ?1984 [1984] by Demod 2304 with 4 at 2
-Id : 2315, {_}: inverse (inverse ?1984) =<= add (inverse (inverse ?1984)) ?1984 [1984] by Demod 2314 with 57 at 2
-Id : 1260, {_}: add (inverse (inverse ?1219)) ?1219 =>= ?1219 [1219] by Super 4 with 1115 at 3
-Id : 2316, {_}: inverse (inverse ?1984) =>= ?1984 [1984] by Demod 2315 with 1260 at 3
-Id : 2403, {_}: add ?2048 ?2047 =<= add ?2048 (add ?2047 ?2048) [2047, 2048] by Demod 2402 with 2316 at 2,2,3
-Id : 2435, {_}: add ?2108 (multiply ?2110 (add ?2109 ?2108)) =<= multiply (add ?2108 ?2110) (add ?2108 ?2109) [2109, 2110, 2108] by Super 8 with 2403 at 2,3
-Id : 2463, {_}: add ?2108 (multiply ?2110 (add ?2109 ?2108)) =>= add ?2108 (multiply ?2110 ?2109) [2109, 2110, 2108] by Demod 2435 with 8 at 3
-Id : 18875, {_}: multiply (add (inverse ?19839) (multiply ?19837 ?19838)) ?19839 =?= multiply ?19839 (multiply ?19837 (add ?19838 (inverse ?19839))) [19838, 19837, 19839] by Super 2049 with 2463 at 1,2
-Id : 151787, {_}: multiply ?278411 (multiply ?278412 ?278413) =<= multiply ?278411 (multiply ?278412 (add ?278413 (inverse ?278411))) [278413, 278412, 278411] by Demod 18875 with 2049 at 2
-Id : 1071, {_}: add (multiply (inverse ?1025) ?1026) ?1025 =>= add ?1025 ?1026 [1026, 1025] by Super 4 with 1065 at 3
-Id : 151803, {_}: multiply ?278483 (multiply ?278484 (multiply (inverse (inverse ?278483)) ?278482)) =>= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278484, 278483] by Super 151787 with 1071 at 2,2,3
-Id : 152295, {_}: multiply ?278483 (multiply ?278484 (multiply ?278483 ?278482)) =<= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278484, 278483] by Demod 151803 with 2316 at 1,2,2,2
-Id : 228, {_}: add ?322 (multiply ?323 additive_identity) =<= multiply (add ?322 ?323) ?322 [323, 322] by Super 8 with 12 at 2,3
-Id : 229, {_}: add ?325 (multiply ?326 additive_identity) =<= multiply (add ?326 ?325) ?325 [326, 325] by Super 228 with 4 at 1,3
-Id : 331, {_}: add ?429 (multiply additive_identity ?430) =<= multiply ?429 (add ?429 ?430) [430, 429] by Super 8 with 12 at 1,3
-Id : 332, {_}: add ?432 (multiply additive_identity ?433) =<= multiply ?432 (add ?433 ?432) [433, 432] by Super 331 with 4 at 2,3
-Id : 73, {_}: add (inverse ?172) ?172 =>= multiplicative_identity [172] by Super 4 with 16 at 3
-Id : 336, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= multiply (inverse ?441) multiplicative_identity [441] by Super 331 with 73 at 2,3
-Id : 355, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= multiply multiplicative_identity (inverse ?441) [441] by Demod 336 with 6 at 3
-Id : 356, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= inverse ?441 [441] by Demod 355 with 65 at 3
-Id : 713, {_}: add (multiply additive_identity ?819) (multiply additive_identity (inverse ?819)) =>= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Super 332 with 356 at 2,3
-Id : 726, {_}: multiply additive_identity (add ?819 (inverse ?819)) =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 713 with 10 at 2
-Id : 727, {_}: multiply additive_identity multiplicative_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 726 with 16 at 2,2
-Id : 728, {_}: multiply multiplicative_identity additive_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 727 with 6 at 2
-Id : 729, {_}: additive_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 728 with 65 at 2
-Id : 730, {_}: additive_identity =<= multiply (inverse ?819) (multiply additive_identity ?819) [819] by Demod 729 with 6 at 3
-Id : 1088, {_}: add ?1069 additive_identity =<= add ?1069 (multiply additive_identity ?1069) [1069] by Super 1077 with 730 at 2,2
-Id : 1118, {_}: ?1069 =<= add ?1069 (multiply additive_identity ?1069) [1069] by Demod 1088 with 12 at 2
-Id : 1283, {_}: add (multiply additive_identity ?1241) (multiply additive_identity ?1241) =>= multiply (multiply additive_identity ?1241) ?1241 [1241] by Super 332 with 1118 at 2,3
-Id : 1319, {_}: multiply additive_identity (add ?1241 ?1241) =<= multiply (multiply additive_identity ?1241) ?1241 [1241] by Demod 1283 with 10 at 2
-Id : 82, {_}: multiply (inverse ?190) ?190 =>= additive_identity [190] by Super 6 with 18 at 3
-Id : 1083, {_}: add ?1056 additive_identity =?= add ?1056 ?1056 [1056] by Super 1077 with 82 at 2,2
-Id : 1116, {_}: ?1056 =<= add ?1056 ?1056 [1056] by Demod 1083 with 12 at 2
-Id : 1320, {_}: multiply additive_identity ?1241 =<= multiply (multiply additive_identity ?1241) ?1241 [1241] by Demod 1319 with 1116 at 2,2
-Id : 1567, {_}: multiply ?1480 (multiply additive_identity ?1480) =>= multiply additive_identity ?1480 [1480] by Super 6 with 1320 at 3
-Id : 2051, {_}: add (inverse (add (inverse additive_identity) ?1804)) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Super 356 with 2041 at 2,2
-Id : 92, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 16 with 57 at 2
-Id : 2095, {_}: add (inverse (add multiplicative_identity ?1804)) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2051 with 92 at 1,1,1,2
-Id : 1081, {_}: add ?1052 (inverse ?1052) =>= add ?1052 multiplicative_identity [1052] by Super 1077 with 14 at 2,2
-Id : 1114, {_}: multiplicative_identity =<= add ?1052 multiplicative_identity [1052] by Demod 1081 with 16 at 2
-Id : 1133, {_}: add multiplicative_identity ?1095 =>= multiplicative_identity [1095] by Super 4 with 1114 at 3
-Id : 2096, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2095 with 1133 at 1,1,2
-Id : 139, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 18 with 65 at 2
-Id : 2097, {_}: add additive_identity (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2096 with 139 at 1,2
-Id : 2098, {_}: multiply additive_identity ?1804 =<= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2097 with 57 at 2
-Id : 2099, {_}: multiply additive_identity ?1804 =<= inverse (add multiplicative_identity ?1804) [1804] by Demod 2098 with 92 at 1,1,3
-Id : 2100, {_}: multiply additive_identity ?1804 =>= inverse multiplicative_identity [1804] by Demod 2099 with 1133 at 1,3
-Id : 2101, {_}: multiply additive_identity ?1804 =>= additive_identity [1804] by Demod 2100 with 139 at 3
-Id : 2167, {_}: multiply ?1480 additive_identity =?= multiply additive_identity ?1480 [1480] by Demod 1567 with 2101 at 2,2
-Id : 2168, {_}: multiply ?1480 additive_identity =>= additive_identity [1480] by Demod 2167 with 2101 at 3
-Id : 2174, {_}: add ?325 additive_identity =<= multiply (add ?326 ?325) ?325 [326, 325] by Demod 229 with 2168 at 2,2
-Id : 2180, {_}: ?325 =<= multiply (add ?326 ?325) ?325 [326, 325] by Demod 2174 with 12 at 2
-Id : 1258, {_}: add ?1213 (multiply ?1214 (inverse (inverse ?1213))) =>= multiply (add ?1213 ?1214) ?1213 [1214, 1213] by Super 8 with 1115 at 2,3
-Id : 55, {_}: add ?130 (multiply ?131 additive_identity) =<= multiply (add ?130 ?131) ?130 [131, 130] by Super 8 with 12 at 2,3
-Id : 1274, {_}: add ?1213 (multiply ?1214 (inverse (inverse ?1213))) =>= add ?1213 (multiply ?1214 additive_identity) [1214, 1213] by Demod 1258 with 55 at 3
-Id : 5845, {_}: add ?1213 (multiply ?1214 ?1213) =?= add ?1213 (multiply ?1214 additive_identity) [1214, 1213] by Demod 1274 with 2316 at 2,2,2
-Id : 5846, {_}: add ?1213 (multiply ?1214 ?1213) =>= add ?1213 additive_identity [1214, 1213] by Demod 5845 with 2168 at 2,3
-Id : 5877, {_}: add ?5881 (multiply ?5882 ?5881) =>= ?5881 [5882, 5881] by Demod 5846 with 12 at 3
-Id : 5878, {_}: add ?5884 (multiply ?5884 ?5885) =>= ?5884 [5885, 5884] by Super 5877 with 6 at 2,2
-Id : 6099, {_}: add ?6204 (multiply ?6206 (multiply ?6204 ?6205)) =>= multiply (add ?6204 ?6206) ?6204 [6205, 6206, 6204] by Super 8 with 5878 at 2,3
-Id : 2175, {_}: add ?130 additive_identity =<= multiply (add ?130 ?131) ?130 [131, 130] by Demod 55 with 2168 at 2,2
-Id : 2179, {_}: ?130 =<= multiply (add ?130 ?131) ?130 [131, 130] by Demod 2175 with 12 at 2
-Id : 6162, {_}: add ?6204 (multiply ?6206 (multiply ?6204 ?6205)) =>= ?6204 [6205, 6206, 6204] by Demod 6099 with 2179 at 3
-Id : 23650, {_}: multiply ?28445 (multiply ?28444 ?28446) =<= multiply ?28444 (multiply ?28445 (multiply ?28444 ?28446)) [28446, 28444, 28445] by Super 2180 with 6162 at 1,3
-Id : 152296, {_}: multiply ?278484 (multiply ?278483 ?278482) =<= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278483, 278484] by Demod 152295 with 23650 at 2
-Id : 2442, {_}: add ?2131 ?2132 =<= add ?2131 (add ?2132 ?2131) [2132, 2131] by Demod 2402 with 2316 at 2,2,3
-Id : 2443, {_}: add ?2134 ?2135 =<= add ?2134 (add ?2134 ?2135) [2135, 2134] by Super 2442 with 4 at 2,3
-Id : 2558, {_}: add ?2283 (multiply ?2285 (add ?2283 ?2284)) =<= multiply (add ?2283 ?2285) (add ?2283 ?2284) [2284, 2285, 2283] by Super 8 with 2443 at 2,3
-Id : 2593, {_}: add ?2283 (multiply ?2285 (add ?2283 ?2284)) =>= add ?2283 (multiply ?2285 ?2284) [2284, 2285, 2283] by Demod 2558 with 8 at 3
-Id : 19422, {_}: multiply (add (inverse ?20977) (multiply ?20975 ?20976)) ?20977 =?= multiply ?20977 (multiply ?20975 (add (inverse ?20977) ?20976)) [20976, 20975, 20977] by Super 2049 with 2593 at 1,2
-Id : 19552, {_}: multiply ?20977 (multiply ?20975 ?20976) =<= multiply ?20977 (multiply ?20975 (add (inverse ?20977) ?20976)) [20976, 20975, 20977] by Demod 19422 with 2049 at 2
-Id : 352787, {_}: multiply ?278484 (multiply ?278483 ?278482) =?= multiply ?278483 (multiply ?278484 ?278482) [278482, 278483, 278484] by Demod 152296 with 19552 at 3
-Id : 2159, {_}: add ?432 additive_identity =<= multiply ?432 (add ?433 ?432) [433, 432] by Demod 332 with 2101 at 2,2
-Id : 2194, {_}: ?432 =<= multiply ?432 (add ?433 ?432) [433, 432] by Demod 2159 with 12 at 2
-Id : 5847, {_}: add ?1213 (multiply ?1214 ?1213) =>= ?1213 [1214, 1213] by Demod 5846 with 12 at 3
-Id : 5862, {_}: add ?5837 (multiply ?5839 (multiply ?5838 ?5837)) =>= multiply (add ?5837 ?5839) ?5837 [5838, 5839, 5837] by Super 8 with 5847 at 2,3
-Id : 5925, {_}: add ?5837 (multiply ?5839 (multiply ?5838 ?5837)) =>= ?5837 [5838, 5839, 5837] by Demod 5862 with 2179 at 3
-Id : 36958, {_}: multiply ?53806 (multiply ?53807 ?53808) =<= multiply (multiply ?53806 (multiply ?53807 ?53808)) ?53808 [53808, 53807, 53806] by Super 2194 with 5925 at 2,3
-Id : 36959, {_}: multiply ?53810 (multiply ?53811 ?53812) =<= multiply (multiply ?53810 (multiply ?53812 ?53811)) ?53812 [53812, 53811, 53810] by Super 36958 with 6 at 2,1,3
-Id : 23651, {_}: multiply ?28449 (multiply ?28448 ?28450) =<= multiply (multiply ?28449 (multiply ?28448 ?28450)) ?28448 [28450, 28448, 28449] by Super 2194 with 6162 at 2,3
-Id : 58893, {_}: multiply ?53810 (multiply ?53811 ?53812) =?= multiply ?53810 (multiply ?53812 ?53811) [53812, 53811, 53810] by Demod 36959 with 23651 at 3
-Id : 355225, {_}: multiply c (multiply b a) === multiply c (multiply b a) [] by Demod 355224 with 58893 at 2
-Id : 355224, {_}: multiply c (multiply a b) =>= multiply c (multiply b a) [] by Demod 91 with 352787 at 2
-Id : 91, {_}: multiply a (multiply c b) =>= multiply c (multiply b a) [] by Demod 90 with 6 at 2,3
-Id : 90, {_}: multiply a (multiply c b) =>= multiply c (multiply a b) [] by Demod 89 with 6 at 3
-Id : 89, {_}: multiply a (multiply c b) =<= multiply (multiply a b) c [] by Demod 2 with 6 at 2,2
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-4.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 95
- additive_inverse is 83
- associativity_of_add is 80
- associativity_of_multiply is 79
- b is 97
- c is 96
- distributivity is 92
- inverse is 89
- l1 is 91
- l2 is 87
- l3 is 90
- l4 is 86
- multiplicative_inverse is 81
- multiply is 94
- n0 is 82
- n1 is 84
- property3 is 88
- property3_dual is 85
- prove_multiply_add_property is 93
-Facts
- Id : 4, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
- Id : 6, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
- Id : 8, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
- Id : 10, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
- Id : 12, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
- Id : 14, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
- Id : 16, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
- Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
- Id : 20, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
- Id : 22, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
- Id : 24, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Goal
- Id : 2, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-Found proof, 20.324508s
-% SZS status Unsatisfiable for BOO031-1.p
-% SZS output start CNFRefutation for BOO031-1.p
-Id : 16, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
-Id : 20, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
-Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-Id : 14, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
-Id : 10, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
-Id : 64, {_}: multiply (multiply (add ?211 ?212) (add ?212 ?213)) ?212 =>= ?212 [213, 212, 211] by l4 ?211 ?212 ?213
-Id : 24, {_}: multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Id : 4, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
-Id : 8, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
-Id : 12, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
-Id : 49, {_}: multiply ?140 (add ?141 (add ?140 ?142)) =>= ?140 [142, 141, 140] by l2 ?140 ?141 ?142
-Id : 6, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
-Id : 30, {_}: add (add (multiply ?60 ?61) (multiply ?61 ?62)) ?61 =>= ?61 [62, 61, 60] by l3 ?60 ?61 ?62
-Id : 22, {_}: add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-Id : 31, {_}: add (multiply ?65 ?66) ?66 =>= ?66 [66, 65] by Super 30 with 6 at 1,2
-Id : 51, {_}: multiply ?151 (add ?152 ?151) =>= ?151 [152, 151] by Super 49 with 6 at 2,2,2
-Id : 568, {_}: add ?1169 (add ?1170 ?1169) =>= add ?1170 ?1169 [1170, 1169] by Super 31 with 51 at 1,2
-Id : 1034, {_}: add (add ?2011 ?2012) ?2011 =>= add ?2012 ?2011 [2012, 2011] by Super 22 with 568 at 3
-Id : 47, {_}: add ?131 (multiply ?134 ?131) =>= ?131 [134, 131] by Super 6 with 12 at 2,2,2
-Id : 54, {_}: multiply ?165 (add ?165 ?166) =>= ?165 [166, 165] by Super 49 with 8 at 2,2
-Id : 673, {_}: add (add ?1383 ?1384) ?1383 =>= add ?1383 ?1384 [1384, 1383] by Super 47 with 54 at 2,2
-Id : 1524, {_}: add ?2011 ?2012 =?= add ?2012 ?2011 [2012, 2011] by Demod 1034 with 673 at 2
-Id : 161, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (multiply (add ?2 ?3) (add ?3 ?4)) (add ?4 ?2) [4, 3, 2] by Demod 4 with 24 at 3
-Id : 727, {_}: multiply (add ?1499 ?1500) ?1500 =>= ?1500 [1500, 1499] by Super 64 with 12 at 1,2
-Id : 733, {_}: multiply ?1519 (multiply ?1518 ?1519) =>= multiply ?1518 ?1519 [1518, 1519] by Super 727 with 47 at 1,2
-Id : 1435, {_}: add (multiply ?2622 ?2620) (add (multiply ?2621 ?2620) (multiply (multiply ?2621 ?2620) ?2622)) =<= multiply (multiply (add ?2622 ?2620) (add ?2620 (multiply ?2621 ?2620))) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Super 161 with 733 at 1,2,2
-Id : 34, {_}: add ?77 (multiply ?77 ?78) =>= ?77 [78, 77] by Super 6 with 10 at 2,2
-Id : 1478, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =<= multiply (multiply (add ?2622 ?2620) (add ?2620 (multiply ?2621 ?2620))) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1435 with 34 at 2,2
-Id : 1479, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =<= multiply (multiply (add ?2622 ?2620) ?2620) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1478 with 47 at 2,1,3
-Id : 72, {_}: multiply (add ?249 ?250) ?250 =>= ?250 [250, 249] by Super 64 with 12 at 1,2
-Id : 1480, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =>= multiply ?2620 (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1479 with 72 at 1,3
-Id : 7843, {_}: multiply ?13007 ?13008 =<= multiply ?13007 (multiply (add ?13009 ?13007) ?13008) [13009, 13008, 13007] by Super 24 with 51 at 1,2
-Id : 582, {_}: multiply ?1218 (add ?1219 ?1218) =>= ?1218 [1219, 1218] by Super 49 with 6 at 2,2,2
-Id : 587, {_}: multiply (multiply ?1235 ?1234) ?1235 =>= multiply ?1235 ?1234 [1234, 1235] by Super 582 with 34 at 2,2
-Id : 1123, {_}: multiply ?2124 ?2125 =<= multiply ?2124 (multiply ?2125 ?2124) [2125, 2124] by Super 24 with 587 at 2
-Id : 1768, {_}: multiply ?2124 ?2125 =?= multiply ?2125 ?2124 [2125, 2124] by Demod 1123 with 733 at 3
-Id : 7897, {_}: multiply ?13228 ?13229 =<= multiply ?13228 (multiply ?13229 (add ?13230 ?13228)) [13230, 13229, 13228] by Super 7843 with 1768 at 2,3
-Id : 586, {_}: multiply ?1232 ?1232 =>= ?1232 [1232] by Super 582 with 31 at 2,2
-Id : 618, {_}: multiply ?1282 ?1283 =<= multiply ?1282 (multiply ?1282 ?1283) [1283, 1282] by Super 24 with 586 at 1,2
-Id : 1266, {_}: add (multiply ?2366 ?2364) (add (multiply ?2364 ?2365) (multiply (multiply ?2364 ?2365) ?2366)) =<= multiply (multiply (add ?2366 ?2364) (add ?2364 (multiply ?2364 ?2365))) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Super 161 with 618 at 1,2,2
-Id : 1308, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =<= multiply (multiply (add ?2366 ?2364) (add ?2364 (multiply ?2364 ?2365))) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1266 with 34 at 2,2
-Id : 1309, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =<= multiply (multiply (add ?2366 ?2364) ?2364) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1308 with 34 at 2,1,3
-Id : 16375, {_}: add (multiply ?29661 ?29662) (multiply ?29662 ?29663) =>= multiply ?29662 (add (multiply ?29662 ?29663) ?29661) [29663, 29662, 29661] by Demod 1309 with 72 at 1,3
-Id : 16381, {_}: add (multiply ?29687 (add ?29686 ?29688)) ?29688 =<= multiply (add ?29686 ?29688) (add (multiply (add ?29686 ?29688) ?29688) ?29687) [29688, 29686, 29687] by Super 16375 with 72 at 2,2
-Id : 16548, {_}: add (multiply ?29687 (add ?29686 ?29688)) ?29688 =>= multiply (add ?29686 ?29688) (add ?29688 ?29687) [29688, 29686, 29687] by Demod 16381 with 72 at 1,2,3
-Id : 91, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 10 with 18 at 1,2
-Id : 101, {_}: n0 =<= inverse n1 [] by Super 91 with 20 at 2
-Id : 206, {_}: add n1 n0 =>= n1 [] by Super 18 with 101 at 2,2
-Id : 214, {_}: multiply n1 (add ?663 n1) =>= n1 [663] by Super 12 with 206 at 2,2,2
-Id : 222, {_}: add ?663 n1 =>= n1 [663] by Demod 214 with 91 at 2
-Id : 259, {_}: multiply ?726 (add ?727 n1) =>= ?726 [727, 726] by Super 12 with 222 at 2,2,2
-Id : 268, {_}: multiply ?726 n1 =>= ?726 [726] by Demod 259 with 222 at 2,2
-Id : 306, {_}: multiply (add ?801 n1) (add n1 ?802) =>= n1 [802, 801] by Super 14 with 268 at 2
-Id : 312, {_}: multiply n1 (add n1 ?802) =>= n1 [802] by Demod 306 with 222 at 1,2
-Id : 313, {_}: add n1 ?802 =>= n1 [802] by Demod 312 with 91 at 2
-Id : 390, {_}: multiply (multiply n1 (add ?884 ?885)) ?884 =>= ?884 [885, 884] by Super 14 with 313 at 1,1,2
-Id : 401, {_}: multiply n1 (multiply (add ?884 ?885) ?884) =>= ?884 [885, 884] by Demod 390 with 24 at 2
-Id : 402, {_}: multiply (add ?884 ?885) ?884 =>= ?884 [885, 884] by Demod 401 with 91 at 2
-Id : 827, {_}: multiply (multiply ?1658 (add ?1656 ?1657)) ?1656 =>= multiply ?1658 ?1656 [1657, 1656, 1658] by Super 24 with 402 at 2,3
-Id : 77, {_}: add (multiply ?268 ?267) (multiply (inverse ?267) ?268) =<= multiply (add ?268 ?267) (multiply (add ?267 (inverse ?267)) (add (inverse ?267) ?268)) [267, 268] by Super 4 with 16 at 2,2
-Id : 88, {_}: add (multiply ?268 ?267) (multiply (inverse ?267) ?268) =>= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 77 with 10 at 2,3
-Id : 1310, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =>= multiply ?2364 (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1309 with 72 at 1,3
-Id : 16342, {_}: add (multiply ?29521 ?29522) (multiply ?29520 ?29521) =>= multiply ?29521 (add (multiply ?29521 ?29522) ?29520) [29520, 29522, 29521] by Super 1524 with 1310 at 3
-Id : 51988, {_}: multiply ?268 (add (multiply ?268 ?267) (inverse ?267)) =?= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 88 with 16342 at 2
-Id : 51989, {_}: multiply ?268 (add (inverse ?267) (multiply ?268 ?267)) =?= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 51988 with 1524 at 2,2
-Id : 52070, {_}: multiply (multiply (add ?105798 ?105797) (add (inverse ?105797) ?105798)) (inverse ?105797) =>= multiply ?105798 (inverse ?105797) [105797, 105798] by Super 827 with 51989 at 1,2
-Id : 52559, {_}: multiply (add ?105798 ?105797) (inverse ?105797) =>= multiply ?105798 (inverse ?105797) [105797, 105798] by Demod 52070 with 827 at 2
-Id : 52560, {_}: multiply (inverse ?105797) (add ?105798 ?105797) =>= multiply ?105798 (inverse ?105797) [105798, 105797] by Demod 52559 with 1768 at 2
-Id : 54336, {_}: add (multiply ?108230 (inverse ?108229)) ?108229 =<= multiply (add ?108230 ?108229) (add ?108229 (inverse ?108229)) [108229, 108230] by Super 16548 with 52560 at 1,2
-Id : 54743, {_}: add (multiply ?108230 (inverse ?108229)) ?108229 =>= multiply (add ?108230 ?108229) n1 [108229, 108230] by Demod 54336 with 18 at 2,3
-Id : 55540, {_}: add (multiply ?110128 (inverse ?110129)) ?110129 =>= add ?110128 ?110129 [110129, 110128] by Demod 54743 with 268 at 3
-Id : 57387, {_}: add (multiply (inverse ?112946) ?112947) ?112946 =>= add ?112947 ?112946 [112947, 112946] by Super 55540 with 1768 at 1,2
-Id : 119, {_}: add (multiply ?10 ?11) (add (multiply ?11 ?12) ?11) =>= ?11 [12, 11, 10] by Demod 8 with 22 at 2
-Id : 216, {_}: multiply (multiply n1 (add n0 ?667)) n0 =>= n0 [667] by Super 14 with 206 at 1,1,2
-Id : 219, {_}: multiply n1 (multiply (add n0 ?667) n0) =>= n0 [667] by Demod 216 with 24 at 2
-Id : 220, {_}: multiply (add n0 ?667) n0 =>= n0 [667] by Demod 219 with 91 at 2
-Id : 100, {_}: add n0 ?26 =>= ?26 [26] by Demod 16 with 20 at 1,2
-Id : 221, {_}: multiply ?667 n0 =>= n0 [667] by Demod 220 with 100 at 1,2
-Id : 225, {_}: add ?674 (multiply ?675 n0) =>= ?674 [675, 674] by Super 6 with 221 at 2,2,2
-Id : 251, {_}: add ?674 n0 =>= ?674 [674] by Demod 225 with 221 at 2,2
-Id : 281, {_}: add (multiply ?753 n0) (multiply n0 ?754) =>= n0 [754, 753] by Super 119 with 251 at 2,2
-Id : 292, {_}: add n0 (multiply n0 ?754) =>= n0 [754] by Demod 281 with 221 at 1,2
-Id : 293, {_}: multiply n0 ?754 =>= n0 [754] by Demod 292 with 100 at 2
-Id : 338, {_}: add n0 (add (multiply ?829 ?830) ?829) =>= ?829 [830, 829] by Super 119 with 293 at 1,2
-Id : 377, {_}: add (multiply ?829 ?830) ?829 =>= ?829 [830, 829] by Demod 338 with 100 at 2
-Id : 38238, {_}: add (multiply ?76482 ?76483) (multiply ?76484 ?76482) =>= multiply ?76482 (add (multiply ?76482 ?76483) ?76484) [76484, 76483, 76482] by Super 1524 with 1310 at 3
-Id : 38322, {_}: add ?76856 (multiply ?76857 (add ?76856 ?76855)) =<= multiply (add ?76856 ?76855) (add (multiply (add ?76856 ?76855) ?76856) ?76857) [76855, 76857, 76856] by Super 38238 with 402 at 1,2
-Id : 47380, {_}: add ?97201 (multiply ?97202 (add ?97201 ?97203)) =>= multiply (add ?97201 ?97203) (add ?97201 ?97202) [97203, 97202, 97201] by Demod 38322 with 402 at 1,2,3
-Id : 47486, {_}: add ?97677 (multiply (add ?97677 ?97679) ?97678) =>= multiply (add ?97677 ?97679) (add ?97677 ?97678) [97678, 97679, 97677] by Super 47380 with 1768 at 2,2
-Id : 52196, {_}: multiply ?106255 (add (inverse ?106256) (multiply ?106255 ?106256)) =?= multiply (add ?106255 ?106256) (add (inverse ?106256) ?106255) [106256, 106255] by Demod 51988 with 1524 at 2,2
-Id : 52239, {_}: multiply ?106398 (add (inverse (inverse ?106398)) (multiply ?106398 (inverse ?106398))) =>= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Super 52196 with 18 at 1,3
-Id : 52779, {_}: multiply ?106398 (add (inverse (inverse ?106398)) n0) =?= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Demod 52239 with 20 at 2,2,2
-Id : 52780, {_}: multiply ?106398 (inverse (inverse ?106398)) =<= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Demod 52779 with 251 at 2,2
-Id : 52781, {_}: multiply ?106398 (inverse (inverse ?106398)) =<= add (inverse (inverse ?106398)) ?106398 [106398] by Demod 52780 with 91 at 3
-Id : 53322, {_}: add (inverse (inverse ?107400)) (multiply (multiply ?107400 (inverse (inverse ?107400))) ?107401) =>= multiply (add (inverse (inverse ?107400)) ?107400) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Super 47486 with 52781 at 1,2,2
-Id : 177, {_}: add ?561 (multiply (multiply ?560 ?561) ?562) =>= ?561 [562, 560, 561] by Super 6 with 24 at 2,2
-Id : 53342, {_}: inverse (inverse ?107400) =<= multiply (add (inverse (inverse ?107400)) ?107400) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Demod 53322 with 177 at 2
-Id : 53343, {_}: inverse (inverse ?107400) =<= multiply (multiply ?107400 (inverse (inverse ?107400))) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Demod 53342 with 52781 at 1,3
-Id : 670, {_}: multiply (multiply ?1373 ?1371) (add ?1371 ?1372) =>= multiply ?1373 ?1371 [1372, 1371, 1373] by Super 24 with 54 at 2,3
-Id : 53344, {_}: inverse (inverse ?107400) =<= multiply ?107400 (inverse (inverse ?107400)) [107400] by Demod 53343 with 670 at 3
-Id : 53988, {_}: add (inverse (inverse ?107962)) ?107962 =>= ?107962 [107962] by Super 377 with 53344 at 1,2
-Id : 53931, {_}: inverse (inverse ?106398) =<= add (inverse (inverse ?106398)) ?106398 [106398] by Demod 52781 with 53344 at 2
-Id : 54117, {_}: inverse (inverse ?107962) =>= ?107962 [107962] by Demod 53988 with 53931 at 2
-Id : 57388, {_}: add (multiply ?112949 ?112950) (inverse ?112949) =>= add ?112950 (inverse ?112949) [112950, 112949] by Super 57387 with 54117 at 1,1,2
-Id : 57660, {_}: add (inverse ?112949) (multiply ?112949 ?112950) =>= add ?112950 (inverse ?112949) [112950, 112949] by Demod 57388 with 1524 at 2
-Id : 1445, {_}: multiply ?2651 (multiply ?2652 ?2651) =>= multiply ?2652 ?2651 [2652, 2651] by Super 727 with 47 at 1,2
-Id : 18543, {_}: multiply ?33695 (multiply ?33696 (multiply ?33697 ?33695)) =>= multiply (multiply ?33696 ?33697) ?33695 [33697, 33696, 33695] by Super 1445 with 24 at 2,2
-Id : 1430, {_}: multiply (multiply ?2603 ?2601) (multiply ?2602 ?2601) =>= multiply ?2603 (multiply ?2602 ?2601) [2602, 2601, 2603] by Super 24 with 733 at 2,3
-Id : 18612, {_}: multiply ?33994 (multiply ?33993 (multiply ?33995 ?33994)) =?= multiply (multiply (multiply ?33993 ?33994) ?33995) ?33994 [33995, 33993, 33994] by Super 18543 with 1430 at 2,2
-Id : 1449, {_}: multiply ?2666 (multiply ?2664 (multiply ?2665 ?2666)) =>= multiply (multiply ?2664 ?2665) ?2666 [2665, 2664, 2666] by Super 1445 with 24 at 2,2
-Id : 18850, {_}: multiply (multiply ?33993 ?33995) ?33994 =<= multiply (multiply (multiply ?33993 ?33994) ?33995) ?33994 [33994, 33995, 33993] by Demod 18612 with 1449 at 2
-Id : 4399, {_}: multiply (multiply (multiply ?6795 ?6794) ?6796) ?6794 =>= multiply (multiply ?6795 ?6794) ?6796 [6796, 6794, 6795] by Super 51 with 177 at 2,2
-Id : 43487, {_}: multiply (multiply ?33993 ?33995) ?33994 =?= multiply (multiply ?33993 ?33994) ?33995 [33994, 33995, 33993] by Demod 18850 with 4399 at 3
-Id : 54429, {_}: multiply (multiply (inverse ?108571) ?108573) (add ?108572 ?108571) =>= multiply (multiply ?108572 (inverse ?108571)) ?108573 [108572, 108573, 108571] by Super 43487 with 52560 at 1,3
-Id : 54563, {_}: multiply (inverse ?108571) (multiply ?108573 (add ?108572 ?108571)) =>= multiply (multiply ?108572 (inverse ?108571)) ?108573 [108572, 108573, 108571] by Demod 54429 with 24 at 2
-Id : 728, {_}: multiply ?1504 (multiply ?1502 (multiply ?1504 ?1503)) =>= multiply ?1502 (multiply ?1504 ?1503) [1503, 1502, 1504] by Super 727 with 6 at 1,2
-Id : 9518, {_}: multiply (multiply ?16547 ?16548) (multiply ?16547 ?16549) =>= multiply ?16548 (multiply ?16547 ?16549) [16549, 16548, 16547] by Super 24 with 728 at 3
-Id : 1122, {_}: multiply (multiply ?2120 ?2121) ?2122 =<= multiply (multiply ?2120 ?2121) (multiply ?2120 ?2122) [2122, 2121, 2120] by Super 24 with 587 at 1,2
-Id : 30202, {_}: multiply (multiply ?16547 ?16548) ?16549 =?= multiply ?16548 (multiply ?16547 ?16549) [16549, 16548, 16547] by Demod 9518 with 1122 at 2
-Id : 54564, {_}: multiply (inverse ?108571) (multiply ?108573 (add ?108572 ?108571)) =>= multiply (inverse ?108571) (multiply ?108572 ?108573) [108572, 108573, 108571] by Demod 54563 with 30202 at 3
-Id : 145944, {_}: add (inverse (inverse ?250795)) (multiply (inverse ?250795) (multiply ?250797 ?250796)) =>= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Super 57660 with 54564 at 2,2
-Id : 146263, {_}: add (multiply ?250797 ?250796) (inverse (inverse ?250795)) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250795, 250796, 250797] by Demod 145944 with 57660 at 2
-Id : 146264, {_}: add (inverse (inverse ?250795)) (multiply ?250797 ?250796) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Demod 146263 with 1524 at 2
-Id : 146265, {_}: add ?250795 (multiply ?250797 ?250796) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Demod 146264 with 54117 at 1,2
-Id : 146266, {_}: add ?250795 (multiply ?250797 ?250796) =<= add (inverse (inverse ?250795)) (multiply ?250796 (add ?250797 ?250795)) [250796, 250797, 250795] by Demod 146265 with 1524 at 3
-Id : 146267, {_}: add ?250795 (multiply ?250797 ?250796) =<= add ?250795 (multiply ?250796 (add ?250797 ?250795)) [250796, 250797, 250795] by Demod 146266 with 54117 at 1,3
-Id : 38316, {_}: add ?76835 (multiply ?76836 (add ?76834 ?76835)) =<= multiply (add ?76834 ?76835) (add (multiply (add ?76834 ?76835) ?76835) ?76836) [76834, 76836, 76835] by Super 38238 with 72 at 1,2
-Id : 38565, {_}: add ?76835 (multiply ?76836 (add ?76834 ?76835)) =>= multiply (add ?76834 ?76835) (add ?76835 ?76836) [76834, 76836, 76835] by Demod 38316 with 72 at 1,2,3
-Id : 146268, {_}: add ?250795 (multiply ?250797 ?250796) =<= multiply (add ?250797 ?250795) (add ?250795 ?250796) [250796, 250797, 250795] by Demod 146267 with 38565 at 3
-Id : 147010, {_}: multiply ?252446 (add ?252445 ?252444) =<= multiply ?252446 (add ?252444 (multiply ?252445 ?252446)) [252444, 252445, 252446] by Super 7897 with 146268 at 2,3
-Id : 152622, {_}: multiply a (add c b) === multiply a (add c b) [] by Demod 152621 with 1524 at 2,3
-Id : 152621, {_}: multiply a (add c b) =<= multiply a (add b c) [] by Demod 19333 with 147010 at 3
-Id : 19333, {_}: multiply a (add c b) =<= multiply a (add c (multiply b a)) [] by Demod 19332 with 1524 at 2,3
-Id : 19332, {_}: multiply a (add c b) =<= multiply a (add (multiply b a) c) [] by Demod 1703 with 1480 at 3
-Id : 1703, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 1702 with 1524 at 3
-Id : 1702, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 2 with 1524 at 2,2
-Id : 2, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
-% SZS output end CNFRefutation for BOO031-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- b is 96
- c is 94
- d is 93
- e is 92
- f is 91
- g is 90
- inverse is 97
- left_inverse is 85
- multiply is 95
- prove_single_axiom is 89
- right_inverse is 84
- ternary_multiply_1 is 87
- ternary_multiply_2 is 86
-Facts
- Id : 4, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
- Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
- Id : 8, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
- Id : 10, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
- Id : 12, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-Goal
- Id : 2, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-Found proof, 2.692905s
-% SZS status Unsatisfiable for BOO034-1.p
-% SZS output start CNFRefutation for BOO034-1.p
-Id : 8, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
-Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-Id : 12, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
-Id : 10, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
-Id : 4, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-Id : 75, {_}: multiply ?212 ?213 ?214 =<= multiply ?212 ?213 (multiply ?215 (multiply ?212 ?213 ?214) ?214) [215, 214, 213, 212] by Super 4 with 6 at 2
-Id : 84, {_}: multiply ?257 ?258 ?259 =<= multiply ?257 ?258 (multiply ?257 ?258 ?259) [259, 258, 257] by Super 75 with 8 at 3,3
-Id : 115, {_}: multiply (multiply ?285 ?286 ?288) ?289 (multiply ?285 ?286 ?287) =?= multiply ?285 ?286 (multiply ?288 ?289 (multiply ?285 ?286 ?287)) [287, 289, 288, 286, 285] by Super 4 with 84 at 3,2
-Id : 298, {_}: multiply ?735 ?736 (multiply ?737 ?738 ?739) =<= multiply ?735 ?736 (multiply ?737 ?738 (multiply ?735 ?736 ?739)) [739, 738, 737, 736, 735] by Demod 115 with 4 at 2
-Id : 184, {_}: multiply ?446 ?447 ?448 =<= multiply ?446 ?447 (multiply ?448 (multiply ?446 ?447 ?448) ?449) [449, 448, 447, 446] by Super 4 with 8 at 2
-Id : 189, {_}: multiply ?470 ?471 (inverse ?471) =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Super 184 with 12 at 2,3,3
-Id : 225, {_}: ?470 =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Demod 189 with 12 at 2
-Id : 321, {_}: multiply (inverse ?865) ?864 (multiply ?864 ?865 ?866) =>= multiply (inverse ?865) ?864 ?864 [866, 864, 865] by Super 298 with 225 at 3,3
-Id : 387, {_}: multiply (inverse ?963) ?964 (multiply ?964 ?963 ?965) =>= ?964 [965, 964, 963] by Demod 321 with 6 at 3
-Id : 389, {_}: multiply (inverse ?974) ?973 ?974 =>= ?973 [973, 974] by Super 387 with 6 at 3,2
-Id : 437, {_}: ?1071 =<= inverse (inverse ?1071) [1071] by Super 12 with 389 at 2
-Id : 462, {_}: multiply ?1119 (inverse ?1119) ?1120 =>= ?1120 [1120, 1119] by Super 10 with 437 at 1,2
-Id : 116, {_}: multiply (multiply ?291 ?292 ?293) ?294 (multiply ?291 ?292 ?295) =?= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Super 4 with 84 at 1,2
-Id : 12671, {_}: multiply ?19232 ?19233 (multiply ?19234 ?19235 ?19236) =<= multiply ?19232 ?19233 (multiply (multiply ?19232 ?19233 ?19234) ?19235 ?19236) [19236, 19235, 19234, 19233, 19232] by Demod 116 with 4 at 2
-Id : 80, {_}: multiply ?236 ?237 (inverse ?237) =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Super 75 with 12 at 2,3,3
-Id : 105, {_}: ?236 =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Demod 80 with 12 at 2
-Id : 996, {_}: ?2202 =<= multiply ?2202 (inverse ?2203) (multiply ?2204 ?2202 ?2203) [2204, 2203, 2202] by Super 105 with 437 at 3,3,3
-Id : 1012, {_}: ?2262 =<= multiply ?2262 (inverse (multiply ?2261 ?2263 (inverse ?2262))) ?2263 [2263, 2261, 2262] by Super 996 with 105 at 3,3
-Id : 459, {_}: ?1109 =<= multiply ?1109 (inverse ?1108) (multiply ?1108 ?1109 ?1110) [1110, 1108, 1109] by Super 225 with 437 at 1,3,3
-Id : 1017, {_}: inverse ?2283 =<= multiply (inverse ?2283) (inverse (multiply ?2283 ?2285 ?2284)) ?2285 [2284, 2285, 2283] by Super 996 with 459 at 3,3
-Id : 1909, {_}: ?3987 =<= multiply ?3987 (inverse (inverse ?3985)) (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Super 1012 with 1017 at 1,2,3
-Id : 1996, {_}: ?3987 =<= multiply ?3987 ?3985 (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Demod 1909 with 437 at 2,3
-Id : 2510, {_}: ?5132 =<= multiply ?5132 (multiply ?5132 (inverse ?5131) ?5133) ?5131 [5133, 5131, 5132] by Super 105 with 1996 at 3,3
-Id : 2812, {_}: multiply ?5719 (inverse (inverse ?5721)) ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Super 105 with 2510 at 3,3
-Id : 2874, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2812 with 437 at 2,2
-Id : 2875, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 ?5721 ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2874 with 437 at 2,1,3
-Id : 12777, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =?= multiply ?19864 ?19863 (multiply ?19864 ?19863 ?19862) [19862, 19863, 19864] by Super 12671 with 2875 at 3,3
-Id : 12993, {_}: multiply ?20226 ?20227 (multiply ?20228 ?20227 ?20226) =>= multiply ?20226 ?20227 ?20228 [20228, 20227, 20226] by Demod 12777 with 84 at 3
-Id : 19, {_}: multiply ?58 ?59 ?61 =<= multiply ?58 ?59 (multiply ?60 (multiply ?58 ?59 ?61) ?61) [60, 61, 59, 58] by Super 4 with 6 at 2
-Id : 463, {_}: multiply ?1122 ?1123 (inverse ?1122) =>= ?1123 [1123, 1122] by Super 389 with 437 at 1,2
-Id : 607, {_}: multiply ?1371 ?1372 (inverse ?1371) =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1372, 1371] by Super 19 with 463 at 2,3,3
-Id : 625, {_}: ?1372 =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1371, 1372] by Demod 607 with 463 at 2
-Id : 460, {_}: ?1113 =<= multiply ?1113 (inverse ?1112) (multiply ?1114 ?1113 ?1112) [1114, 1112, 1113] by Super 105 with 437 at 3,3,3
-Id : 1018, {_}: inverse ?2287 =<= multiply (inverse ?2287) (inverse (multiply ?2288 ?2289 ?2287)) ?2289 [2289, 2288, 2287] by Super 996 with 460 at 3,3
-Id : 2078, {_}: ?4356 =<= multiply ?4356 (inverse (inverse ?4354)) (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Super 1012 with 1018 at 1,2,3
-Id : 2124, {_}: ?4356 =<= multiply ?4356 ?4354 (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Demod 2078 with 437 at 2,3
-Id : 3650, {_}: ?7215 =<= multiply ?7215 (multiply ?7216 (inverse ?7214) ?7215) ?7214 [7214, 7216, 7215] by Super 105 with 2124 at 3,3
-Id : 4032, {_}: multiply ?7968 (inverse (inverse ?7969)) ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Super 625 with 3650 at 3,3
-Id : 4103, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Demod 4032 with 437 at 2,2
-Id : 4104, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 ?7969 ?7967) ?7967 [7967, 7969, 7968] by Demod 4103 with 437 at 2,2,3
-Id : 13062, {_}: multiply ?20502 (multiply ?20501 ?20503 ?20502) (multiply ?20501 ?20503 ?20502) =>= multiply ?20502 (multiply ?20501 ?20503 ?20502) ?20503 [20503, 20501, 20502] by Super 12993 with 4104 at 3,2
-Id : 13612, {_}: multiply ?21322 ?21323 ?21324 =<= multiply ?21324 (multiply ?21322 ?21323 ?21324) ?21323 [21324, 21323, 21322] by Demod 13062 with 6 at 2
-Id : 12903, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =>= multiply ?19864 ?19863 ?19862 [19862, 19863, 19864] by Demod 12777 with 84 at 3
-Id : 13625, {_}: multiply ?21368 ?21369 (multiply ?21367 ?21369 ?21368) =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Super 13612 with 12903 at 2,3
-Id : 13783, {_}: multiply ?21368 ?21369 ?21367 =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Demod 13625 with 12903 at 2
-Id : 34256, {_}: multiply (multiply ?56219 ?56220 ?56221) ?56222 ?56219 =<= multiply ?56219 ?56220 (multiply ?56221 ?56222 (multiply ?56223 ?56219 (inverse ?56220))) [56223, 56222, 56221, 56220, 56219] by Super 4 with 105 at 3,2
-Id : 34781, {_}: multiply (multiply ?57676 ?57677 ?57678) ?57678 ?57676 =>= multiply ?57676 ?57677 ?57678 [57678, 57677, 57676] by Super 34256 with 8 at 3,3
-Id : 34858, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =?= multiply ?57993 (multiply ?57992 ?57993 ?57994) ?57994 [57994, 57993, 57992] by Super 34781 with 4104 at 1,2
-Id : 35129, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =>= multiply ?57992 ?57993 ?57994 [57994, 57993, 57992] by Demod 34858 with 4104 at 3
-Id : 36343, {_}: multiply (multiply ?60132 ?60133 ?60134) ?60134 ?60133 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Super 13783 with 35129 at 2,3
-Id : 36700, {_}: multiply ?60132 ?60133 ?60134 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Demod 36343 with 35129 at 2
-Id : 36701, {_}: multiply ?60132 ?60133 ?60134 =<= multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134) [60134, 60133, 60132] by Demod 36700 with 35129 at 3
-Id : 136, {_}: multiply ?291 ?292 (multiply ?293 ?294 ?295) =<= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Demod 116 with 4 at 2
-Id : 2796, {_}: multiply ?5648 (inverse (inverse ?5650)) ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Super 625 with 2510 at 3,3
-Id : 2887, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Demod 2796 with 437 at 2,2
-Id : 2888, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 ?5650 ?5649) ?5648 [5649, 5650, 5648] by Demod 2887 with 437 at 2,2,3
-Id : 34853, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =?= multiply ?57973 (multiply ?57974 ?57973 ?57972) ?57974 [57972, 57973, 57974] by Super 34781 with 2888 at 1,2
-Id : 35120, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =>= multiply ?57974 ?57973 ?57972 [57972, 57973, 57974] by Demod 34853 with 2888 at 3
-Id : 35775, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =?= multiply ?59268 ?59269 (multiply ?59268 ?59269 ?59270) [59270, 59269, 59268] by Super 136 with 35120 at 3,3
-Id : 36064, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =>= multiply ?59268 ?59269 ?59270 [59270, 59269, 59268] by Demod 35775 with 84 at 3
-Id : 37436, {_}: multiply ?60132 ?60133 ?60134 =?= multiply ?60133 ?60134 ?60132 [60134, 60133, 60132] by Demod 36701 with 36064 at 3
-Id : 25, {_}: multiply ?84 ?85 ?86 =<= multiply ?84 ?85 (multiply ?86 (multiply ?84 ?85 ?86) ?87) [87, 86, 85, 84] by Super 4 with 8 at 2
-Id : 317, {_}: multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?848) =?= multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?845) [848, 847, 846, 845] by Super 298 with 25 at 3,3
-Id : 24761, {_}: multiply ?36657 (multiply ?36658 ?36659 ?36657) (multiply ?36658 ?36659 ?36660) =>= multiply ?36658 ?36659 ?36657 [36660, 36659, 36658, 36657] by Demod 317 with 6 at 3
-Id : 24766, {_}: multiply ?36681 (multiply ?36682 ?36683 ?36681) ?36682 =>= multiply ?36682 ?36683 ?36681 [36683, 36682, 36681] by Super 24761 with 12 at 3,2
-Id : 37850, {_}: multiply ?63783 ?63784 (multiply ?63783 ?63785 ?63784) =>= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Super 24766 with 37436 at 2
-Id : 37801, {_}: multiply ?63587 ?63589 (multiply ?63587 ?63588 ?63589) =>= multiply ?63587 ?63589 ?63588 [63588, 63589, 63587] by Super 12903 with 37436 at 3,2
-Id : 41412, {_}: multiply ?63783 ?63784 ?63785 =?= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Demod 37850 with 37801 at 2
-Id : 42484, {_}: b === b [] by Demod 42483 with 12 at 2
-Id : 42483, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 42482 with 41412 at 3,1,3,2
-Id : 42482, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 42481 with 41412 at 1,3,2
-Id : 42481, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 42480 with 41412 at 2,2
-Id : 42480, {_}: multiply b (multiply d (multiply g f e) c) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 38492 with 41412 at 2
-Id : 38492, {_}: multiply b (inverse (multiply d (multiply g e f) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38491 with 37436 at 2,1,2,2
-Id : 38491, {_}: multiply b (inverse (multiply d (multiply f g e) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38490 with 37436 at 2,1,2,2
-Id : 38490, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 595 with 37436 at 1,2,2
-Id : 595, {_}: multiply b (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 53 with 462 at 1,2
-Id : 53, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 2 with 4 at 1,2,2
-Id : 2, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
-% SZS output end CNFRefutation for BOO034-1.p
-Order
- == is 100
- _ is 99
- a is 97
- add is 96
- b is 98
- dn1 is 93
- huntinton_1 is 95
- inverse is 94
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-Found proof, 0.405036s
-% SZS status Unsatisfiable for BOO072-1.p
-% SZS output start CNFRefutation for BOO072-1.p
-Id : 5, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
-Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
-Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
-Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
-Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
-Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
-Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
-Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
-Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
-Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
-Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
-Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
-Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
-Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
-Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
-Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
-Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
-Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
-Id : 835, {_}: add (inverse ?1599) ?1600 =<= add ?1600 (inverse (add ?1599 (inverse (add (inverse ?1599) ?1600)))) [1600, 1599] by Demod 447 with 427 at 2
-Id : 839, {_}: add (inverse (inverse ?1617)) ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Super 835 with 427 at 1,1,2,1,2,3
-Id : 866, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Demod 839 with 427 at 1,2
-Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
-Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
-Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 443, {_}: inverse (inverse ?1079) =<= add (inverse (add ?1079 (inverse ?1079))) ?1079 [1079] by Super 441 with 22 at 1,2
-Id : 476, {_}: ?1141 =<= add (inverse (add ?1141 (inverse ?1141))) ?1141 [1141] by Demod 443 with 427 at 2
-Id : 483, {_}: inverse ?1163 =<= add (inverse (add (inverse ?1163) ?1163)) (inverse ?1163) [1163] by Super 476 with 427 at 2,1,1,3
-Id : 545, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1237)) ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Super 428 with 483 at 1,1,1,1,1,1,1,2
-Id : 596, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 545 with 427 at 1,1,1,1,1,1,2
-Id : 597, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) ?1237)) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 596 with 427 at 2,1,1,1,2
-Id : 1828, {_}: inverse (add (inverse (add (inverse (add ?2824 ?2825)) ?2824)) (inverse ?2824)) =>= ?2824 [2825, 2824] by Demod 597 with 427 at 3
-Id : 1862, {_}: inverse (add ?2924 (inverse (inverse (add ?2923 ?2924)))) =>= inverse (add ?2923 ?2924) [2923, 2924] by Super 1828 with 57 at 1,1,2
-Id : 1957, {_}: inverse (add ?2924 (add ?2923 ?2924)) =>= inverse (add ?2923 ?2924) [2923, 2924] by Demod 1862 with 427 at 2,1,2
-Id : 1989, {_}: inverse (inverse (add ?3044 ?3043)) =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Super 427 with 1957 at 1,2
-Id : 2126, {_}: add ?3204 ?3205 =<= add ?3205 (add ?3204 ?3205) [3205, 3204] by Demod 1989 with 427 at 2
-Id : 733, {_}: inverse ?1452 =<= add (inverse (add ?1453 ?1452)) (inverse (add (inverse ?1453) ?1452)) [1453, 1452] by Super 441 with 141 at 1,2
-Id : 738, {_}: inverse ?1475 =<= add (inverse (add (inverse ?1474) ?1475)) (inverse (add ?1474 ?1475)) [1474, 1475] by Super 733 with 427 at 1,1,2,3
-Id : 2134, {_}: add (inverse (add (inverse ?3224) ?3223)) (inverse (add ?3224 ?3223)) =>= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3223, 3224] by Super 2126 with 738 at 2,3
-Id : 2159, {_}: inverse ?3223 =<= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3224, 3223] by Demod 2134 with 738 at 2
-Id : 2197, {_}: inverse (add (inverse (inverse ?3289)) (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Super 57 with 2159 at 1,1,1,2
-Id : 2249, {_}: inverse (add ?3289 (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Demod 2197 with 427 at 1,1,2
-Id : 2455, {_}: add (inverse ?3654) (inverse (add ?3653 (inverse (inverse ?3654)))) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Super 459 with 2249 at 2,1,2,3
-Id : 2497, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2455 with 427 at 2,1,2,2
-Id : 2498, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2497 with 427 at 2,1,1,3
-Id : 2499, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 ?3654)) [3653, 3654] by Demod 2498 with 427 at 2,1,2,3
-Id : 2500, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =?= add (inverse (add ?3653 ?3654)) (inverse ?3654) [3653, 3654] by Demod 2499 with 418 at 1,2,3
-Id : 2501, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =>= inverse ?3654 [3653, 3654] by Demod 2500 with 2159 at 3
-Id : 2761, {_}: add (inverse ?4078) (inverse (add ?4079 ?4078)) =>= inverse ?4078 [4079, 4078] by Demod 2500 with 2159 at 3
-Id : 2775, {_}: add (inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Super 2761 with 4 at 2,2
-Id : 2871, {_}: add (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Demod 2775 with 427 at 1,2
-Id : 4872, {_}: add (add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487))))) ?6486 =>= add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487)))) [6487, 6486, 6485] by Demod 2871 with 427 at 3
-Id : 4906, {_}: add (inverse (inverse (add ?6624 ?6625))) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Super 4872 with 2501 at 1,2
-Id : 5128, {_}: add (add ?6624 ?6625) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Demod 4906 with 427 at 1,2
-Id : 5129, {_}: add (add ?6624 ?6625) ?6624 =>= inverse (inverse (add ?6624 ?6625)) [6625, 6624] by Demod 5128 with 2501 at 3
-Id : 5130, {_}: add (add ?6624 ?6625) ?6624 =>= add ?6624 ?6625 [6625, 6624] by Demod 5129 with 427 at 3
-Id : 5176, {_}: add (inverse ?6745) (inverse (add ?6745 ?6746)) =>= inverse ?6745 [6746, 6745] by Super 2501 with 5130 at 1,2,2
-Id : 5963, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (inverse ?1617)) [1618, 1617] by Demod 866 with 5176 at 1,2,3
-Id : 5973, {_}: add ?1617 ?1618 =?= add ?1618 ?1617 [1618, 1617] by Demod 5963 with 427 at 2,3
-Id : 6201, {_}: add a b === add a b [] by Demod 2 with 5973 at 2
-Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-% SZS output end CNFRefutation for BOO072-1.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 96
- b is 97
- c is 95
- dn1 is 92
- huntinton_2 is 94
- inverse is 93
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-Found proof, 88.839419s
-% SZS status Unsatisfiable for BOO073-1.p
-% SZS output start CNFRefutation for BOO073-1.p
-Id : 5, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
-Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
-Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
-Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
-Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
-Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
-Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
-Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
-Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
-Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
-Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
-Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
-Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
-Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
-Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
-Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
-Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
-Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
-Id : 835, {_}: add (inverse ?1599) ?1600 =<= add ?1600 (inverse (add ?1599 (inverse (add (inverse ?1599) ?1600)))) [1600, 1599] by Demod 447 with 427 at 2
-Id : 839, {_}: add (inverse (inverse ?1617)) ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Super 835 with 427 at 1,1,2,1,2,3
-Id : 866, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Demod 839 with 427 at 1,2
-Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
-Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
-Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 443, {_}: inverse (inverse ?1079) =<= add (inverse (add ?1079 (inverse ?1079))) ?1079 [1079] by Super 441 with 22 at 1,2
-Id : 476, {_}: ?1141 =<= add (inverse (add ?1141 (inverse ?1141))) ?1141 [1141] by Demod 443 with 427 at 2
-Id : 483, {_}: inverse ?1163 =<= add (inverse (add (inverse ?1163) ?1163)) (inverse ?1163) [1163] by Super 476 with 427 at 2,1,1,3
-Id : 545, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1237)) ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Super 428 with 483 at 1,1,1,1,1,1,1,2
-Id : 596, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 545 with 427 at 1,1,1,1,1,1,2
-Id : 597, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) ?1237)) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 596 with 427 at 2,1,1,1,2
-Id : 1828, {_}: inverse (add (inverse (add (inverse (add ?2824 ?2825)) ?2824)) (inverse ?2824)) =>= ?2824 [2825, 2824] by Demod 597 with 427 at 3
-Id : 1862, {_}: inverse (add ?2924 (inverse (inverse (add ?2923 ?2924)))) =>= inverse (add ?2923 ?2924) [2923, 2924] by Super 1828 with 57 at 1,1,2
-Id : 1957, {_}: inverse (add ?2924 (add ?2923 ?2924)) =>= inverse (add ?2923 ?2924) [2923, 2924] by Demod 1862 with 427 at 2,1,2
-Id : 1989, {_}: inverse (inverse (add ?3044 ?3043)) =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Super 427 with 1957 at 1,2
-Id : 2126, {_}: add ?3204 ?3205 =<= add ?3205 (add ?3204 ?3205) [3205, 3204] by Demod 1989 with 427 at 2
-Id : 733, {_}: inverse ?1452 =<= add (inverse (add ?1453 ?1452)) (inverse (add (inverse ?1453) ?1452)) [1453, 1452] by Super 441 with 141 at 1,2
-Id : 738, {_}: inverse ?1475 =<= add (inverse (add (inverse ?1474) ?1475)) (inverse (add ?1474 ?1475)) [1474, 1475] by Super 733 with 427 at 1,1,2,3
-Id : 2134, {_}: add (inverse (add (inverse ?3224) ?3223)) (inverse (add ?3224 ?3223)) =>= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3223, 3224] by Super 2126 with 738 at 2,3
-Id : 2159, {_}: inverse ?3223 =<= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3224, 3223] by Demod 2134 with 738 at 2
-Id : 2197, {_}: inverse (add (inverse (inverse ?3289)) (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Super 57 with 2159 at 1,1,1,2
-Id : 2249, {_}: inverse (add ?3289 (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Demod 2197 with 427 at 1,1,2
-Id : 2455, {_}: add (inverse ?3654) (inverse (add ?3653 (inverse (inverse ?3654)))) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Super 459 with 2249 at 2,1,2,3
-Id : 2497, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2455 with 427 at 2,1,2,2
-Id : 2498, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2497 with 427 at 2,1,1,3
-Id : 2499, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 ?3654)) [3653, 3654] by Demod 2498 with 427 at 2,1,2,3
-Id : 2500, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =?= add (inverse (add ?3653 ?3654)) (inverse ?3654) [3653, 3654] by Demod 2499 with 418 at 1,2,3
-Id : 2501, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =>= inverse ?3654 [3653, 3654] by Demod 2500 with 2159 at 3
-Id : 2761, {_}: add (inverse ?4078) (inverse (add ?4079 ?4078)) =>= inverse ?4078 [4079, 4078] by Demod 2500 with 2159 at 3
-Id : 2775, {_}: add (inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Super 2761 with 4 at 2,2
-Id : 2871, {_}: add (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Demod 2775 with 427 at 1,2
-Id : 4872, {_}: add (add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487))))) ?6486 =>= add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487)))) [6487, 6486, 6485] by Demod 2871 with 427 at 3
-Id : 4906, {_}: add (inverse (inverse (add ?6624 ?6625))) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Super 4872 with 2501 at 1,2
-Id : 5128, {_}: add (add ?6624 ?6625) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Demod 4906 with 427 at 1,2
-Id : 5129, {_}: add (add ?6624 ?6625) ?6624 =>= inverse (inverse (add ?6624 ?6625)) [6625, 6624] by Demod 5128 with 2501 at 3
-Id : 5130, {_}: add (add ?6624 ?6625) ?6624 =>= add ?6624 ?6625 [6625, 6624] by Demod 5129 with 427 at 3
-Id : 5176, {_}: add (inverse ?6745) (inverse (add ?6745 ?6746)) =>= inverse ?6745 [6746, 6745] by Super 2501 with 5130 at 1,2,2
-Id : 5963, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (inverse ?1617)) [1618, 1617] by Demod 866 with 5176 at 1,2,3
-Id : 5973, {_}: add ?1617 ?1618 =?= add ?1618 ?1617 [1618, 1617] by Demod 5963 with 427 at 2,3
-Id : 445, {_}: inverse ?1086 =<= add (inverse (add (inverse (add ?1084 ?1085)) ?1086)) (inverse (add ?1084 ?1086)) [1085, 1084, 1086] by Super 441 with 57 at 1,2
-Id : 3282, {_}: inverse ?4640 =<= add (inverse (add (inverse (add ?4641 ?4642)) ?4640)) (inverse (add ?4641 ?4640)) [4642, 4641, 4640] by Super 441 with 57 at 1,2
-Id : 3306, {_}: inverse ?4739 =<= add (inverse (add (inverse (add ?4738 ?4740)) ?4739)) (inverse (add ?4740 ?4739)) [4740, 4738, 4739] by Super 3282 with 866 at 1,1,1,1,3
-Id : 9402, {_}: inverse (inverse (add ?10628 ?10626)) =<= add (inverse (inverse ?10626)) (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Super 445 with 3306 at 1,1,3
-Id : 9643, {_}: add ?10628 ?10626 =<= add (inverse (inverse ?10626)) (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Demod 9402 with 427 at 2
-Id : 9644, {_}: add ?10628 ?10626 =<= add ?10626 (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Demod 9643 with 427 at 1,3
-Id : 3277, {_}: add (inverse (add (inverse (add ?4621 ?4622)) ?4620)) (inverse (add ?4621 ?4620)) =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (inverse (add (inverse (add ?4621 ?4622)) ?4620))) (inverse (inverse ?4620)))) [4620, 4622, 4621] by Super 866 with 445 at 1,2,1,2,3
-Id : 3341, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (inverse (add (inverse (add ?4621 ?4622)) ?4620))) (inverse (inverse ?4620)))) [4622, 4621, 4620] by Demod 3277 with 445 at 2
-Id : 3342, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (add (inverse (add ?4621 ?4622)) ?4620) (inverse (inverse ?4620)))) [4622, 4621, 4620] by Demod 3341 with 427 at 1,1,2,3
-Id : 3343, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (add (inverse (add ?4621 ?4622)) ?4620) ?4620)) [4622, 4621, 4620] by Demod 3342 with 427 at 2,1,2,3
-Id : 2463, {_}: inverse (add ?3677 (inverse (add ?3678 (inverse ?3677)))) =>= inverse ?3677 [3678, 3677] by Demod 2197 with 427 at 1,1,2
-Id : 2485, {_}: inverse (add (add ?3744 ?3746) ?3746) =>= inverse (add ?3744 ?3746) [3746, 3744] by Super 2463 with 57 at 2,1,2
-Id : 2605, {_}: add (add ?3852 ?3853) ?3853 =<= add ?3853 (inverse (add (inverse (add ?3852 ?3853)) (inverse (add ?3852 ?3853)))) [3853, 3852] by Super 866 with 2485 at 2,1,2,3
-Id : 2630, {_}: add (add ?3852 ?3853) ?3853 =<= add ?3853 (inverse (inverse (add ?3852 ?3853))) [3853, 3852] by Demod 2605 with 418 at 1,2,3
-Id : 2631, {_}: add (add ?3852 ?3853) ?3853 =?= add ?3853 (add ?3852 ?3853) [3853, 3852] by Demod 2630 with 427 at 2,3
-Id : 2044, {_}: add ?3044 ?3043 =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Demod 1989 with 427 at 2
-Id : 2632, {_}: add (add ?3852 ?3853) ?3853 =>= add ?3852 ?3853 [3853, 3852] by Demod 2631 with 2044 at 3
-Id : 3344, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (add ?4621 ?4622)) ?4620)) [4622, 4621, 4620] by Demod 3343 with 2632 at 1,2,3
-Id : 9856, {_}: inverse (inverse (add (inverse (add ?11316 ?11317)) ?11315)) =<= add (inverse (inverse ?11315)) (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Super 445 with 3344 at 1,1,3
-Id : 10050, {_}: add (inverse (add ?11316 ?11317)) ?11315 =<= add (inverse (inverse ?11315)) (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Demod 9856 with 427 at 2
-Id : 10051, {_}: add (inverse (add ?11316 ?11317)) ?11315 =<= add ?11315 (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Demod 10050 with 427 at 1,3
-Id : 27274, {_}: add (inverse (add ?27240 ?27241)) ?27242 =<= add ?27242 (inverse (add ?27240 (inverse (add (inverse (add ?27240 ?27241)) ?27242)))) [27242, 27241, 27240] by Demod 10050 with 427 at 1,3
-Id : 446, {_}: inverse ?1089 =<= add (inverse (add ?1088 ?1089)) (inverse (add (inverse ?1088) ?1089)) [1088, 1089] by Super 441 with 141 at 1,2
-Id : 3303, {_}: inverse ?4728 =<= add (inverse (add (inverse (inverse ?4726)) ?4728)) (inverse (add (inverse (add ?4727 ?4726)) ?4728)) [4727, 4726, 4728] by Super 3282 with 446 at 1,1,1,1,3
-Id : 3407, {_}: inverse ?4728 =<= add (inverse (add ?4726 ?4728)) (inverse (add (inverse (add ?4727 ?4726)) ?4728)) [4727, 4726, 4728] by Demod 3303 with 427 at 1,1,1,3
-Id : 27388, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= add ?27679 (inverse (inverse ?27679)) [27679, 27678] by Super 27274 with 3407 at 1,2,3
-Id : 27835, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= add ?27679 ?27679 [27679, 27678] by Demod 27388 with 427 at 2,3
-Id : 27836, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= ?27679 [27679, 27678] by Demod 27835 with 418 at 3
-Id : 35831, {_}: add ?35916 (inverse (add (inverse (add ?35917 ?35916)) ?35917)) =>= ?35916 [35917, 35916] by Super 5973 with 27836 at 3
-Id : 35837, {_}: add ?35933 (inverse (add (inverse (add ?35933 ?35934)) ?35934)) =>= ?35933 [35934, 35933] by Super 35831 with 5973 at 1,1,1,2,2
-Id : 43017, {_}: add (inverse (add ?44930 ?44931)) ?44931 =>= add ?44931 (inverse ?44930) [44931, 44930] by Super 10051 with 35837 at 1,2,3
-Id : 43043, {_}: add (inverse (inverse ?45008)) (inverse ?45008) =<= add (inverse ?45008) (inverse (inverse (add ?45009 ?45008))) [45009, 45008] by Super 43017 with 2159 at 1,1,2
-Id : 43373, {_}: add ?45008 (inverse ?45008) =<= add (inverse ?45008) (inverse (inverse (add ?45009 ?45008))) [45009, 45008] by Demod 43043 with 427 at 1,2
-Id : 44805, {_}: add ?46602 (inverse ?46602) =<= add (inverse ?46602) (add ?46603 ?46602) [46603, 46602] by Demod 43373 with 427 at 2,3
-Id : 895, {_}: inverse (inverse (add ?1666 ?1665)) =<= add (inverse (inverse ?1665)) (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Super 446 with 738 at 1,1,3
-Id : 960, {_}: add ?1666 ?1665 =<= add (inverse (inverse ?1665)) (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 895 with 427 at 2
-Id : 961, {_}: add ?1666 ?1665 =<= add ?1665 (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 960 with 427 at 1,3
-Id : 962, {_}: add ?1666 ?1665 =<= add ?1665 (inverse (add (add (inverse ?1666) ?1665) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 961 with 427 at 1,1,2,3
-Id : 5181, {_}: add (add ?6762 ?6763) ?6762 =<= add ?6762 (inverse (add (add (inverse (add ?6762 ?6763)) ?6762) (inverse (add ?6762 ?6763)))) [6763, 6762] by Super 962 with 5130 at 1,2,1,2,3
-Id : 5222, {_}: add ?6762 ?6763 =<= add ?6762 (inverse (add (add (inverse (add ?6762 ?6763)) ?6762) (inverse (add ?6762 ?6763)))) [6763, 6762] by Demod 5181 with 5130 at 2
-Id : 6255, {_}: add ?7893 ?7894 =<= add ?7893 (inverse (add (inverse (add ?7893 ?7894)) ?7893)) [7894, 7893] by Demod 5222 with 5130 at 1,2,3
-Id : 6261, {_}: add ?7910 ?7911 =<= add ?7910 (inverse (add (inverse (add ?7911 ?7910)) ?7910)) [7911, 7910] by Super 6255 with 5973 at 1,1,1,2,3
-Id : 27395, {_}: add (inverse (add ?27697 ?27698)) (inverse (add ?27698 ?27697)) =?= add (inverse (add ?27698 ?27697)) (inverse (add ?27698 ?27697)) [27698, 27697] by Super 27274 with 9644 at 1,2,3
-Id : 27857, {_}: add (inverse (add ?27697 ?27698)) (inverse (add ?27698 ?27697)) =>= inverse (add ?27698 ?27697) [27698, 27697] by Demod 27395 with 418 at 3
-Id : 28327, {_}: add (inverse (add ?28496 ?28495)) (inverse (add ?28495 ?28496)) =<= add (inverse (add ?28496 ?28495)) (inverse (add (inverse (inverse (add ?28496 ?28495))) (inverse (add ?28496 ?28495)))) [28495, 28496] by Super 6261 with 27857 at 1,1,1,2,3
-Id : 28628, {_}: inverse (add ?28495 ?28496) =<= add (inverse (add ?28496 ?28495)) (inverse (add (inverse (inverse (add ?28496 ?28495))) (inverse (add ?28496 ?28495)))) [28496, 28495] by Demod 28327 with 27857 at 2
-Id : 2450, {_}: inverse (inverse ?3637) =<= add ?3637 (inverse (add ?3638 (inverse ?3637))) [3638, 3637] by Super 427 with 2249 at 1,2
-Id : 2506, {_}: ?3637 =<= add ?3637 (inverse (add ?3638 (inverse ?3637))) [3638, 3637] by Demod 2450 with 427 at 2
-Id : 5163, {_}: ?6702 =<= add ?6702 (inverse (add (inverse ?6702) ?6701)) [6701, 6702] by Super 2506 with 5130 at 1,2,3
-Id : 28629, {_}: inverse (add ?28495 ?28496) =?= inverse (add ?28496 ?28495) [28496, 28495] by Demod 28628 with 5163 at 3
-Id : 44870, {_}: add (add ?46807 ?46808) (inverse (add ?46807 ?46808)) =<= add (inverse (add ?46808 ?46807)) (add ?46809 (add ?46807 ?46808)) [46809, 46808, 46807] by Super 44805 with 28629 at 1,3
-Id : 45240, {_}: add (inverse (add ?46807 ?46808)) (add ?46807 ?46808) =<= add (inverse (add ?46808 ?46807)) (add ?46809 (add ?46807 ?46808)) [46809, 46808, 46807] by Demod 44870 with 5973 at 2
-Id : 75570, {_}: inverse (add ?71946 (add ?71944 ?71945)) =<= add (inverse (add ?71945 (add ?71946 (add ?71944 ?71945)))) (inverse (add (inverse (add ?71944 ?71945)) (add ?71944 ?71945))) [71945, 71944, 71946] by Super 3344 with 45240 at 1,2,3
-Id : 2205, {_}: inverse ?3320 =<= add (inverse (add ?3321 ?3320)) (inverse ?3320) [3321, 3320] by Demod 2134 with 738 at 2
-Id : 2209, {_}: inverse (inverse ?3338) =<= add (inverse (add ?3339 (inverse ?3338))) ?3338 [3339, 3338] by Super 2205 with 427 at 2,3
-Id : 2281, {_}: ?3338 =<= add (inverse (add ?3339 (inverse ?3338))) ?3338 [3339, 3338] by Demod 2209 with 427 at 2
-Id : 5175, {_}: ?6743 =<= add (inverse (add (inverse ?6743) ?6742)) ?6743 [6742, 6743] by Super 2281 with 5130 at 1,1,3
-Id : 43053, {_}: add (inverse ?45043) ?45043 =<= add ?45043 (inverse (inverse (add (inverse ?45043) ?45042))) [45042, 45043] by Super 43017 with 5175 at 1,1,2
-Id : 43393, {_}: add (inverse ?45043) ?45043 =<= add ?45043 (add (inverse ?45043) ?45042) [45042, 45043] by Demod 43053 with 427 at 2,3
-Id : 46219, {_}: add (add (inverse ?47976) ?47977) ?47976 =>= add (inverse ?47976) ?47976 [47977, 47976] by Super 5973 with 43393 at 3
-Id : 2228, {_}: inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389)))))) =<= add ?3388 (inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389))))))) [3389, 3388, 3386] by Super 2205 with 4 at 1,3
-Id : 2327, {_}: add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389)))) =<= add ?3388 (inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389))))))) [3389, 3388, 3386] by Demod 2228 with 427 at 2
-Id : 4116, {_}: add ?5774 (inverse (add (inverse ?5775) (inverse (add ?5775 ?5776)))) =<= add ?5775 (add ?5774 (inverse (add (inverse ?5775) (inverse (add ?5775 ?5776))))) [5776, 5775, 5774] by Demod 2327 with 427 at 2,3
-Id : 4147, {_}: add (inverse (inverse (add ?5900 ?5901))) (inverse (add (inverse ?5900) (inverse (add ?5900 ?5901)))) =>= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Super 4116 with 2501 at 2,3
-Id : 4368, {_}: inverse (inverse (add ?5900 ?5901)) =<= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Demod 4147 with 2501 at 2
-Id : 4369, {_}: add ?5900 ?5901 =<= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Demod 4368 with 427 at 2
-Id : 4370, {_}: add ?5900 ?5901 =<= add ?5900 (add ?5900 ?5901) [5901, 5900] by Demod 4369 with 427 at 2,3
-Id : 43050, {_}: add (inverse (add ?45034 ?45033)) (add ?45034 ?45033) =>= add (add ?45034 ?45033) (inverse ?45034) [45033, 45034] by Super 43017 with 4370 at 1,1,2
-Id : 43389, {_}: add (inverse (add ?45034 ?45033)) (add ?45034 ?45033) =>= add (inverse ?45034) (add ?45034 ?45033) [45033, 45034] by Demod 43050 with 5973 at 3
-Id : 43042, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add (add ?45005 ?45006) (inverse ?45006) [45006, 45005] by Super 43017 with 2044 at 1,1,2
-Id : 43372, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add (inverse ?45006) (add ?45005 ?45006) [45006, 45005] by Demod 43042 with 5973 at 3
-Id : 43374, {_}: add ?45008 (inverse ?45008) =<= add (inverse ?45008) (add ?45009 ?45008) [45009, 45008] by Demod 43373 with 427 at 2,3
-Id : 48043, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add ?45006 (inverse ?45006) [45006, 45005] by Demod 43372 with 43374 at 3
-Id : 49303, {_}: add ?45033 (inverse ?45033) =?= add (inverse ?45034) (add ?45034 ?45033) [45034, 45033] by Demod 43389 with 48043 at 2
-Id : 5166, {_}: inverse ?6709 =<= add (inverse (add ?6709 ?6710)) (inverse ?6709) [6710, 6709] by Super 2159 with 5130 at 1,1,3
-Id : 43052, {_}: add (inverse (inverse ?45039)) (inverse ?45039) =<= add (inverse ?45039) (inverse (inverse (add ?45039 ?45040))) [45040, 45039] by Super 43017 with 5166 at 1,1,2
-Id : 43391, {_}: add ?45039 (inverse ?45039) =<= add (inverse ?45039) (inverse (inverse (add ?45039 ?45040))) [45040, 45039] by Demod 43052 with 427 at 1,2
-Id : 43392, {_}: add ?45039 (inverse ?45039) =<= add (inverse ?45039) (add ?45039 ?45040) [45040, 45039] by Demod 43391 with 427 at 2,3
-Id : 49304, {_}: add ?45033 (inverse ?45033) =?= add ?45034 (inverse ?45034) [45034, 45033] by Demod 49303 with 43392 at 3
-Id : 49415, {_}: ?50953 =<= add (inverse (add ?50954 (inverse ?50954))) ?50953 [50954, 50953] by Super 2281 with 49304 at 1,1,3
-Id : 50053, {_}: add ?51918 (add ?51919 (inverse ?51919)) =?= add (inverse (add ?51919 (inverse ?51919))) (add ?51919 (inverse ?51919)) [51919, 51918] by Super 46219 with 49415 at 1,2
-Id : 50133, {_}: add ?51918 (add ?51919 (inverse ?51919)) =?= add (inverse ?51919) (inverse (inverse ?51919)) [51919, 51918] by Demod 50053 with 48043 at 3
-Id : 50134, {_}: add ?51918 (add ?51919 (inverse ?51919)) =>= add (inverse ?51919) ?51919 [51919, 51918] by Demod 50133 with 427 at 2,3
-Id : 50710, {_}: ?52352 =<= add ?52352 (inverse (add (inverse ?52351) ?52351)) [52351, 52352] by Super 5163 with 50134 at 1,2,3
-Id : 75914, {_}: inverse (add ?71946 (add ?71944 ?71945)) =<= inverse (add ?71945 (add ?71946 (add ?71944 ?71945))) [71945, 71944, 71946] by Demod 75570 with 50710 at 3
-Id : 77144, {_}: add ?73328 (add ?73326 (add ?73327 ?73328)) =<= add (add ?73326 (add ?73327 ?73328)) (inverse (add (inverse (add ?73329 ?73328)) (inverse (add ?73326 (add ?73327 ?73328))))) [73329, 73327, 73326, 73328] by Super 9644 with 75914 at 2,1,2,3
-Id : 77399, {_}: add ?73328 (add ?73326 (add ?73327 ?73328)) =<= add (inverse (add (inverse (add ?73329 ?73328)) (inverse (add ?73326 (add ?73327 ?73328))))) (add ?73326 (add ?73327 ?73328)) [73329, 73327, 73326, 73328] by Demod 77144 with 5973 at 3
-Id : 77889, {_}: add ?74480 (add ?74481 (add ?74482 ?74480)) =>= add ?74481 (add ?74482 ?74480) [74482, 74481, 74480] by Demod 77399 with 2281 at 3
-Id : 77893, {_}: add ?74496 (add ?74497 (add ?74496 ?74495)) =?= add ?74497 (add (add ?74496 ?74495) ?74496) [74495, 74497, 74496] by Super 77889 with 5130 at 2,2,2
-Id : 78169, {_}: add ?74496 (add ?74497 (add ?74496 ?74495)) =>= add ?74497 (add ?74496 ?74495) [74495, 74497, 74496] by Demod 77893 with 5130 at 2,3
-Id : 77895, {_}: add ?74503 (add ?74504 (add ?74503 ?74505)) =>= add ?74504 (add ?74505 ?74503) [74505, 74504, 74503] by Super 77889 with 5973 at 2,2,2
-Id : 80396, {_}: add ?74497 (add ?74495 ?74496) =?= add ?74497 (add ?74496 ?74495) [74496, 74495, 74497] by Demod 78169 with 77895 at 2
-Id : 80521, {_}: add (add (add ?78514 ?78515) ?78516) (add ?78515 ?78514) =>= add (add ?78514 ?78515) ?78516 [78516, 78515, 78514] by Super 5130 with 80396 at 2
-Id : 79247, {_}: add ?76425 (add ?76426 (add ?76425 ?76427)) =>= add ?76426 (add ?76427 ?76425) [76427, 76426, 76425] by Super 77889 with 5973 at 2,2,2
-Id : 79331, {_}: add ?76775 (add (add ?76775 ?76776) ?76774) =<= add (add (add ?76775 ?76776) ?76774) (add ?76776 ?76775) [76774, 76776, 76775] by Super 79247 with 5130 at 2,2
-Id : 79332, {_}: add ?76778 (add (add ?76778 ?76780) ?76779) =>= add ?76779 (add ?76780 ?76778) [76779, 76780, 76778] by Super 79247 with 5973 at 2,2
-Id : 135898, {_}: add ?76774 (add ?76776 ?76775) =<= add (add (add ?76775 ?76776) ?76774) (add ?76776 ?76775) [76775, 76776, 76774] by Demod 79331 with 79332 at 2
-Id : 140658, {_}: add ?78516 (add ?78515 ?78514) =?= add (add ?78514 ?78515) ?78516 [78514, 78515, 78516] by Demod 80521 with 135898 at 2
-Id : 43039, {_}: add (inverse (inverse ?44995)) (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) [44997, 44996, 44995] by Super 43017 with 445 at 1,1,2
-Id : 43360, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) [44997, 44996, 44995] by Demod 43039 with 427 at 1,2
-Id : 43361, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) (inverse (add ?44996 ?44995)) [44997, 44996, 44995] by Demod 43360 with 5973 at 3
-Id : 43362, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (add (inverse (add ?44996 ?44997)) ?44995) (inverse (add ?44996 ?44995)) [44997, 44996, 44995] by Demod 43361 with 427 at 1,3
-Id : 43363, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (add (inverse (add ?44996 ?44997)) ?44995) [44997, 44996, 44995] by Demod 43362 with 5973 at 3
-Id : 42258, {_}: add (inverse (add ?43873 ?43874)) ?43874 =>= add ?43874 (inverse ?43873) [43874, 43873] by Super 10051 with 35837 at 1,2,3
-Id : 42969, {_}: add ?44778 (inverse (add ?44777 ?44778)) =>= add ?44778 (inverse ?44777) [44777, 44778] by Super 5973 with 42258 at 3
-Id : 415299, {_}: add ?44995 (inverse ?44996) =<= add (inverse (add ?44996 ?44995)) (add (inverse (add ?44996 ?44997)) ?44995) [44997, 44996, 44995] by Demod 43363 with 42969 at 2
-Id : 415494, {_}: add (inverse (add ?628669 ?628668)) (add (inverse (add ?628669 ?628670)) ?628668) =<= add (add (inverse (add ?628669 ?628670)) ?628668) (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) [628670, 628668, 628669] by Super 10051 with 415299 at 1,2,1,2,3
-Id : 416655, {_}: add ?628668 (inverse ?628669) =<= add (add (inverse (add ?628669 ?628670)) ?628668) (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) [628670, 628669, 628668] by Demod 415494 with 415299 at 2
-Id : 416656, {_}: add ?628668 (inverse ?628669) =<= add (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) (add (inverse (add ?628669 ?628670)) ?628668) [628670, 628669, 628668] by Demod 416655 with 5973 at 3
-Id : 418876, {_}: add ?634385 (inverse ?634386) =<= add (inverse ?634386) (add (inverse (add ?634386 ?634387)) ?634385) [634387, 634386, 634385] by Demod 416656 with 2506 at 1,1,3
-Id : 9436, {_}: inverse ?10759 =<= add (inverse (add (inverse (add ?10760 ?10761)) ?10759)) (inverse (add ?10761 ?10759)) [10761, 10760, 10759] by Super 3282 with 866 at 1,1,1,1,3
-Id : 18533, {_}: inverse ?18554 =<= add (inverse (add (inverse (add ?18555 ?18556)) ?18554)) (inverse (add ?18554 ?18556)) [18556, 18555, 18554] by Super 9436 with 5973 at 1,2,3
-Id : 18582, {_}: inverse ?18755 =<= add (inverse (add (inverse ?18756) ?18755)) (inverse (add ?18755 ?18756)) [18756, 18755] by Super 18533 with 418 at 1,1,1,1,3
-Id : 19155, {_}: add (inverse (add ?19200 ?19201)) (inverse (add (inverse ?19201) ?19200)) =>= inverse ?19200 [19201, 19200] by Super 5973 with 18582 at 3
-Id : 418883, {_}: add ?634414 (inverse (inverse (add ?634412 ?634413))) =<= add (inverse (inverse (add ?634412 ?634413))) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Super 418876 with 19155 at 1,1,2,3
-Id : 420154, {_}: add ?634414 (add ?634412 ?634413) =<= add (inverse (inverse (add ?634412 ?634413))) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Demod 418883 with 427 at 2,2
-Id : 420155, {_}: add ?634414 (add ?634412 ?634413) =<= add (add ?634412 ?634413) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Demod 420154 with 427 at 1,3
-Id : 420156, {_}: add ?634414 (add ?634412 ?634413) =<= add (add ?634412 ?634413) (add ?634412 ?634414) [634413, 634412, 634414] by Demod 420155 with 427 at 1,2,3
-Id : 421396, {_}: add (add ?637936 ?637935) (add ?637937 ?637936) =>= add ?637935 (add ?637936 ?637937) [637937, 637935, 637936] by Super 140658 with 420156 at 3
-Id : 421337, {_}: add (add ?637673 ?637674) (add ?637672 ?637673) =>= add ?637672 (add ?637673 ?637674) [637672, 637674, 637673] by Super 80396 with 420156 at 3
-Id : 428375, {_}: add ?637937 (add ?637936 ?637935) =?= add ?637935 (add ?637936 ?637937) [637935, 637936, 637937] by Demod 421396 with 421337 at 2
-Id : 421398, {_}: add ?637944 (add ?637945 ?637946) =<= add (add ?637944 ?637945) (add ?637945 ?637946) [637946, 637945, 637944] by Super 140658 with 420156 at 2
-Id : 418964, {_}: add ?634834 (inverse (inverse (add ?634833 ?634832))) =<= add (inverse (inverse (add ?634833 ?634832))) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Super 418876 with 446 at 1,1,2,3
-Id : 420298, {_}: add ?634834 (add ?634833 ?634832) =<= add (inverse (inverse (add ?634833 ?634832))) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Demod 418964 with 427 at 2,2
-Id : 420299, {_}: add ?634834 (add ?634833 ?634832) =<= add (add ?634833 ?634832) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Demod 420298 with 427 at 1,3
-Id : 420300, {_}: add ?634834 (add ?634833 ?634832) =<= add (add ?634833 ?634832) (add ?634832 ?634834) [634832, 634833, 634834] by Demod 420299 with 427 at 1,2,3
-Id : 431824, {_}: add ?637944 (add ?637945 ?637946) =?= add ?637946 (add ?637944 ?637945) [637946, 637945, 637944] by Demod 421398 with 420300 at 3
-Id : 435227, {_}: add c (add b a) === add c (add b a) [] by Demod 435226 with 80396 at 3
-Id : 435226, {_}: add c (add b a) =<= add c (add a b) [] by Demod 431823 with 431824 at 3
-Id : 431823, {_}: add c (add b a) =<= add b (add c a) [] by Demod 6203 with 428375 at 3
-Id : 6203, {_}: add c (add b a) =<= add a (add c b) [] by Demod 6202 with 5973 at 2,3
-Id : 6202, {_}: add c (add b a) =<= add a (add b c) [] by Demod 6201 with 5973 at 2,2
-Id : 6201, {_}: add c (add a b) =<= add a (add b c) [] by Demod 2 with 5973 at 2
-Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-% SZS output end CNFRefutation for BOO073-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- nand is 95
- prove_meredith_2_basis_2 is 94
- sh_1 is 93
-Facts
- Id : 4, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-Last chance: 1246037795.9
-Last chance: all is indexed 1246038082.63
-Last chance: failed over 100 goal 1246038082.65
-FAILURE in 0 iterations
-% SZS status Timeout for BOO076-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246038383.09
-Last chance: all is indexed 1246039114.07
-Last chance: failed over 100 goal 1246039114.19
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-12.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246039420.58
-Last chance: all is indexed 1246040215.63
-Last chance: failed over 100 goal 1246040481.46
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246040786.39
-Last chance: all is indexed 1246041551.8
-Last chance: failed over 100 goal 1246041551.9
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-20.p
-Order
- == is 100
- _ is 99
- apply is 96
- fixed_pt is 97
- k is 92
- k_definition is 91
- prove_strong_fixed_point is 95
- s is 94
- s_definition is 93
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
- Id : 6, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246041853.36
-Last chance: all is indexed 1246043148.51
-Last chance: failed over 100 goal 1246043148.61
-FAILURE in 0 iterations
-% SZS status Timeout for COL006-6.p
-Order
- == is 100
- _ is 99
- apply is 97
- combinator is 98
- o is 95
- o_definition is 94
- prove_fixed_point is 96
- q1 is 93
- q1_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
- Id : 6, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-Goal
- Id : 2, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-Last chance: 1246043453.25
-Last chance: all is indexed 1246044101.73
-Last chance: failed over 100 goal 1246044104.01
-FAILURE in 0 iterations
-% SZS status Timeout for COL011-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246044405.58
-Last chance: all is indexed 1246045687.02
-Last chance: failed over 100 goal 1246047742.94
-FAILURE in 0 iterations
-% SZS status Timeout for COL037-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 93
- m_definition is 92
- prove_fixed_point is 96
- v is 91
- v_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
- Id : 8, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246048045.65
-Last chance: all is indexed 1246048609.34
-Last chance: failed over 100 goal 1246048629.8
-FAILURE in 0 iterations
-% SZS status Timeout for COL038-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- h is 92
- h_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246048932.
-Last chance: all is indexed 1246050149.29
-Last chance: failed over 100 goal 1246050149.38
-FAILURE in 0 iterations
-% SZS status Timeout for COL043-3.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- n is 92
- n_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246050450.39
-Last chance: all is indexed 1246051298.02
-Last chance: failed over 100 goal 1246051298.1
-FAILURE in 0 iterations
-% SZS status Timeout for COL044-8.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- m is 91
- m_definition is 90
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246051601.26
-Last chance: all is indexed 1246052740.68
-Last chance: failed over 100 goal 1246053297.04
-FAILURE in 0 iterations
-% SZS status Timeout for COL046-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 91
- m_definition is 90
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
- Id : 8, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246053599.67
-Last chance: all is indexed 1246054318.64
-Last chance: failed over 100 goal 1246054325.15
-FAILURE in 0 iterations
-% SZS status Timeout for COL049-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- i is 89
- i_definition is 88
- prove_strong_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
- Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246054626.38
-Last chance: all is indexed 1246055200.41
-Last chance: failed over 100 goal 1246055315.25
-FAILURE in 0 iterations
-% SZS status Timeout for COL057-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-Goal subsumed
-Found proof, 0.118431s
-% SZS status Unsatisfiable for COL060-1.p
-% SZS output start CNFRefutation for COL060-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 410, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 408 with 4 at 2
-Id : 408, {_}: apply (apply (apply ?1205 (g (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1205)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1205)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1205)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) [1205] by Super 389 with 6 at 1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (apply (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (apply (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (g (apply (apply b (apply t ?57)) ?58)) (apply (f (apply (apply b (apply t ?57)) ?58)) (h (apply (apply b (apply t ?57)) ?58))) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (g (apply (apply b ?24) ?25)) (apply (f (apply (apply b ?24) ?25)) (h (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
-% SZS output end CNFRefutation for COL060-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q1_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-Goal subsumed
-Found proof, 0.119590s
-% SZS status Unsatisfiable for COL061-1.p
-% SZS output start CNFRefutation for COL061-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 410, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 409 with 6 at 2,2
-Id : 409, {_}: apply (f (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (apply (apply ?1207 (g (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) [1207] by Super 389 with 4 at 2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (f (apply (apply b (apply t ?57)) ?58)) (apply (h (apply (apply b (apply t ?57)) ?58)) (g (apply (apply b (apply t ?57)) ?58))) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (f (apply (apply b ?24) ?25)) (apply (h (apply (apply b ?24) ?25)) (g (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
-% SZS output end CNFRefutation for COL061-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_f_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-Goal subsumed
-Found proof, 2.017016s
-% SZS status Unsatisfiable for COL063-1.p
-% SZS output start CNFRefutation for COL063-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 3084, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3079 with 6 at 2
-Id : 3079, {_}: apply (apply ?9991 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) [9991] by Super 3059 with 6 at 2,2
-Id : 3059, {_}: apply (apply ?9940 (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (apply (apply ?9941 (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) =>= apply (apply (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) [9941, 9940] by Super 405 with 4 at 2
-Id : 405, {_}: apply (apply (apply ?1195 (apply ?1196 (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (apply ?1197 (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) =>= apply (apply (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196))))) (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) [1197, 1196, 1195] by Super 389 with 4 at 1,1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (apply (h (apply (apply b (apply t ?57)) ?58)) (g (apply (apply b (apply t ?57)) ?58))) (f (apply (apply b (apply t ?57)) ?58)) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (apply (h (apply (apply b ?24) ?25)) (g (apply (apply b ?24) ?25))) (f (apply (apply b ?24) ?25)) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
-% SZS output end CNFRefutation for COL063-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_v_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-Goal subsumed
-Found proof, 14.407016s
-% SZS status Unsatisfiable for COL064-1.p
-% SZS output start CNFRefutation for COL064-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 10866, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10865 with 6 at 2
-Id : 10865, {_}: apply (apply ?36992 (g (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) [36992] by Super 3088 with 4 at 2
-Id : 3088, {_}: apply (apply (apply ?10013 (apply ?10014 (g (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) [10014, 10013] by Super 3083 with 4 at 1,1,2
-Id : 3083, {_}: apply (apply (apply ?10003 (g (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) [10003] by Super 3059 with 6 at 2
-Id : 3059, {_}: apply (apply ?9940 (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (apply (apply ?9941 (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) =>= apply (apply (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) [9941, 9940] by Super 405 with 4 at 2
-Id : 405, {_}: apply (apply (apply ?1195 (apply ?1196 (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (apply ?1197 (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) =>= apply (apply (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196))))) (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) [1197, 1196, 1195] by Super 389 with 4 at 1,1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (apply (h (apply (apply b (apply t ?57)) ?58)) (f (apply (apply b (apply t ?57)) ?58))) (g (apply (apply b (apply t ?57)) ?58)) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (apply (h (apply (apply b ?24) ?25)) (f (apply (apply b ?24) ?25))) (g (apply (apply b ?24) ?25)) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
-% SZS output end CNFRefutation for COL064-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 92
- b_definition is 91
- f is 98
- g is 96
- h is 95
- i is 94
- prove_g_combinator is 93
- t is 90
- t_definition is 89
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-Goal subsumed
-Found proof, 71.220473s
-% SZS status Unsatisfiable for COL065-1.p
-% SZS output start CNFRefutation for COL065-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 24512, {_}: apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) === apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) [] by Super 24511 with 6 at 2
-Id : 24511, {_}: apply (apply ?78509 (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))))) (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) [78509] by Super 5051 with 4 at 2
-Id : 5051, {_}: apply (apply (apply ?14812 (apply ?14813 (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))))) (f (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) [14813, 14812] by Super 5049 with 4 at 1,1,2
-Id : 5049, {_}: apply (apply (apply ?14808 (apply (g (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))))) (f (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) (i (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) [14808] by Super 5030 with 6 at 1,2
-Id : 5030, {_}: apply (apply (apply ?14754 (f (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) (apply ?14755 (apply (g (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (h (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))))) (i (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (i (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (h (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) [14755, 14754] by Super 388 with 4 at 1,2
-Id : 388, {_}: apply (apply (apply (apply ?1025 (apply ?1026 (f (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))))) ?1027) (apply (g (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (h (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))))) (i (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (i (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (h (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026))))) [1027, 1026, 1025] by Super 132 with 4 at 1,1,1,2
-Id : 132, {_}: apply (apply (apply (apply ?316 (f (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) ?315) (apply (g (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (h (apply (apply b b) (apply (apply b (apply t ?315)) ?316))))) (i (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (i (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) (apply (g (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (h (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) [315, 316] by Super 34 with 6 at 1,1,2
-Id : 34, {_}: apply (apply (apply ?76 (apply ?77 (f (apply (apply b b) (apply (apply b ?76) ?77))))) (apply (g (apply (apply b b) (apply (apply b ?76) ?77))) (h (apply (apply b b) (apply (apply b ?76) ?77))))) (i (apply (apply b b) (apply (apply b ?76) ?77))) =>= apply (apply (f (apply (apply b b) (apply (apply b ?76) ?77))) (i (apply (apply b b) (apply (apply b ?76) ?77)))) (apply (g (apply (apply b b) (apply (apply b ?76) ?77))) (h (apply (apply b b) (apply (apply b ?76) ?77)))) [77, 76] by Super 31 with 4 at 1,1,2
-Id : 31, {_}: apply (apply (apply ?69 (f (apply (apply b b) ?69))) (apply (g (apply (apply b b) ?69)) (h (apply (apply b b) ?69)))) (i (apply (apply b b) ?69)) =>= apply (apply (f (apply (apply b b) ?69)) (i (apply (apply b b) ?69))) (apply (g (apply (apply b b) ?69)) (h (apply (apply b b) ?69))) [69] by Super 11 with 4 at 1,2
-Id : 11, {_}: apply (apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25))) (i (apply (apply b ?24) ?25)) =>= apply (apply (f (apply (apply b ?24) ?25)) (i (apply (apply b ?24) ?25))) (apply (g (apply (apply b ?24) ?25)) (h (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,1,2
-Id : 2, {_}: apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) =>= apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) [1] by prove_g_combinator ?1
-% SZS output end CNFRefutation for COL065-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- group_axiom is 92
- inverse is 93
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 3.169341s
-% SZS status Unsatisfiable for GRP014-1.p
-% SZS output start CNFRefutation for GRP014-1.p
-Id : 5, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
-Id : 4, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Id : 7, {_}: multiply ?22 (inverse (multiply (multiply (inverse (multiply (inverse ?23) ?20)) ?24) (inverse (multiply ?23 ?24)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?19) (multiply (inverse (inverse ?22)) ?20))) ?21) (inverse (multiply ?19 ?21))) [21, 19, 24, 20, 23, 22] by Super 5 with 4 at 2,1,1,1,1,2,2
-Id : 65, {_}: multiply (inverse ?586) (multiply ?586 (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587, 586] by Super 4 with 7 at 2,2
-Id : 66, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?596) (multiply (inverse (inverse ?593)) (multiply (inverse ?593) ?598)))) ?597) (inverse (multiply ?596 ?597))) =>= ?598 [597, 598, 593, 596] by Super 4 with 7 at 2
-Id : 285, {_}: multiply (inverse ?2327) (multiply ?2327 ?2328) =?= multiply (inverse (inverse ?2329)) (multiply (inverse ?2329) ?2328) [2329, 2328, 2327] by Super 65 with 66 at 2,2,2
-Id : 188, {_}: multiply (inverse ?1696) (multiply ?1696 ?1694) =?= multiply (inverse (inverse ?1693)) (multiply (inverse ?1693) ?1694) [1693, 1694, 1696] by Super 65 with 66 at 2,2,2
-Id : 299, {_}: multiply (inverse ?2421) (multiply ?2421 ?2422) =?= multiply (inverse ?2420) (multiply ?2420 ?2422) [2420, 2422, 2421] by Super 285 with 188 at 3
-Id : 379, {_}: multiply ?2799 (inverse (multiply (multiply (inverse ?2798) (multiply ?2798 ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2798, 2799] by Super 4 with 299 at 1,1,2,2
-Id : 550, {_}: multiply ?3835 (inverse (multiply (multiply (inverse (multiply (inverse ?3836) (multiply ?3836 ?3837))) ?3838) (inverse (multiply (inverse ?3835) ?3838)))) =>= ?3837 [3838, 3837, 3836, 3835] by Super 4 with 188 at 1,1,1,1,2,2
-Id : 2860, {_}: multiply ?17926 (inverse (multiply (multiply (inverse (multiply (inverse ?17927) (multiply ?17927 ?17928))) (multiply ?17926 ?17929)) (inverse (multiply (inverse ?17930) (multiply ?17930 ?17929))))) =>= ?17928 [17930, 17929, 17928, 17927, 17926] by Super 550 with 299 at 1,2,1,2,2
-Id : 2947, {_}: multiply (multiply (inverse ?18671) (multiply ?18671 ?18672)) (inverse (multiply ?18669 (inverse (multiply (inverse ?18673) (multiply ?18673 (inverse (multiply (multiply (inverse (multiply (inverse ?18668) ?18669)) ?18670) (inverse (multiply ?18668 ?18670))))))))) =>= ?18672 [18670, 18668, 18673, 18669, 18672, 18671] by Super 2860 with 65 at 1,1,2,2
-Id : 2989, {_}: multiply (multiply (inverse ?18671) (multiply ?18671 ?18672)) (inverse (multiply ?18669 (inverse ?18669))) =>= ?18672 [18669, 18672, 18671] by Demod 2947 with 65 at 1,2,1,2,2
-Id : 3000, {_}: multiply ?18805 (inverse (multiply (multiply (inverse ?18806) (multiply ?18806 (inverse (multiply ?18804 (inverse ?18804))))) (inverse (multiply (inverse ?18805) ?18803)))) =>= ?18803 [18803, 18804, 18806, 18805] by Super 379 with 2989 at 2,1,2,1,2,2
-Id : 7432, {_}: multiply (inverse ?40377) (multiply (multiply (inverse (inverse ?40377)) ?40378) (inverse (multiply ?40379 (inverse ?40379)))) =>= ?40378 [40379, 40378, 40377] by Super 65 with 3000 at 2,2
-Id : 3646, {_}: multiply ?23036 (inverse (multiply (multiply (inverse ?23037) (multiply ?23037 (inverse (multiply ?23038 (inverse ?23038))))) (inverse (multiply (inverse ?23036) ?23039)))) =>= ?23039 [23039, 23038, 23037, 23036] by Super 379 with 2989 at 2,1,2,1,2,2
-Id : 3702, {_}: multiply ?23470 (inverse (inverse (multiply ?23472 (inverse ?23472)))) =>= inverse (inverse ?23470) [23472, 23470] by Super 3646 with 2989 at 1,2,2
-Id : 3804, {_}: multiply (inverse ?23847) (multiply ?23847 (inverse (inverse (multiply ?23846 (inverse ?23846))))) =?= multiply (inverse ?23845) (inverse (inverse ?23845)) [23845, 23846, 23847] by Super 299 with 3702 at 2,3
-Id : 4420, {_}: multiply (inverse ?26554) (inverse (inverse ?26554)) =?= multiply (inverse ?26555) (inverse (inverse ?26555)) [26555, 26554] by Demod 3804 with 3702 at 2,2
-Id : 190, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1706) (multiply (inverse (inverse ?1707)) (multiply (inverse ?1707) ?1708)))) ?1709) (inverse (multiply ?1706 ?1709))) =>= ?1708 [1709, 1708, 1707, 1706] by Super 4 with 7 at 2
-Id : 198, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1768) (multiply (inverse (inverse ?1769)) (multiply (inverse ?1769) ?1770)))) ?1771) (inverse (multiply ?1768 ?1771))))) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1771, 1770, 1769, 1768, 1772] by Super 190 with 66 at 1,2,2,1,1,1,1,2
-Id : 223, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse ?1770) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1770, 1772] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
-Id : 4421, {_}: multiply (inverse ?26561) (inverse (inverse ?26561)) =?= multiply (inverse (multiply (multiply (inverse (multiply (inverse ?26557) (multiply (inverse ?26558) (multiply ?26558 ?26559)))) ?26560) (inverse (multiply ?26557 ?26560)))) (inverse ?26559) [26560, 26559, 26558, 26557, 26561] by Super 4420 with 223 at 1,2,3
-Id : 4696, {_}: multiply (inverse ?27771) (inverse (inverse ?27771)) =?= multiply ?27772 (inverse ?27772) [27772, 27771] by Demod 4421 with 223 at 1,3
-Id : 4493, {_}: multiply (inverse ?26561) (inverse (inverse ?26561)) =?= multiply ?26559 (inverse ?26559) [26559, 26561] by Demod 4421 with 223 at 1,3
-Id : 4736, {_}: multiply ?27992 (inverse ?27992) =?= multiply ?27994 (inverse ?27994) [27994, 27992] by Super 4696 with 4493 at 2
-Id : 7526, {_}: multiply (inverse ?40902) (multiply ?40901 (inverse ?40901)) =>= inverse (inverse (inverse ?40902)) [40901, 40902] by Super 7432 with 4736 at 2,2
-Id : 7653, {_}: multiply (inverse ?41400) (multiply ?41400 (inverse ?41399)) =>= inverse (inverse (inverse ?41399)) [41399, 41400] by Super 299 with 7526 at 3
-Id : 8053, {_}: multiply ?18805 (inverse (multiply (inverse (inverse (inverse (multiply ?18804 (inverse ?18804))))) (inverse (multiply (inverse ?18805) ?18803)))) =>= ?18803 [18803, 18804, 18805] by Demod 3000 with 7653 at 1,1,2,2
-Id : 395, {_}: multiply (inverse ?2916) (multiply ?2916 (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915, 2916] by Super 65 with 299 at 1,1,1,1,2,2,2
-Id : 8051, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915] by Demod 395 with 7653 at 2
-Id : 8154, {_}: multiply (inverse ?43172) (multiply ?43172 (inverse ?43173)) =>= inverse (inverse (inverse ?43173)) [43173, 43172] by Super 299 with 7526 at 3
-Id : 474, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?3355) (multiply (inverse ?3356) (multiply ?3356 ?3357)))) ?3358) (inverse (multiply ?3355 ?3358))) =>= ?3357 [3358, 3357, 3356, 3355] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
-Id : 505, {_}: inverse (multiply (multiply (inverse ?3589) (multiply ?3589 ?3588)) (inverse (multiply ?3590 (multiply (multiply (inverse ?3590) (multiply (inverse ?3591) (multiply ?3591 ?3592))) ?3588)))) =>= ?3592 [3592, 3591, 3590, 3588, 3589] by Super 474 with 299 at 1,1,2
-Id : 3283, {_}: inverse (multiply (multiply (inverse ?20660) (multiply ?20660 (inverse (multiply ?20661 (inverse ?20661))))) (inverse (multiply (inverse ?20662) (multiply ?20662 ?20663)))) =>= ?20663 [20663, 20662, 20661, 20660] by Super 505 with 2989 at 2,1,2,1,2
-Id : 251, {_}: multiply ?2088 (inverse (multiply (multiply (inverse (multiply (inverse ?2086) (multiply ?2086 ?2087))) ?2089) (inverse (multiply (inverse ?2088) ?2089)))) =>= ?2087 [2089, 2087, 2086, 2088] by Super 4 with 188 at 1,1,1,1,2,2
-Id : 3330, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?21019) (multiply ?21019 ?21020))) ?21020) (inverse (multiply (inverse ?21022) (multiply ?21022 ?21023)))) =>= ?21023 [21023, 21022, 21020, 21019] by Super 3283 with 251 at 2,1,1,2
-Id : 8160, {_}: multiply (inverse ?43212) (multiply ?43212 ?43211) =?= inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?43208) (multiply ?43208 ?43209))) ?43209) (inverse (multiply (inverse ?43210) (multiply ?43210 ?43211)))))) [43210, 43209, 43208, 43211, 43212] by Super 8154 with 3330 at 2,2,2
-Id : 8246, {_}: multiply (inverse ?43212) (multiply ?43212 ?43211) =>= inverse (inverse ?43211) [43211, 43212] by Demod 8160 with 3330 at 1,1,3
-Id : 8276, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8051 with 8246 at 1,1,1,1,1,1,2
-Id : 3034, {_}: multiply (multiply (inverse ?19018) (multiply ?19018 ?19019)) (inverse (multiply ?19020 (inverse ?19020))) =>= ?19019 [19020, 19019, 19018] by Demod 2947 with 65 at 1,2,1,2,2
-Id : 3049, {_}: multiply (multiply (inverse (inverse ?19126)) (multiply (inverse ?19128) (multiply ?19128 ?19127))) (inverse (multiply ?19129 (inverse ?19129))) =>= multiply ?19126 ?19127 [19129, 19127, 19128, 19126] by Super 3034 with 299 at 2,1,2
-Id : 7592, {_}: multiply (multiply (inverse (inverse ?41055)) (multiply (inverse (inverse ?41053)) (inverse (inverse (inverse ?41053))))) (inverse (multiply ?41056 (inverse ?41056))) =?= multiply ?41055 (multiply ?41054 (inverse ?41054)) [41054, 41056, 41053, 41055] by Super 3049 with 7526 at 2,2,1,2
-Id : 6756, {_}: multiply (multiply (inverse ?37293) (multiply ?37294 (inverse ?37294))) (inverse (multiply ?37295 (inverse ?37295))) =>= inverse ?37293 [37295, 37294, 37293] by Super 2989 with 4736 at 2,1,2
-Id : 6813, {_}: multiply (multiply ?37621 (multiply ?37623 (inverse ?37623))) (inverse (multiply ?37624 (inverse ?37624))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?37619) (multiply (inverse ?37620) (multiply ?37620 ?37621)))) ?37622) (inverse (multiply ?37619 ?37622))) [37622, 37620, 37619, 37624, 37623, 37621] by Super 6756 with 223 at 1,1,2
-Id : 6857, {_}: multiply (multiply ?37621 (multiply ?37623 (inverse ?37623))) (inverse (multiply ?37624 (inverse ?37624))) =>= ?37621 [37624, 37623, 37621] by Demod 6813 with 223 at 3
-Id : 7919, {_}: inverse (inverse ?42462) =<= multiply ?42462 (multiply ?42463 (inverse ?42463)) [42463, 42462] by Demod 7592 with 6857 at 2
-Id : 2998, {_}: inverse (multiply (multiply (inverse ?18792) (multiply ?18792 (inverse (multiply ?18791 (inverse ?18791))))) (inverse (multiply (inverse ?18793) (multiply ?18793 ?18794)))) =>= ?18794 [18794, 18793, 18791, 18792] by Super 505 with 2989 at 2,1,2,1,2
-Id : 5265, {_}: inverse (multiply ?30443 (inverse ?30443)) =?= inverse (multiply ?30444 (inverse ?30444)) [30444, 30443] by Super 2998 with 4736 at 1,2
-Id : 5279, {_}: inverse (multiply ?30523 (inverse ?30523)) =?= inverse (inverse (inverse (inverse (multiply ?30522 (inverse ?30522))))) [30522, 30523] by Super 5265 with 3702 at 1,3
-Id : 7936, {_}: inverse (inverse ?42552) =<= multiply ?42552 (multiply (inverse (inverse (inverse (multiply ?42551 (inverse ?42551))))) (inverse (multiply ?42550 (inverse ?42550)))) [42550, 42551, 42552] by Super 7919 with 5279 at 2,2,3
-Id : 7778, {_}: inverse (inverse ?41055) =<= multiply ?41055 (multiply ?41054 (inverse ?41054)) [41054, 41055] by Demod 7592 with 6857 at 2
-Id : 7804, {_}: multiply (inverse (inverse ?37621)) (inverse (multiply ?37624 (inverse ?37624))) =>= ?37621 [37624, 37621] by Demod 6857 with 7778 at 1,2
-Id : 8036, {_}: inverse (inverse ?42552) =<= multiply ?42552 (inverse (multiply ?42551 (inverse ?42551))) [42551, 42552] by Demod 7936 with 7804 at 2,3
-Id : 8529, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?44275))) (inverse (multiply ?44274 (inverse ?44274)))) (inverse (inverse (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44274, 44275] by Super 8276 with 8036 at 1,2,1,1,1,2
-Id : 8588, {_}: inverse (inverse (inverse (multiply (inverse (inverse (inverse (inverse (inverse ?44275))))) (inverse (inverse (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8529 with 8036 at 1,1,1,1,2
-Id : 401, {_}: multiply (inverse ?2949) (multiply ?2949 ?2950) =?= multiply (inverse ?2951) (multiply ?2951 ?2950) [2951, 2950, 2949] by Super 285 with 188 at 3
-Id : 407, {_}: multiply (inverse ?2992) (multiply ?2992 (multiply ?2989 ?2990)) =?= multiply (inverse (inverse ?2989)) (multiply (inverse ?2991) (multiply ?2991 ?2990)) [2991, 2990, 2989, 2992] by Super 401 with 299 at 2,3
-Id : 8291, {_}: inverse (inverse (multiply ?2989 ?2990)) =<= multiply (inverse (inverse ?2989)) (multiply (inverse ?2991) (multiply ?2991 ?2990)) [2991, 2990, 2989] by Demod 407 with 8246 at 2
-Id : 8292, {_}: inverse (inverse (multiply ?2989 ?2990)) =<= multiply (inverse (inverse ?2989)) (inverse (inverse ?2990)) [2990, 2989] by Demod 8291 with 8246 at 2,3
-Id : 8589, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?44275))) (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8588 with 8292 at 1,1,1,2
-Id : 8446, {_}: inverse (inverse (inverse (inverse ?37621))) =>= ?37621 [37621] by Demod 7804 with 8036 at 2
-Id : 8590, {_}: inverse (multiply (inverse (inverse (inverse ?44275))) (inverse ?44273)) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8589 with 8446 at 2
-Id : 8757, {_}: multiply ?18805 (multiply (multiply (inverse ?18805) ?18803) (multiply ?18804 (inverse ?18804))) =>= ?18803 [18804, 18803, 18805] by Demod 8053 with 8590 at 2,2
-Id : 8758, {_}: multiply ?18805 (inverse (inverse (multiply (inverse ?18805) ?18803))) =>= ?18803 [18803, 18805] by Demod 8757 with 7778 at 2,2
-Id : 8857, {_}: inverse (multiply (inverse (inverse (inverse ?44963))) (inverse ?44964)) =>= multiply ?44964 ?44963 [44964, 44963] by Demod 8589 with 8446 at 2
-Id : 8919, {_}: inverse (multiply ?45241 (inverse ?45242)) =>= multiply ?45242 (inverse ?45241) [45242, 45241] by Super 8857 with 8446 at 1,1,2
-Id : 9051, {_}: multiply ?2 (multiply (multiply ?3 ?5) (inverse (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5))) =>= ?4 [4, 5, 3, 2] by Demod 4 with 8919 at 2,2
-Id : 137, {_}: multiply (inverse ?1284) (multiply ?1284 (inverse (multiply (multiply (inverse (multiply (inverse ?1285) ?1286)) ?1287) (inverse (multiply ?1285 ?1287))))) =>= ?1286 [1287, 1286, 1285, 1284] by Super 4 with 7 at 2,2
-Id : 156, {_}: multiply (inverse ?1443) (multiply ?1443 (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439, 1443] by Super 137 with 7 at 2,2,2
-Id : 8285, {_}: inverse (inverse (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439] by Demod 156 with 8246 at 2
-Id : 9071, {_}: inverse (multiply (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442))) (inverse ?1439)) =>= multiply (inverse (inverse ?1439)) ?1441 [1439, 1442, 1441, 1440] by Demod 8285 with 8919 at 1,2
-Id : 9072, {_}: multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439] by Demod 9071 with 8919 at 2
-Id : 9073, {_}: multiply ?1439 (multiply (multiply ?1440 ?1442) (inverse (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442))) =>= multiply (inverse (inverse ?1439)) ?1441 [1441, 1442, 1440, 1439] by Demod 9072 with 8919 at 2,2
-Id : 9086, {_}: multiply (inverse (inverse ?2)) (multiply (inverse ?2) ?4) =>= ?4 [4, 2] by Demod 9051 with 9073 at 2
-Id : 9087, {_}: inverse (inverse ?4) =>= ?4 [4] by Demod 9086 with 8246 at 2
-Id : 9094, {_}: multiply ?18805 (multiply (inverse ?18805) ?18803) =>= ?18803 [18803, 18805] by Demod 8758 with 9087 at 2,2
-Id : 9160, {_}: inverse (multiply ?45446 (inverse ?45447)) =>= multiply ?45447 (inverse ?45446) [45447, 45446] by Super 8857 with 8446 at 1,1,2
-Id : 9162, {_}: inverse (multiply ?45454 ?45453) =<= multiply (inverse ?45453) (inverse ?45454) [45453, 45454] by Super 9160 with 9087 at 2,1,2
-Id : 9195, {_}: multiply ?45501 (inverse (multiply ?45500 ?45501)) =>= inverse ?45500 [45500, 45501] by Super 9094 with 9162 at 2,2
-Id : 8933, {_}: inverse ?45303 =<= multiply (inverse (multiply (inverse (inverse (inverse (inverse ?45304)))) ?45303)) ?45304 [45304, 45303] by Super 8857 with 8758 at 1,2
-Id : 9467, {_}: inverse ?46002 =<= multiply (inverse (multiply ?46003 ?46002)) ?46003 [46003, 46002] by Demod 8933 with 8446 at 1,1,1,3
-Id : 8287, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (inverse (inverse ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1772] by Demod 223 with 8246 at 2,1,1,1,1,2
-Id : 9069, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (inverse (multiply (inverse ?1772) (inverse (inverse ?1773)))) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 8287 with 8919 at 2
-Id : 9070, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (multiply (inverse ?1773) (inverse (inverse ?1772))) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 9069 with 8919 at 1,1,2,2
-Id : 9090, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (multiply (inverse ?1773) ?1772) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 9070 with 9087 at 2,1,1,2,2
-Id : 9469, {_}: inverse (inverse (multiply (multiply (inverse ?46010) ?46008) ?46009)) =>= multiply (inverse ?46010) (multiply ?46008 ?46009) [46009, 46008, 46010] by Super 9467 with 9090 at 1,1,3
-Id : 9509, {_}: multiply (multiply (inverse ?46010) ?46008) ?46009 =>= multiply (inverse ?46010) (multiply ?46008 ?46009) [46009, 46008, 46010] by Demod 9469 with 9087 at 2
-Id : 9851, {_}: multiply ?46565 (inverse (multiply (inverse ?46563) (multiply ?46564 ?46565))) =>= inverse (multiply (inverse ?46563) ?46564) [46564, 46563, 46565] by Super 9195 with 9509 at 1,2,2
-Id : 9213, {_}: inverse (multiply ?45576 ?45577) =<= multiply (inverse ?45577) (inverse ?45576) [45577, 45576] by Super 9160 with 9087 at 2,1,2
-Id : 9215, {_}: inverse (multiply (inverse ?45583) ?45584) =>= multiply (inverse ?45584) ?45583 [45584, 45583] by Super 9213 with 9087 at 2,3
-Id : 9934, {_}: multiply ?46565 (multiply (inverse (multiply ?46564 ?46565)) ?46563) =>= inverse (multiply (inverse ?46563) ?46564) [46563, 46564, 46565] by Demod 9851 with 9215 at 2,2
-Id : 12550, {_}: multiply ?50696 (multiply (inverse (multiply ?50697 ?50696)) ?50698) =>= multiply (inverse ?50697) ?50698 [50698, 50697, 50696] by Demod 9934 with 9215 at 3
-Id : 9075, {_}: inverse (inverse (multiply (multiply ?2913 ?2917) (inverse (multiply (inverse (inverse (inverse ?2914))) ?2917)))) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 8276 with 8919 at 1,1,2
-Id : 9076, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 9075 with 8919 at 1,2
-Id : 9077, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse (inverse (inverse ?2914))) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9076 with 8919 at 2
-Id : 9102, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse ?2914) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9077 with 9087 at 1,1,2,2
-Id : 9248, {_}: multiply (multiply ?2913 ?2917) (multiply (inverse ?2917) ?2914) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9102 with 9215 at 2,2
-Id : 9533, {_}: multiply (inverse ?46084) (multiply (inverse (inverse (multiply ?46084 ?46083))) ?46085) =>= multiply ?46083 ?46085 [46085, 46083, 46084] by Super 9248 with 9195 at 1,2
-Id : 9598, {_}: multiply (inverse ?46084) (multiply (multiply ?46084 ?46083) ?46085) =>= multiply ?46083 ?46085 [46085, 46083, 46084] by Demod 9533 with 9087 at 1,2,2
-Id : 12590, {_}: multiply ?50874 (multiply ?50872 ?50873) =<= multiply (inverse ?50875) (multiply (multiply (multiply ?50875 ?50874) ?50872) ?50873) [50875, 50873, 50872, 50874] by Super 12550 with 9598 at 2,2
-Id : 12312, {_}: multiply (multiply ?50214 ?50215) ?50216 =<= multiply (inverse ?50213) (multiply (multiply (multiply ?50213 ?50214) ?50215) ?50216) [50213, 50216, 50215, 50214] by Super 9509 with 9598 at 1,2
-Id : 29878, {_}: multiply ?50874 (multiply ?50872 ?50873) =?= multiply (multiply ?50874 ?50872) ?50873 [50873, 50872, 50874] by Demod 12590 with 12312 at 3
-Id : 30629, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 2 with 29878 at 3
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for GRP014-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_commutator is 86
- b is 97
- c is 96
- commutator is 95
- identity is 92
- inverse is 90
- left_identity is 91
- left_inverse is 89
- multiply is 94
- name is 87
- prove_center is 93
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
- Id : 12, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-Goal
- Id : 2, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-Last chance: 1246055716.7
-Last chance: all is indexed 1246056832.19
-Last chance: failed over 100 goal 1246056832.19
-FAILURE in 0 iterations
-% SZS status Timeout for GRP024-5.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- identity is 93
- intersection is 85
- intersection_associative is 79
- intersection_commutative is 81
- intersection_idempotent is 84
- intersection_union_absorbtion is 76
- inverse is 91
- inverse_involution is 87
- inverse_of_identity is 88
- inverse_product_lemma is 86
- left_identity is 92
- left_inverse is 90
- multiply is 95
- multiply_intersection1 is 74
- multiply_intersection2 is 72
- multiply_union1 is 75
- multiply_union2 is 73
- negative_part is 96
- positive_part is 97
- prove_product is 94
- union is 83
- union_associative is 78
- union_commutative is 80
- union_idempotent is 82
- union_intersection_absorbtion is 77
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
- Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
- Id : 14, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
- Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
- Id : 18, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
- Id : 20, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
- Id : 22, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
- Id : 24, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
- Id : 26, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
- Id : 28, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
- Id : 30, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
- Id : 32, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
- Id : 34, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
- Id : 36, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
- Id : 38, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
- Id : 40, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
- Id : 42, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-Goal
- Id : 2, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-Found proof, 2.752118s
-% SZS status Unsatisfiable for GRP114-1.p
-% SZS output start CNFRefutation for GRP114-1.p
-Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-Id : 24, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
-Id : 34, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-Id : 28, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
-Id : 26, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
-Id : 267, {_}: multiply (union ?680 ?681) ?682 =<= union (multiply ?680 ?682) (multiply ?681 ?682) [682, 681, 680] by multiply_union2 ?680 ?681 ?682
-Id : 30, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
-Id : 230, {_}: multiply ?593 (intersection ?594 ?595) =<= intersection (multiply ?593 ?594) (multiply ?593 ?595) [595, 594, 593] by multiply_intersection1 ?593 ?594 ?595
-Id : 42, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
-Id : 20, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
-Id : 303, {_}: multiply (intersection ?770 ?771) ?772 =<= intersection (multiply ?770 ?772) (multiply ?771 ?772) [772, 771, 770] by multiply_intersection2 ?770 ?771 ?772
-Id : 14, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
-Id : 22, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
-Id : 40, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
-Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
-Id : 32, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-Id : 79, {_}: inverse (multiply ?142 ?143) =<= multiply (inverse ?143) (inverse ?142) [143, 142] by inverse_product_lemma ?142 ?143
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 47, {_}: multiply (multiply ?68 ?69) ?70 =?= multiply ?68 (multiply ?69 ?70) [70, 69, 68] by associativity ?68 ?69 ?70
-Id : 56, {_}: multiply identity ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Super 47 with 6 at 1,2
-Id : 8890, {_}: ?10861 =<= multiply (inverse ?10862) (multiply ?10862 ?10861) [10862, 10861] by Demod 56 with 4 at 2
-Id : 81, {_}: inverse (multiply (inverse ?147) ?148) =>= multiply (inverse ?148) ?147 [148, 147] by Super 79 with 12 at 2,3
-Id : 80, {_}: inverse (multiply identity ?145) =<= multiply (inverse ?145) identity [145] by Super 79 with 10 at 2,3
-Id : 450, {_}: inverse ?990 =<= multiply (inverse ?990) identity [990] by Demod 80 with 4 at 1,2
-Id : 452, {_}: inverse (inverse ?993) =<= multiply ?993 identity [993] by Super 450 with 12 at 1,3
-Id : 467, {_}: ?993 =<= multiply ?993 identity [993] by Demod 452 with 12 at 2
-Id : 472, {_}: multiply ?1004 (union ?1005 identity) =?= union (multiply ?1004 ?1005) ?1004 [1005, 1004] by Super 32 with 467 at 2,3
-Id : 3162, {_}: multiply ?4224 (positive_part ?4225) =<= union (multiply ?4224 ?4225) ?4224 [4225, 4224] by Demod 472 with 40 at 2,2
-Id : 3164, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= union identity (inverse ?4229) [4229] by Super 3162 with 6 at 1,3
-Id : 336, {_}: union identity ?835 =>= positive_part ?835 [835] by Super 22 with 40 at 3
-Id : 3201, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= positive_part (inverse ?4229) [4229] by Demod 3164 with 336 at 3
-Id : 3231, {_}: inverse (positive_part (inverse ?4304)) =<= multiply (inverse (positive_part ?4304)) ?4304 [4304] by Super 81 with 3201 at 1,2
-Id : 8905, {_}: ?10899 =<= multiply (inverse (inverse (positive_part ?10899))) (inverse (positive_part (inverse ?10899))) [10899] by Super 8890 with 3231 at 2,3
-Id : 8940, {_}: ?10899 =<= inverse (multiply (positive_part (inverse ?10899)) (inverse (positive_part ?10899))) [10899] by Demod 8905 with 14 at 3
-Id : 83, {_}: inverse (multiply ?153 (inverse ?152)) =>= multiply ?152 (inverse ?153) [152, 153] by Super 79 with 12 at 1,3
-Id : 8941, {_}: ?10899 =<= multiply (positive_part ?10899) (inverse (positive_part (inverse ?10899))) [10899] by Demod 8940 with 83 at 3
-Id : 310, {_}: multiply (intersection (inverse ?798) ?797) ?798 =>= intersection identity (multiply ?797 ?798) [797, 798] by Super 303 with 6 at 1,3
-Id : 355, {_}: intersection identity ?867 =>= negative_part ?867 [867] by Super 20 with 42 at 3
-Id : 15926, {_}: multiply (intersection (inverse ?16735) ?16736) ?16735 =>= negative_part (multiply ?16736 ?16735) [16736, 16735] by Demod 310 with 355 at 3
-Id : 15951, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part (multiply identity ?16817) [16817] by Super 15926 with 42 at 1,2
-Id : 15996, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15951 with 4 at 1,3
-Id : 237, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= intersection identity (multiply (inverse ?620) ?621) [621, 620] by Super 230 with 6 at 1,3
-Id : 9389, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= negative_part (multiply (inverse ?620) ?621) [621, 620] by Demod 237 with 355 at 3
-Id : 387, {_}: intersection (positive_part ?915) ?915 =>= ?915 [915] by Super 30 with 336 at 1,2
-Id : 274, {_}: multiply (union (inverse ?708) ?707) ?708 =>= union identity (multiply ?707 ?708) [707, 708] by Super 267 with 6 at 1,3
-Id : 9866, {_}: multiply (union (inverse ?12356) ?12357) ?12356 =>= positive_part (multiply ?12357 ?12356) [12357, 12356] by Demod 274 with 336 at 3
-Id : 384, {_}: union identity (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Super 26 with 336 at 1,3
-Id : 394, {_}: positive_part (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Demod 384 with 336 at 2
-Id : 339, {_}: union ?842 (union ?843 identity) =>= positive_part (union ?842 ?843) [843, 842] by Super 26 with 40 at 3
-Id : 350, {_}: union ?842 (positive_part ?843) =<= positive_part (union ?842 ?843) [843, 842] by Demod 339 with 40 at 2,2
-Id : 667, {_}: union ?906 (positive_part ?907) =?= union (positive_part ?906) ?907 [907, 906] by Demod 394 with 350 at 2
-Id : 414, {_}: union (negative_part ?942) ?942 =>= ?942 [942] by Super 28 with 355 at 1,2
-Id : 479, {_}: multiply ?1021 (intersection ?1022 identity) =?= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Super 34 with 467 at 2,3
-Id : 2583, {_}: multiply ?3618 (negative_part ?3619) =<= intersection (multiply ?3618 ?3619) ?3618 [3619, 3618] by Demod 479 with 42 at 2,2
-Id : 2585, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= intersection identity (inverse ?3623) [3623] by Super 2583 with 6 at 1,3
-Id : 2636, {_}: multiply (inverse ?3692) (negative_part ?3692) =>= negative_part (inverse ?3692) [3692] by Demod 2585 with 355 at 3
-Id : 358, {_}: intersection ?874 (intersection ?875 identity) =>= negative_part (intersection ?874 ?875) [875, 874] by Super 24 with 42 at 3
-Id : 603, {_}: intersection ?1157 (negative_part ?1158) =<= negative_part (intersection ?1157 ?1158) [1158, 1157] by Demod 358 with 42 at 2,2
-Id : 613, {_}: intersection ?1189 (negative_part identity) =>= negative_part (negative_part ?1189) [1189] by Super 603 with 42 at 1,3
-Id : 354, {_}: negative_part identity =>= identity [] by Super 16 with 42 at 2
-Id : 624, {_}: intersection ?1189 identity =<= negative_part (negative_part ?1189) [1189] by Demod 613 with 354 at 2,2
-Id : 625, {_}: negative_part ?1189 =<= negative_part (negative_part ?1189) [1189] by Demod 624 with 42 at 2
-Id : 2642, {_}: multiply (inverse (negative_part ?3706)) (negative_part ?3706) =>= negative_part (inverse (negative_part ?3706)) [3706] by Super 2636 with 625 at 2,2
-Id : 2662, {_}: identity =<= negative_part (inverse (negative_part ?3706)) [3706] by Demod 2642 with 6 at 2
-Id : 2732, {_}: union identity (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Super 414 with 2662 at 1,2
-Id : 2769, {_}: positive_part (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Demod 2732 with 336 at 2
-Id : 2879, {_}: union (inverse (negative_part ?3906)) (positive_part ?3907) =>= union (inverse (negative_part ?3906)) ?3907 [3907, 3906] by Super 667 with 2769 at 1,3
-Id : 9889, {_}: multiply (union (inverse (negative_part ?12432)) ?12433) (negative_part ?12432) =>= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12433, 12432] by Super 9866 with 2879 at 1,2
-Id : 9846, {_}: multiply (union (inverse ?708) ?707) ?708 =>= positive_part (multiply ?707 ?708) [707, 708] by Demod 274 with 336 at 3
-Id : 9923, {_}: positive_part (multiply ?12433 (negative_part ?12432)) =<= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12432, 12433] by Demod 9889 with 9846 at 2
-Id : 492, {_}: multiply ?1021 (negative_part ?1022) =<= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Demod 479 with 42 at 2,2
-Id : 9892, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part (multiply identity ?12441) [12441] by Super 9866 with 40 at 1,2
-Id : 9926, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part ?12441 [12441] by Demod 9892 with 4 at 1,3
-Id : 9949, {_}: multiply (positive_part (inverse ?12495)) (negative_part ?12495) =>= intersection (positive_part ?12495) (positive_part (inverse ?12495)) [12495] by Super 492 with 9926 at 1,3
-Id : 10776, {_}: positive_part (multiply (inverse ?13313) (negative_part ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Super 9923 with 9949 at 1,3
-Id : 2613, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= negative_part (inverse ?3623) [3623] by Demod 2585 with 355 at 3
-Id : 10814, {_}: positive_part (negative_part (inverse ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10776 with 2613 at 1,2
-Id : 334, {_}: positive_part (intersection ?832 identity) =>= identity [832] by Super 28 with 40 at 2
-Id : 507, {_}: positive_part (negative_part ?832) =>= identity [832] by Demod 334 with 42 at 1,2
-Id : 10815, {_}: identity =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10814 with 507 at 2
-Id : 51491, {_}: intersection identity (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Super 387 with 10815 at 1,2
-Id : 51798, {_}: negative_part (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51491 with 355 at 2
-Id : 369, {_}: intersection ?874 (negative_part ?875) =<= negative_part (intersection ?874 ?875) [875, 874] by Demod 358 with 42 at 2,2
-Id : 51799, {_}: intersection (positive_part ?50477) (negative_part (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51798 with 369 at 2
-Id : 51800, {_}: intersection (negative_part (positive_part (inverse ?50477))) (positive_part ?50477) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51799 with 20 at 2
-Id : 411, {_}: intersection identity (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Super 24 with 355 at 1,3
-Id : 421, {_}: negative_part (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Demod 411 with 355 at 2
-Id : 795, {_}: intersection ?1452 (negative_part ?1453) =?= intersection (negative_part ?1452) ?1453 [1453, 1452] by Demod 421 with 369 at 2
-Id : 353, {_}: negative_part (union ?864 identity) =>= identity [864] by Super 30 with 42 at 2
-Id : 371, {_}: negative_part (positive_part ?864) =>= identity [864] by Demod 353 with 40 at 1,2
-Id : 797, {_}: intersection (positive_part ?1457) (negative_part ?1458) =>= intersection identity ?1458 [1458, 1457] by Super 795 with 371 at 1,3
-Id : 834, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= intersection identity ?1458 [1457, 1458] by Demod 797 with 20 at 2
-Id : 835, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= negative_part ?1458 [1457, 1458] by Demod 834 with 355 at 3
-Id : 51801, {_}: negative_part (positive_part (inverse ?50477)) =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51800 with 835 at 2
-Id : 51802, {_}: identity =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51801 with 371 at 2
-Id : 52174, {_}: multiply (inverse (positive_part ?50853)) identity =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Super 9389 with 51802 at 2,2
-Id : 52262, {_}: inverse (positive_part ?50853) =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Demod 52174 with 467 at 2
-Id : 65, {_}: ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Demod 56 with 4 at 2
-Id : 9954, {_}: multiply (positive_part (inverse ?12505)) ?12505 =>= positive_part ?12505 [12505] by Demod 9892 with 4 at 1,3
-Id : 9956, {_}: multiply (positive_part ?12508) (inverse ?12508) =>= positive_part (inverse ?12508) [12508] by Super 9954 with 12 at 1,1,2
-Id : 10049, {_}: inverse ?12562 =<= multiply (inverse (positive_part ?12562)) (positive_part (inverse ?12562)) [12562] by Super 65 with 9956 at 2,3
-Id : 52263, {_}: inverse (positive_part ?50853) =<= negative_part (inverse ?50853) [50853] by Demod 52262 with 10049 at 1,3
-Id : 52532, {_}: multiply (inverse (positive_part ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15996 with 52263 at 1,2
-Id : 52563, {_}: inverse (positive_part (inverse ?16817)) =>= negative_part ?16817 [16817] by Demod 52532 with 3231 at 2
-Id : 52572, {_}: ?10899 =<= multiply (positive_part ?10899) (negative_part ?10899) [10899] by Demod 8941 with 52563 at 2,3
-Id : 52951, {_}: a === a [] by Demod 2 with 52572 at 2
-Id : 2, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
-% SZS output end CNFRefutation for GRP114-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 87
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 89
- least_upper_bound is 95
- left_identity is 90
- left_inverse is 88
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 91
- prove_distrun is 93
- symmetry_of_glb is 86
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-Last chance: 1246057135.58
-Last chance: all is indexed 1246058747.63
-Last chance: failed over 100 goal 1246058747.74
-FAILURE in 0 iterations
-% SZS status Timeout for GRP164-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 84
- associativity_of_lub is 83
- glb_absorbtion is 79
- greatest_lower_bound is 88
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 93
- inverse is 91
- lat4_1 is 74
- lat4_2 is 73
- lat4_3 is 72
- lat4_4 is 71
- least_upper_bound is 86
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- negative_part is 96
- positive_part is 97
- prove_lat4 is 94
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
- Id : 36, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
- Id : 38, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
- Id : 40, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-Goal
- Id : 2, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-Found proof, 4.771401s
-% SZS status Unsatisfiable for GRP167-1.p
-% SZS output start CNFRefutation for GRP167-1.p
-Id : 202, {_}: multiply ?551 (greatest_lower_bound ?552 ?553) =<= greatest_lower_bound (multiply ?551 ?552) (multiply ?551 ?553) [553, 552, 551] by monotony_glb1 ?551 ?552 ?553
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 171, {_}: multiply ?475 (least_upper_bound ?476 ?477) =<= least_upper_bound (multiply ?475 ?476) (multiply ?475 ?477) [477, 476, 475] by monotony_lub1 ?475 ?476 ?477
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 384, {_}: greatest_lower_bound ?977 (least_upper_bound ?978 ?979) =<= least_upper_bound (greatest_lower_bound ?977 ?978) (greatest_lower_bound ?977 ?979) [979, 978, 977] by lat4_4 ?977 ?978 ?979
-Id : 34, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 236, {_}: multiply (least_upper_bound ?630 ?631) ?632 =<= least_upper_bound (multiply ?630 ?632) (multiply ?631 ?632) [632, 631, 630] by monotony_lub2 ?630 ?631 ?632
-Id : 36, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 269, {_}: multiply (greatest_lower_bound ?712 ?713) ?714 =<= greatest_lower_bound (multiply ?712 ?714) (multiply ?713 ?714) [714, 713, 712] by monotony_glb2 ?712 ?713 ?714
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 45, {_}: multiply (multiply ?70 ?71) ?72 =?= multiply ?70 (multiply ?71 ?72) [72, 71, 70] by associativity ?70 ?71 ?72
-Id : 54, {_}: multiply identity ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Super 45 with 6 at 1,2
-Id : 63, {_}: ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Demod 54 with 4 at 2
-Id : 275, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= greatest_lower_bound identity (multiply ?735 ?736) [735, 736] by Super 269 with 6 at 1,3
-Id : 314, {_}: greatest_lower_bound identity ?795 =>= negative_part ?795 [795] by Super 10 with 36 at 3
-Id : 16391, {_}: multiply (greatest_lower_bound (inverse ?19768) ?19769) ?19768 =>= negative_part (multiply ?19769 ?19768) [19769, 19768] by Demod 275 with 314 at 3
-Id : 16415, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part (multiply identity ?19845) [19845] by Super 16391 with 36 at 1,2
-Id : 16452, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part ?19845 [19845] by Demod 16415 with 4 at 1,3
-Id : 16463, {_}: ?19856 =<= multiply (inverse (negative_part (inverse ?19856))) (negative_part ?19856) [19856] by Super 63 with 16452 at 2,3
-Id : 242, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= least_upper_bound identity (multiply ?653 ?654) [653, 654] by Super 236 with 6 at 1,3
-Id : 298, {_}: least_upper_bound identity ?767 =>= positive_part ?767 [767] by Super 12 with 34 at 3
-Id : 14215, {_}: multiply (least_upper_bound (inverse ?17599) ?17600) ?17599 =>= positive_part (multiply ?17600 ?17599) [17600, 17599] by Demod 242 with 298 at 3
-Id : 14238, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part (multiply identity ?17673) [17673] by Super 14215 with 34 at 1,2
-Id : 14268, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14238 with 4 at 1,3
-Id : 14200, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= positive_part (multiply ?653 ?654) [653, 654] by Demod 242 with 298 at 3
-Id : 393, {_}: greatest_lower_bound ?1016 (least_upper_bound ?1017 identity) =<= least_upper_bound (greatest_lower_bound ?1016 ?1017) (negative_part ?1016) [1017, 1016] by Super 384 with 36 at 2,3
-Id : 17844, {_}: greatest_lower_bound ?21384 (positive_part ?21385) =<= least_upper_bound (greatest_lower_bound ?21384 ?21385) (negative_part ?21384) [21385, 21384] by Demod 393 with 34 at 2,2
-Id : 17873, {_}: greatest_lower_bound ?21489 (positive_part ?21490) =<= least_upper_bound (greatest_lower_bound ?21490 ?21489) (negative_part ?21489) [21490, 21489] by Super 17844 with 10 at 1,3
-Id : 16475, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19889)) ?19890) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Super 32 with 16452 at 1,3
-Id : 480, {_}: greatest_lower_bound identity (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Super 14 with 314 at 1,3
-Id : 492, {_}: negative_part (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 480 with 314 at 2
-Id : 317, {_}: greatest_lower_bound ?802 (greatest_lower_bound ?803 identity) =>= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Super 14 with 36 at 3
-Id : 326, {_}: greatest_lower_bound ?802 (negative_part ?803) =<= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Demod 317 with 36 at 2,2
-Id : 770, {_}: greatest_lower_bound ?1137 (negative_part ?1138) =?= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 492 with 326 at 2
-Id : 16503, {_}: multiply (greatest_lower_bound (inverse ?19889) (negative_part ?19890)) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Demod 16475 with 770 at 1,2
-Id : 16376, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= negative_part (multiply ?735 ?736) [735, 736] by Demod 275 with 314 at 3
-Id : 16504, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19889, 19890] by Demod 16503 with 16376 at 2
-Id : 16505, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (multiply ?19890 ?19889) (negative_part ?19889) [19889, 19890] by Demod 16504 with 10 at 3
-Id : 47, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= multiply ?77 identity [78, 77] by Super 45 with 6 at 2,3
-Id : 4534, {_}: multiply (multiply ?6403 (inverse ?6404)) ?6404 =>= multiply ?6403 identity [6404, 6403] by Super 45 with 6 at 2,3
-Id : 4537, {_}: multiply identity ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Super 4534 with 6 at 1,2
-Id : 4552, {_}: ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Demod 4537 with 4 at 2
-Id : 46, {_}: multiply (multiply ?74 identity) ?75 =>= multiply ?74 ?75 [75, 74] by Super 45 with 4 at 2,3
-Id : 4557, {_}: multiply ?6432 ?6433 =<= multiply (inverse (inverse ?6432)) ?6433 [6433, 6432] by Super 46 with 4552 at 1,2
-Id : 4577, {_}: ?6410 =<= multiply ?6410 identity [6410] by Demod 4552 with 4557 at 3
-Id : 4578, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= ?77 [78, 77] by Demod 47 with 4577 at 3
-Id : 4593, {_}: inverse (inverse ?6519) =<= multiply ?6519 identity [6519] by Super 4577 with 4557 at 3
-Id : 4599, {_}: inverse (inverse ?6519) =>= ?6519 [6519] by Demod 4593 with 4577 at 3
-Id : 4627, {_}: multiply (multiply ?6536 ?6535) (inverse ?6535) =>= ?6536 [6535, 6536] by Super 4578 with 4599 at 2,1,2
-Id : 62773, {_}: inverse ?65768 =<= multiply (inverse (multiply ?65769 ?65768)) ?65769 [65769, 65768] by Super 63 with 4627 at 2,3
-Id : 177, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= least_upper_bound identity (multiply (inverse ?498) ?499) [499, 498] by Super 171 with 6 at 1,3
-Id : 4722, {_}: multiply (inverse ?6711) (least_upper_bound ?6711 ?6712) =>= positive_part (multiply (inverse ?6711) ?6712) [6712, 6711] by Demod 177 with 298 at 3
-Id : 4745, {_}: multiply (inverse ?6778) (positive_part ?6778) =?= positive_part (multiply (inverse ?6778) identity) [6778] by Super 4722 with 34 at 2,2
-Id : 4793, {_}: multiply (inverse ?6833) (positive_part ?6833) =>= positive_part (inverse ?6833) [6833] by Demod 4745 with 4577 at 1,3
-Id : 4805, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part (inverse (inverse ?6862)) [6862] by Super 4793 with 4599 at 1,2
-Id : 4824, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part ?6862 [6862] by Demod 4805 with 4599 at 1,3
-Id : 62790, {_}: inverse (positive_part (inverse ?65816)) =<= multiply (inverse (positive_part ?65816)) ?65816 [65816] by Super 62773 with 4824 at 1,1,3
-Id : 63210, {_}: negative_part (multiply (negative_part (inverse (positive_part ?66345))) ?66345) =>= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Super 16505 with 62790 at 1,3
-Id : 303, {_}: greatest_lower_bound ?780 (positive_part ?780) =>= ?780 [780] by Super 24 with 34 at 2,2
-Id : 535, {_}: greatest_lower_bound (positive_part ?1185) ?1185 =>= ?1185 [1185] by Super 10 with 303 at 3
-Id : 301, {_}: least_upper_bound ?774 (least_upper_bound ?775 identity) =>= positive_part (least_upper_bound ?774 ?775) [775, 774] by Super 16 with 34 at 3
-Id : 566, {_}: least_upper_bound ?1228 (positive_part ?1229) =<= positive_part (least_upper_bound ?1228 ?1229) [1229, 1228] by Demod 301 with 34 at 2,2
-Id : 576, {_}: least_upper_bound ?1260 (positive_part identity) =>= positive_part (positive_part ?1260) [1260] by Super 566 with 34 at 1,3
-Id : 297, {_}: positive_part identity =>= identity [] by Super 18 with 34 at 2
-Id : 590, {_}: least_upper_bound ?1260 identity =<= positive_part (positive_part ?1260) [1260] by Demod 576 with 297 at 2,2
-Id : 591, {_}: positive_part ?1260 =<= positive_part (positive_part ?1260) [1260] by Demod 590 with 34 at 2
-Id : 4802, {_}: multiply (inverse (positive_part ?6856)) (positive_part ?6856) =>= positive_part (inverse (positive_part ?6856)) [6856] by Super 4793 with 591 at 2,2
-Id : 4819, {_}: identity =<= positive_part (inverse (positive_part ?6856)) [6856] by Demod 4802 with 6 at 2
-Id : 4905, {_}: greatest_lower_bound identity (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Super 535 with 4819 at 1,2
-Id : 4952, {_}: negative_part (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Demod 4905 with 314 at 2
-Id : 63307, {_}: negative_part (multiply (inverse (positive_part ?66345)) ?66345) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63210 with 4952 at 1,1,2
-Id : 63308, {_}: negative_part (inverse (positive_part (inverse ?66345))) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63307 with 62790 at 1,2
-Id : 63309, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63308 with 4952 at 2
-Id : 5097, {_}: greatest_lower_bound (inverse (positive_part ?7140)) (negative_part ?7141) =>= greatest_lower_bound (inverse (positive_part ?7140)) ?7141 [7141, 7140] by Super 770 with 4952 at 1,3
-Id : 63310, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) ?66345 [66345] by Demod 63309 with 5097 at 3
-Id : 63817, {_}: greatest_lower_bound ?66966 (positive_part (inverse (positive_part (inverse ?66966)))) =>= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Super 17873 with 63310 at 1,3
-Id : 64085, {_}: greatest_lower_bound ?66966 identity =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 63817 with 4819 at 2,2
-Id : 64086, {_}: negative_part ?66966 =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 64085 with 36 at 2
-Id : 81154, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (positive_part (inverse ?80770))) [80770] by Super 14200 with 64086 at 1,2
-Id : 4710, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= positive_part (multiply (inverse ?498) ?499) [499, 498] by Demod 177 with 298 at 3
-Id : 444, {_}: least_upper_bound identity (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Super 16 with 298 at 1,3
-Id : 455, {_}: positive_part (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 444 with 298 at 2
-Id : 310, {_}: least_upper_bound ?774 (positive_part ?775) =<= positive_part (least_upper_bound ?774 ?775) [775, 774] by Demod 301 with 34 at 2,2
-Id : 677, {_}: least_upper_bound ?1100 (positive_part ?1101) =?= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 455 with 310 at 2
-Id : 483, {_}: least_upper_bound identity (negative_part ?1146) =>= identity [1146] by Super 22 with 314 at 2,2
-Id : 491, {_}: positive_part (negative_part ?1146) =>= identity [1146] by Demod 483 with 298 at 2
-Id : 4795, {_}: multiply (inverse (negative_part ?6836)) identity =>= positive_part (inverse (negative_part ?6836)) [6836] by Super 4793 with 491 at 2,2
-Id : 4816, {_}: inverse (negative_part ?6836) =<= positive_part (inverse (negative_part ?6836)) [6836] by Demod 4795 with 4577 at 2
-Id : 4838, {_}: least_upper_bound (inverse (negative_part ?6900)) (positive_part ?6901) =>= least_upper_bound (inverse (negative_part ?6900)) ?6901 [6901, 6900] by Super 677 with 4816 at 1,3
-Id : 6365, {_}: multiply (inverse (inverse (negative_part ?8525))) (least_upper_bound (inverse (negative_part ?8525)) ?8526) =>= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Super 4710 with 4838 at 2,2
-Id : 6403, {_}: positive_part (multiply (inverse (inverse (negative_part ?8525))) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6365 with 4710 at 2
-Id : 6404, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6403 with 4599 at 1,1,2
-Id : 6405, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (negative_part ?8525) (positive_part ?8526)) [8526, 8525] by Demod 6404 with 4599 at 1,1,3
-Id : 81274, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (inverse ?80770)) [80770] by Demod 81154 with 6405 at 3
-Id : 16478, {_}: multiply (negative_part (inverse ?19896)) ?19896 =>= negative_part ?19896 [19896] by Demod 16415 with 4 at 1,3
-Id : 16480, {_}: multiply (negative_part ?19899) (inverse ?19899) =>= negative_part (inverse ?19899) [19899] by Super 16478 with 4599 at 1,1,2
-Id : 81275, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= positive_part (negative_part (inverse ?80770)) [80770] by Demod 81274 with 16480 at 1,3
-Id : 81276, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= identity [80770] by Demod 81275 with 491 at 3
-Id : 81601, {_}: positive_part (inverse ?81005) =<= multiply (inverse (negative_part ?81005)) identity [81005] by Super 63 with 81276 at 2,3
-Id : 81716, {_}: positive_part (inverse ?81005) =>= inverse (negative_part ?81005) [81005] by Demod 81601 with 4577 at 3
-Id : 81904, {_}: multiply (inverse (negative_part ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14268 with 81716 at 1,2
-Id : 208, {_}: multiply (inverse ?574) (greatest_lower_bound ?574 ?575) =>= greatest_lower_bound identity (multiply (inverse ?574) ?575) [575, 574] by Super 202 with 6 at 1,3
-Id : 13518, {_}: multiply (inverse ?16653) (greatest_lower_bound ?16653 ?16654) =>= negative_part (multiply (inverse ?16653) ?16654) [16654, 16653] by Demod 208 with 314 at 3
-Id : 13544, {_}: multiply (inverse ?16729) (negative_part ?16729) =?= negative_part (multiply (inverse ?16729) identity) [16729] by Super 13518 with 36 at 2,2
-Id : 13624, {_}: multiply (inverse ?16816) (negative_part ?16816) =>= negative_part (inverse ?16816) [16816] by Demod 13544 with 4577 at 1,3
-Id : 13651, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part (inverse (inverse ?16885)) [16885] by Super 13624 with 4599 at 1,2
-Id : 13713, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part ?16885 [16885] by Demod 13651 with 4599 at 1,3
-Id : 62794, {_}: inverse (negative_part (inverse ?65826)) =<= multiply (inverse (negative_part ?65826)) ?65826 [65826] by Super 62773 with 13713 at 1,1,3
-Id : 81928, {_}: inverse (negative_part (inverse ?17673)) =>= positive_part ?17673 [17673] by Demod 81904 with 62794 at 2
-Id : 81935, {_}: ?19856 =<= multiply (positive_part ?19856) (negative_part ?19856) [19856] by Demod 16463 with 81928 at 1,3
-Id : 82404, {_}: a === a [] by Demod 2 with 81935 at 3
-Id : 2, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 90
- least_upper_bound is 86
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- p09b_1 is 74
- p09b_2 is 73
- p09b_3 is 72
- p09b_4 is 71
- prove_p09b is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
- Id : 36, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
- Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
- Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-Found proof, 197.640612s
-% SZS status Unsatisfiable for GRP178-2.p
-% SZS output start CNFRefutation for GRP178-2.p
-Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 171, {_}: multiply ?467 (least_upper_bound ?468 ?469) =<= least_upper_bound (multiply ?467 ?468) (multiply ?467 ?469) [469, 468, 467] by monotony_lub1 ?467 ?468 ?469
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 202, {_}: multiply ?543 (greatest_lower_bound ?544 ?545) =<= greatest_lower_bound (multiply ?543 ?544) (multiply ?543 ?545) [545, 544, 543] by monotony_glb1 ?543 ?544 ?545
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 45, {_}: multiply (multiply ?62 ?63) ?64 =?= multiply ?62 (multiply ?63 ?64) [64, 63, 62] by associativity ?62 ?63 ?64
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 54, {_}: multiply identity ?97 =<= multiply (inverse ?96) (multiply ?96 ?97) [96, 97] by Super 45 with 6 at 1,2
-Id : 63, {_}: ?97 =<= multiply (inverse ?96) (multiply ?96 ?97) [96, 97] by Demod 54 with 4 at 2
-Id : 47, {_}: multiply (multiply ?69 (inverse ?70)) ?70 =>= multiply ?69 identity [70, 69] by Super 45 with 6 at 2,3
-Id : 9265, {_}: multiply (multiply ?8232 (inverse ?8233)) ?8233 =>= multiply ?8232 identity [8233, 8232] by Super 45 with 6 at 2,3
-Id : 9268, {_}: multiply identity ?8239 =<= multiply (inverse (inverse ?8239)) identity [8239] by Super 9265 with 6 at 1,2
-Id : 9283, {_}: ?8239 =<= multiply (inverse (inverse ?8239)) identity [8239] by Demod 9268 with 4 at 2
-Id : 46, {_}: multiply (multiply ?66 identity) ?67 =>= multiply ?66 ?67 [67, 66] by Super 45 with 4 at 2,3
-Id : 9288, {_}: multiply ?8261 ?8262 =<= multiply (inverse (inverse ?8261)) ?8262 [8262, 8261] by Super 46 with 9283 at 1,2
-Id : 9304, {_}: ?8239 =<= multiply ?8239 identity [8239] by Demod 9283 with 9288 at 3
-Id : 9305, {_}: multiply (multiply ?69 (inverse ?70)) ?70 =>= ?69 [70, 69] by Demod 47 with 9304 at 3
-Id : 9320, {_}: inverse (inverse ?8348) =<= multiply ?8348 identity [8348] by Super 9304 with 9288 at 3
-Id : 9326, {_}: inverse (inverse ?8348) =>= ?8348 [8348] by Demod 9320 with 9304 at 3
-Id : 9354, {_}: multiply (multiply ?8365 ?8364) (inverse ?8364) =>= ?8365 [8364, 8365] by Super 9305 with 9326 at 2,1,2
-Id : 9315, {_}: multiply ?8330 (inverse ?8330) =>= identity [8330] by Super 6 with 9288 at 2
-Id : 9365, {_}: multiply ?8382 (greatest_lower_bound ?8383 (inverse ?8382)) =>= greatest_lower_bound (multiply ?8382 ?8383) identity [8383, 8382] by Super 28 with 9315 at 2,3
-Id : 9386, {_}: multiply ?8382 (greatest_lower_bound ?8383 (inverse ?8382)) =>= greatest_lower_bound identity (multiply ?8382 ?8383) [8383, 8382] by Demod 9365 with 10 at 3
-Id : 137579, {_}: multiply (inverse ?85743) (greatest_lower_bound ?85743 ?85744) =>= greatest_lower_bound identity (multiply (inverse ?85743) ?85744) [85744, 85743] by Super 202 with 6 at 1,3
-Id : 4862, {_}: greatest_lower_bound (least_upper_bound ?4719 ?4720) ?4719 =>= ?4719 [4720, 4719] by Super 10 with 24 at 3
-Id : 4863, {_}: greatest_lower_bound (least_upper_bound ?4723 ?4722) ?4722 =>= ?4722 [4722, 4723] by Super 4862 with 12 at 1,2
-Id : 173, {_}: multiply (inverse ?475) (least_upper_bound ?474 ?475) =>= least_upper_bound (multiply (inverse ?475) ?474) identity [474, 475] by Super 171 with 6 at 2,3
-Id : 9616, {_}: multiply (inverse ?8736) (least_upper_bound ?8737 ?8736) =>= least_upper_bound identity (multiply (inverse ?8736) ?8737) [8737, 8736] by Demod 173 with 12 at 3
-Id : 336, {_}: greatest_lower_bound b a =>= identity [] by Demod 40 with 10 at 2
-Id : 337, {_}: least_upper_bound b identity =>= b [] by Super 22 with 336 at 2,2
-Id : 349, {_}: least_upper_bound identity b =>= b [] by Demod 337 with 12 at 2
-Id : 9624, {_}: multiply (inverse b) b =<= least_upper_bound identity (multiply (inverse b) identity) [] by Super 9616 with 349 at 2,2
-Id : 9699, {_}: identity =<= least_upper_bound identity (multiply (inverse b) identity) [] by Demod 9624 with 6 at 2
-Id : 9700, {_}: identity =<= least_upper_bound identity (inverse b) [] by Demod 9699 with 9304 at 2,3
-Id : 9734, {_}: greatest_lower_bound identity (inverse b) =>= inverse b [] by Super 4863 with 9700 at 1,2
-Id : 9886, {_}: greatest_lower_bound ?8962 (inverse b) =<= greatest_lower_bound (greatest_lower_bound ?8962 identity) (inverse b) [8962] by Super 14 with 9734 at 2,2
-Id : 9910, {_}: greatest_lower_bound ?8962 (inverse b) =<= greatest_lower_bound (inverse b) (greatest_lower_bound ?8962 identity) [8962] by Demod 9886 with 10 at 3
-Id : 138060, {_}: multiply (inverse (inverse b)) (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply (inverse (inverse b)) (greatest_lower_bound ?86438 identity)) [86438] by Super 137579 with 9910 at 2,2
-Id : 139832, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply (inverse (inverse b)) (greatest_lower_bound ?86438 identity)) [86438] by Demod 138060 with 9326 at 1,2
-Id : 139833, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?86438 identity)) [86438] by Demod 139832 with 9326 at 1,2,3
-Id : 190, {_}: multiply (inverse ?475) (least_upper_bound ?474 ?475) =>= least_upper_bound identity (multiply (inverse ?475) ?474) [474, 475] by Demod 173 with 12 at 3
-Id : 299, {_}: greatest_lower_bound ?761 identity =<= greatest_lower_bound (greatest_lower_bound ?761 identity) a [761] by Super 14 with 34 at 2,2
-Id : 308, {_}: greatest_lower_bound ?761 identity =<= greatest_lower_bound a (greatest_lower_bound ?761 identity) [761] by Demod 299 with 10 at 3
-Id : 691, {_}: least_upper_bound a (greatest_lower_bound ?1150 identity) =>= a [1150] by Super 22 with 308 at 2,2
-Id : 693, {_}: least_upper_bound a identity =>= a [] by Super 691 with 20 at 2,2
-Id : 704, {_}: least_upper_bound identity a =>= a [] by Demod 693 with 12 at 2
-Id : 707, {_}: least_upper_bound ?1166 a =<= least_upper_bound (least_upper_bound ?1166 identity) a [1166] by Super 16 with 704 at 2,2
-Id : 1790, {_}: least_upper_bound ?1985 a =<= least_upper_bound a (least_upper_bound ?1985 identity) [1985] by Demod 707 with 12 at 3
-Id : 1791, {_}: least_upper_bound ?1987 a =<= least_upper_bound a (least_upper_bound identity ?1987) [1987] by Super 1790 with 12 at 2,3
-Id : 9745, {_}: least_upper_bound (inverse b) a =>= least_upper_bound a identity [] by Super 1791 with 9700 at 2,3
-Id : 9760, {_}: least_upper_bound a (inverse b) =>= least_upper_bound a identity [] by Demod 9745 with 12 at 2
-Id : 9761, {_}: least_upper_bound a (inverse b) =>= least_upper_bound identity a [] by Demod 9760 with 12 at 3
-Id : 9762, {_}: least_upper_bound a (inverse b) =>= a [] by Demod 9761 with 704 at 3
-Id : 9940, {_}: multiply (inverse (inverse b)) a =<= least_upper_bound identity (multiply (inverse (inverse b)) a) [] by Super 190 with 9762 at 2,2
-Id : 9943, {_}: multiply b a =<= least_upper_bound identity (multiply (inverse (inverse b)) a) [] by Demod 9940 with 9326 at 1,2
-Id : 9944, {_}: multiply b a =<= least_upper_bound identity (multiply b a) [] by Demod 9943 with 9326 at 1,2,3
-Id : 10784, {_}: greatest_lower_bound identity (multiply b a) =>= identity [] by Super 24 with 9944 at 2,2
-Id : 47323, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply b a) ?32510) =>= greatest_lower_bound identity ?32510 [32510] by Super 14 with 10784 at 1,3
-Id : 69234, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound a ?46169)) =>= greatest_lower_bound identity (multiply b ?46169) [46169] by Super 47323 with 28 at 2,2
-Id : 339, {_}: greatest_lower_bound ?788 identity =<= greatest_lower_bound (greatest_lower_bound ?788 b) a [788] by Super 14 with 336 at 2,2
-Id : 348, {_}: greatest_lower_bound ?788 identity =<= greatest_lower_bound a (greatest_lower_bound ?788 b) [788] by Demod 339 with 10 at 3
-Id : 69253, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 identity)) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 b)) [46206] by Super 69234 with 348 at 2,2,2
-Id : 353, {_}: least_upper_bound ?797 b =<= least_upper_bound (least_upper_bound ?797 identity) b [797] by Super 16 with 349 at 2,2
-Id : 607, {_}: least_upper_bound ?1066 b =<= least_upper_bound b (least_upper_bound ?1066 identity) [1066] by Demod 353 with 12 at 3
-Id : 608, {_}: least_upper_bound ?1068 b =<= least_upper_bound b (least_upper_bound identity ?1068) [1068] by Super 607 with 12 at 2,3
-Id : 9739, {_}: least_upper_bound (inverse b) b =>= least_upper_bound b identity [] by Super 608 with 9700 at 2,3
-Id : 9768, {_}: least_upper_bound b (inverse b) =>= least_upper_bound b identity [] by Demod 9739 with 12 at 2
-Id : 9769, {_}: least_upper_bound b (inverse b) =>= least_upper_bound identity b [] by Demod 9768 with 12 at 3
-Id : 9770, {_}: least_upper_bound b (inverse b) =>= b [] by Demod 9769 with 349 at 3
-Id : 9967, {_}: multiply (inverse (inverse b)) b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Super 190 with 9770 at 2,2
-Id : 10010, {_}: multiply b b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Demod 9967 with 9326 at 1,2
-Id : 10011, {_}: multiply b b =<= least_upper_bound identity (multiply b b) [] by Demod 10010 with 9326 at 1,2,3
-Id : 10830, {_}: greatest_lower_bound identity (multiply b b) =>= identity [] by Super 24 with 10011 at 2,2
-Id : 11235, {_}: greatest_lower_bound ?9614 identity =<= greatest_lower_bound (greatest_lower_bound ?9614 identity) (multiply b b) [9614] by Super 14 with 10830 at 2,2
-Id : 394, {_}: greatest_lower_bound ?844 identity =<= greatest_lower_bound a (greatest_lower_bound ?844 identity) [844] by Demod 299 with 10 at 3
-Id : 395, {_}: greatest_lower_bound ?846 identity =<= greatest_lower_bound a (greatest_lower_bound identity ?846) [846] by Super 394 with 10 at 2,3
-Id : 721, {_}: greatest_lower_bound a (greatest_lower_bound (greatest_lower_bound identity ?1178) ?1179) =>= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Super 14 with 395 at 1,3
-Id : 751, {_}: greatest_lower_bound a (greatest_lower_bound identity (greatest_lower_bound ?1178 ?1179)) =>= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 721 with 14 at 2,2
-Id : 752, {_}: greatest_lower_bound (greatest_lower_bound ?1178 ?1179) identity =?= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 751 with 395 at 2
-Id : 753, {_}: greatest_lower_bound identity (greatest_lower_bound ?1178 ?1179) =<= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 752 with 10 at 2
-Id : 47765, {_}: greatest_lower_bound ?32774 identity =<= greatest_lower_bound identity (greatest_lower_bound ?32774 (multiply b b)) [32774] by Demod 11235 with 753 at 3
-Id : 47777, {_}: greatest_lower_bound (multiply b ?32794) identity =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?32794 b)) [32794] by Super 47765 with 28 at 2,3
-Id : 47888, {_}: greatest_lower_bound identity (multiply b ?32794) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?32794 b)) [32794] by Demod 47777 with 10 at 2
-Id : 112860, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 identity)) =>= greatest_lower_bound identity (multiply b ?46206) [46206] by Demod 69253 with 47888 at 3
-Id : 139834, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =>= greatest_lower_bound identity (multiply b ?86438) [86438] by Demod 139833 with 112860 at 3
-Id : 758814, {_}: greatest_lower_bound ?433915 (inverse b) =<= multiply (inverse b) (greatest_lower_bound identity (multiply b ?433915)) [433915] by Super 63 with 139834 at 2,3
-Id : 9363, {_}: multiply (greatest_lower_bound ?8377 ?8376) (inverse ?8376) =>= greatest_lower_bound (multiply ?8377 (inverse ?8376)) identity [8376, 8377] by Super 32 with 9315 at 2,3
-Id : 389839, {_}: multiply (greatest_lower_bound ?219201 ?219202) (inverse ?219202) =>= greatest_lower_bound identity (multiply ?219201 (inverse ?219202)) [219202, 219201] by Demod 9363 with 10 at 3
-Id : 389867, {_}: multiply identity (inverse a) =<= greatest_lower_bound identity (multiply b (inverse a)) [] by Super 389839 with 336 at 1,2
-Id : 390920, {_}: inverse a =<= greatest_lower_bound identity (multiply b (inverse a)) [] by Demod 389867 with 4 at 2
-Id : 758889, {_}: greatest_lower_bound (inverse a) (inverse b) =<= multiply (inverse b) (inverse a) [] by Super 758814 with 390920 at 2,3
-Id : 759137, {_}: greatest_lower_bound (inverse b) (inverse a) =<= multiply (inverse b) (inverse a) [] by Demod 758889 with 10 at 2
-Id : 9373, {_}: multiply (least_upper_bound ?8405 ?8404) (inverse ?8404) =>= least_upper_bound (multiply ?8405 (inverse ?8404)) identity [8404, 8405] by Super 30 with 9315 at 2,3
-Id : 379748, {_}: multiply (least_upper_bound ?213200 ?213201) (inverse ?213201) =>= least_upper_bound identity (multiply ?213200 (inverse ?213201)) [213201, 213200] by Demod 9373 with 12 at 3
-Id : 9632, {_}: multiply (inverse a) a =<= least_upper_bound identity (multiply (inverse a) identity) [] by Super 9616 with 704 at 2,2
-Id : 9704, {_}: identity =<= least_upper_bound identity (multiply (inverse a) identity) [] by Demod 9632 with 6 at 2
-Id : 9705, {_}: identity =<= least_upper_bound identity (inverse a) [] by Demod 9704 with 9304 at 2,3
-Id : 9791, {_}: least_upper_bound (inverse a) b =>= least_upper_bound b identity [] by Super 608 with 9705 at 2,3
-Id : 9810, {_}: least_upper_bound b (inverse a) =>= least_upper_bound b identity [] by Demod 9791 with 12 at 2
-Id : 9811, {_}: least_upper_bound b (inverse a) =>= least_upper_bound identity b [] by Demod 9810 with 12 at 3
-Id : 9812, {_}: least_upper_bound b (inverse a) =>= b [] by Demod 9811 with 349 at 3
-Id : 10144, {_}: multiply (inverse (inverse a)) b =<= least_upper_bound identity (multiply (inverse (inverse a)) b) [] by Super 190 with 9812 at 2,2
-Id : 10186, {_}: multiply a b =<= least_upper_bound identity (multiply (inverse (inverse a)) b) [] by Demod 10144 with 9326 at 1,2
-Id : 10187, {_}: multiply a b =<= least_upper_bound identity (multiply a b) [] by Demod 10186 with 9326 at 1,2,3
-Id : 380544, {_}: multiply (multiply a b) (inverse (multiply a b)) =>= least_upper_bound identity (multiply identity (inverse (multiply a b))) [] by Super 379748 with 10187 at 1,2
-Id : 382056, {_}: multiply a (multiply b (inverse (multiply a b))) =>= least_upper_bound identity (multiply identity (inverse (multiply a b))) [] by Demod 380544 with 8 at 2
-Id : 382057, {_}: multiply a (multiply b (inverse (multiply a b))) =>= least_upper_bound identity (inverse (multiply a b)) [] by Demod 382056 with 4 at 2,3
-Id : 10969, {_}: multiply (inverse (multiply a b)) (multiply a b) =>= least_upper_bound identity (multiply (inverse (multiply a b)) identity) [] by Super 190 with 10187 at 2,2
-Id : 10972, {_}: identity =<= least_upper_bound identity (multiply (inverse (multiply a b)) identity) [] by Demod 10969 with 6 at 2
-Id : 10973, {_}: identity =<= least_upper_bound identity (inverse (multiply a b)) [] by Demod 10972 with 9304 at 2,3
-Id : 382058, {_}: multiply a (multiply b (inverse (multiply a b))) =>= identity [] by Demod 382057 with 10973 at 3
-Id : 383433, {_}: multiply b (inverse (multiply a b)) =>= multiply (inverse a) identity [] by Super 63 with 382058 at 2,3
-Id : 383436, {_}: multiply b (inverse (multiply a b)) =>= inverse a [] by Demod 383433 with 9304 at 3
-Id : 383449, {_}: inverse (multiply a b) =<= multiply (inverse b) (inverse a) [] by Super 63 with 383436 at 2,3
-Id : 759138, {_}: greatest_lower_bound (inverse b) (inverse a) =>= inverse (multiply a b) [] by Demod 759137 with 383449 at 3
-Id : 759204, {_}: multiply a (inverse (multiply a b)) =>= greatest_lower_bound identity (multiply a (inverse b)) [] by Super 9386 with 759138 at 2,2
-Id : 368035, {_}: multiply (greatest_lower_bound ?208569 ?208570) (inverse ?208569) =>= greatest_lower_bound identity (multiply ?208570 (inverse ?208569)) [208570, 208569] by Super 32 with 9315 at 1,3
-Id : 368063, {_}: multiply identity (inverse b) =<= greatest_lower_bound identity (multiply a (inverse b)) [] by Super 368035 with 336 at 1,2
-Id : 369182, {_}: inverse b =<= greatest_lower_bound identity (multiply a (inverse b)) [] by Demod 368063 with 4 at 2
-Id : 759234, {_}: multiply a (inverse (multiply a b)) =>= inverse b [] by Demod 759204 with 369182 at 3
-Id : 759348, {_}: inverse (multiply a b) =<= multiply (inverse a) (inverse b) [] by Super 63 with 759234 at 2,3
-Id : 380530, {_}: multiply (multiply b a) (inverse (multiply b a)) =>= least_upper_bound identity (multiply identity (inverse (multiply b a))) [] by Super 379748 with 9944 at 1,2
-Id : 382029, {_}: multiply b (multiply a (inverse (multiply b a))) =>= least_upper_bound identity (multiply identity (inverse (multiply b a))) [] by Demod 380530 with 8 at 2
-Id : 382030, {_}: multiply b (multiply a (inverse (multiply b a))) =>= least_upper_bound identity (inverse (multiply b a)) [] by Demod 382029 with 4 at 2,3
-Id : 10793, {_}: multiply (inverse (multiply b a)) (multiply b a) =>= least_upper_bound identity (multiply (inverse (multiply b a)) identity) [] by Super 190 with 9944 at 2,2
-Id : 10796, {_}: identity =<= least_upper_bound identity (multiply (inverse (multiply b a)) identity) [] by Demod 10793 with 6 at 2
-Id : 10797, {_}: identity =<= least_upper_bound identity (inverse (multiply b a)) [] by Demod 10796 with 9304 at 2,3
-Id : 382031, {_}: multiply b (multiply a (inverse (multiply b a))) =>= identity [] by Demod 382030 with 10797 at 3
-Id : 382929, {_}: multiply a (inverse (multiply b a)) =>= multiply (inverse b) identity [] by Super 63 with 382031 at 2,3
-Id : 382932, {_}: multiply a (inverse (multiply b a)) =>= inverse b [] by Demod 382929 with 9304 at 3
-Id : 382945, {_}: inverse (multiply b a) =<= multiply (inverse a) (inverse b) [] by Super 63 with 382932 at 2,3
-Id : 759368, {_}: inverse (multiply a b) =>= inverse (multiply b a) [] by Demod 759348 with 382945 at 3
-Id : 759573, {_}: inverse (inverse (multiply b a)) =>= multiply a b [] by Super 9326 with 759368 at 1,2
-Id : 759596, {_}: multiply b a =<= multiply a b [] by Demod 759573 with 9326 at 2
-Id : 760017, {_}: multiply (multiply b a) (inverse b) =>= a [] by Super 9354 with 759596 at 1,2
-Id : 760034, {_}: multiply b (multiply a (inverse b)) =>= a [] by Demod 760017 with 8 at 2
-Id : 760418, {_}: multiply a (inverse b) =<= multiply (inverse b) a [] by Super 63 with 760034 at 2,3
-Id : 760473, {_}: multiply (multiply a (inverse b)) ?434336 =>= multiply (inverse b) (multiply a ?434336) [434336] by Super 8 with 760418 at 1,2
-Id : 760489, {_}: multiply a (multiply (inverse b) ?434336) =<= multiply (inverse b) (multiply a ?434336) [434336] by Demod 760473 with 8 at 2
-Id : 763912, {_}: multiply a (greatest_lower_bound b ?436084) =<= greatest_lower_bound (multiply b a) (multiply a ?436084) [436084] by Super 28 with 759596 at 1,3
-Id : 760023, {_}: multiply (multiply b a) ?434182 =>= multiply a (multiply b ?434182) [434182] by Super 8 with 759596 at 1,2
-Id : 760032, {_}: multiply b (multiply a ?434182) =<= multiply a (multiply b ?434182) [434182] by Demod 760023 with 8 at 2
-Id : 763932, {_}: multiply a (greatest_lower_bound b (multiply b ?436118)) =<= greatest_lower_bound (multiply b a) (multiply b (multiply a ?436118)) [436118] by Super 763912 with 760032 at 2,3
-Id : 764080, {_}: multiply a (greatest_lower_bound b (multiply b ?436118)) =>= multiply b (greatest_lower_bound a (multiply a ?436118)) [436118] by Demod 763932 with 28 at 3
-Id : 768933, {_}: multiply a (multiply (inverse b) (greatest_lower_bound b (multiply b ?438632))) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Super 760489 with 764080 at 2,3
-Id : 208, {_}: multiply (inverse ?566) (greatest_lower_bound ?566 ?567) =>= greatest_lower_bound identity (multiply (inverse ?566) ?567) [567, 566] by Super 202 with 6 at 1,3
-Id : 768988, {_}: multiply a (greatest_lower_bound identity (multiply (inverse b) (multiply b ?438632))) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Demod 768933 with 208 at 2,2
-Id : 768989, {_}: multiply a (greatest_lower_bound identity ?438632) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Demod 768988 with 63 at 2,2,2
-Id : 769075, {_}: multiply a (greatest_lower_bound identity ?438774) =>= greatest_lower_bound a (multiply a ?438774) [438774] by Demod 768989 with 63 at 3
-Id : 325, {_}: greatest_lower_bound ?779 identity =<= greatest_lower_bound (greatest_lower_bound ?779 identity) c [779] by Super 14 with 38 at 2,2
-Id : 334, {_}: greatest_lower_bound ?779 identity =<= greatest_lower_bound c (greatest_lower_bound ?779 identity) [779] by Demod 325 with 10 at 3
-Id : 1055, {_}: least_upper_bound c (greatest_lower_bound ?1435 identity) =>= c [1435] by Super 22 with 334 at 2,2
-Id : 1057, {_}: least_upper_bound c identity =>= c [] by Super 1055 with 20 at 2,2
-Id : 1068, {_}: least_upper_bound identity c =>= c [] by Demod 1057 with 12 at 2
-Id : 1072, {_}: least_upper_bound ?1452 c =<= least_upper_bound (least_upper_bound ?1452 identity) c [1452] by Super 16 with 1068 at 2,2
-Id : 2044, {_}: least_upper_bound ?2196 c =<= least_upper_bound c (least_upper_bound ?2196 identity) [2196] by Demod 1072 with 12 at 3
-Id : 2045, {_}: least_upper_bound ?2198 c =<= least_upper_bound c (least_upper_bound identity ?2198) [2198] by Super 2044 with 12 at 2,3
-Id : 9738, {_}: least_upper_bound (inverse b) c =>= least_upper_bound c identity [] by Super 2045 with 9700 at 2,3
-Id : 9771, {_}: least_upper_bound c (inverse b) =>= least_upper_bound c identity [] by Demod 9738 with 12 at 2
-Id : 9772, {_}: least_upper_bound c (inverse b) =>= least_upper_bound identity c [] by Demod 9771 with 12 at 3
-Id : 9773, {_}: least_upper_bound c (inverse b) =>= c [] by Demod 9772 with 1068 at 3
-Id : 10029, {_}: multiply (inverse (inverse b)) c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Super 190 with 9773 at 2,2
-Id : 10032, {_}: multiply b c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Demod 10029 with 9326 at 1,2
-Id : 10033, {_}: multiply b c =<= least_upper_bound identity (multiply b c) [] by Demod 10032 with 9326 at 1,2,3
-Id : 10872, {_}: greatest_lower_bound identity (multiply b c) =>= identity [] by Super 24 with 10033 at 2,2
-Id : 47955, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply b c) ?32868) =>= greatest_lower_bound identity ?32868 [32868] by Super 14 with 10872 at 1,3
-Id : 70757, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound b ?47489) c) =>= greatest_lower_bound identity (multiply ?47489 c) [47489] by Super 47955 with 32 at 2,2
-Id : 338, {_}: greatest_lower_bound b (greatest_lower_bound a ?786) =>= greatest_lower_bound identity ?786 [786] by Super 14 with 336 at 1,3
-Id : 70764, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound identity ?47501) c) =<= greatest_lower_bound identity (multiply (greatest_lower_bound a ?47501) c) [47501] by Super 70757 with 338 at 1,2,2
-Id : 9792, {_}: least_upper_bound (inverse a) c =>= least_upper_bound c identity [] by Super 2045 with 9705 at 2,3
-Id : 9807, {_}: least_upper_bound c (inverse a) =>= least_upper_bound c identity [] by Demod 9792 with 12 at 2
-Id : 9808, {_}: least_upper_bound c (inverse a) =>= least_upper_bound identity c [] by Demod 9807 with 12 at 3
-Id : 9809, {_}: least_upper_bound c (inverse a) =>= c [] by Demod 9808 with 1068 at 3
-Id : 10119, {_}: multiply (inverse (inverse a)) c =<= least_upper_bound identity (multiply (inverse (inverse a)) c) [] by Super 190 with 9809 at 2,2
-Id : 10122, {_}: multiply a c =<= least_upper_bound identity (multiply (inverse (inverse a)) c) [] by Demod 10119 with 9326 at 1,2
-Id : 10123, {_}: multiply a c =<= least_upper_bound identity (multiply a c) [] by Demod 10122 with 9326 at 1,2,3
-Id : 10918, {_}: greatest_lower_bound identity (multiply a c) =>= identity [] by Super 24 with 10123 at 2,2
-Id : 48295, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply a c) ?33053) =>= greatest_lower_bound identity ?33053 [33053] by Super 14 with 10918 at 1,3
-Id : 48305, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound a ?33073) c) =>= greatest_lower_bound identity (multiply ?33073 c) [33073] by Super 48295 with 32 at 2,2
-Id : 115728, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound identity ?47501) c) =>= greatest_lower_bound identity (multiply ?47501 c) [47501] by Demod 70764 with 48305 at 3
-Id : 204, {_}: multiply (inverse ?551) (greatest_lower_bound ?550 ?551) =>= greatest_lower_bound (multiply (inverse ?551) ?550) identity [550, 551] by Super 202 with 6 at 2,3
-Id : 142360, {_}: multiply (inverse ?87937) (greatest_lower_bound ?87938 ?87937) =>= greatest_lower_bound identity (multiply (inverse ?87937) ?87938) [87938, 87937] by Demod 204 with 10 at 3
-Id : 142374, {_}: multiply (inverse a) identity =<= greatest_lower_bound identity (multiply (inverse a) b) [] by Super 142360 with 336 at 2,2
-Id : 143139, {_}: inverse a =<= greatest_lower_bound identity (multiply (inverse a) b) [] by Demod 142374 with 9304 at 2
-Id : 144455, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (multiply (multiply (inverse a) b) c) [] by Super 115728 with 143139 at 1,2,2
-Id : 144470, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (multiply (inverse a) (multiply b c)) [] by Demod 144455 with 8 at 2,3
-Id : 769471, {_}: multiply a (greatest_lower_bound identity (multiply (inverse a) c)) =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Super 769075 with 144470 at 2,2
-Id : 768990, {_}: multiply a (greatest_lower_bound identity ?438632) =>= greatest_lower_bound a (multiply a ?438632) [438632] by Demod 768989 with 63 at 3
-Id : 770016, {_}: greatest_lower_bound a (multiply a (multiply (inverse a) c)) =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 769471 with 768990 at 2
-Id : 9368, {_}: multiply identity ?8392 =<= multiply ?8391 (multiply (inverse ?8391) ?8392) [8391, 8392] by Super 8 with 9315 at 1,2
-Id : 9385, {_}: ?8392 =<= multiply ?8391 (multiply (inverse ?8391) ?8392) [8391, 8392] by Demod 9368 with 4 at 2
-Id : 770017, {_}: greatest_lower_bound a c =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 770016 with 9385 at 2,2
-Id : 770018, {_}: greatest_lower_bound c a =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 770017 with 10 at 2
-Id : 770019, {_}: greatest_lower_bound c a =<= greatest_lower_bound a (multiply b c) [] by Demod 770018 with 9385 at 2,3
-Id : 770827, {_}: greatest_lower_bound c a === greatest_lower_bound c a [] by Demod 350 with 770019 at 2
-Id : 350, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound c a [] by Demod 2 with 10 at 3
-Id : 2, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c [] by prove_p09b
-% SZS output end CNFRefutation for GRP178-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- c is 72
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 94
- p12x_1 is 75
- p12x_2 is 74
- p12x_3 is 73
- p12x_4 is 71
- p12x_5 is 70
- p12x_6 is 69
- p12x_7 is 68
- prove_p12x is 96
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p12x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
- Id : 40, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
- Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
- Id : 44, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
- Id : 46, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-Goal
- Id : 2, {_}: a =>= b [] by prove_p12x
-Found proof, 11.818806s
-% SZS status Unsatisfiable for GRP181-4.p
-% SZS output start CNFRefutation for GRP181-4.p
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-Id : 177, {_}: multiply ?477 (least_upper_bound ?478 ?479) =<= least_upper_bound (multiply ?477 ?478) (multiply ?477 ?479) [479, 478, 477] by monotony_lub1 ?477 ?478 ?479
-Id : 46, {_}: inverse (least_upper_bound ?61 ?62) =<= greatest_lower_bound (inverse ?61) (inverse ?62) [62, 61] by p12x_7 ?61 ?62
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 40, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 44, {_}: inverse (greatest_lower_bound ?58 ?59) =<= least_upper_bound (inverse ?58) (inverse ?59) [59, 58] by p12x_6 ?58 ?59
-Id : 375, {_}: inverse (greatest_lower_bound ?877 ?878) =<= least_upper_bound (inverse ?877) (inverse ?878) [878, 877] by p12x_6 ?877 ?878
-Id : 398, {_}: inverse (least_upper_bound ?920 ?921) =<= greatest_lower_bound (inverse ?920) (inverse ?921) [921, 920] by p12x_7 ?920 ?921
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 208, {_}: multiply ?553 (greatest_lower_bound ?554 ?555) =<= greatest_lower_bound (multiply ?553 ?554) (multiply ?553 ?555) [555, 554, 553] by monotony_glb1 ?553 ?554 ?555
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 34, {_}: inverse identity =>= identity [] by p12x_1
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 51, {_}: multiply (multiply ?72 ?73) ?74 =?= multiply ?72 (multiply ?73 ?74) [74, 73, 72] by associativity ?72 ?73 ?74
-Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-Id : 324, {_}: inverse (multiply ?822 ?823) =<= multiply (inverse ?823) (inverse ?822) [823, 822] by p12x_3 ?822 ?823
-Id : 328, {_}: inverse (multiply ?833 (inverse ?832)) =>= multiply ?832 (inverse ?833) [832, 833] by Super 324 with 36 at 1,3
-Id : 53, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= multiply ?79 identity [80, 79] by Super 51 with 6 at 2,3
-Id : 325, {_}: inverse (multiply identity ?825) =<= multiply (inverse ?825) identity [825] by Super 324 with 34 at 2,3
-Id : 428, {_}: inverse ?975 =<= multiply (inverse ?975) identity [975] by Demod 325 with 4 at 1,2
-Id : 430, {_}: inverse (inverse ?978) =<= multiply ?978 identity [978] by Super 428 with 36 at 1,3
-Id : 441, {_}: ?978 =<= multiply ?978 identity [978] by Demod 430 with 36 at 2
-Id : 28686, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= ?79 [80, 79] by Demod 53 with 441 at 3
-Id : 28700, {_}: inverse ?20638 =<= multiply ?20639 (inverse (multiply ?20638 (inverse (inverse ?20639)))) [20639, 20638] by Super 328 with 28686 at 1,2
-Id : 28729, {_}: inverse ?20638 =<= multiply ?20639 (multiply (inverse ?20639) (inverse ?20638)) [20639, 20638] by Demod 28700 with 328 at 2,3
-Id : 28730, {_}: inverse ?20638 =<= multiply ?20639 (inverse (multiply ?20638 ?20639)) [20639, 20638] by Demod 28729 with 38 at 2,3
-Id : 307, {_}: multiply ?771 (inverse ?771) =>= identity [771] by Super 6 with 36 at 1,2
-Id : 598, {_}: multiply (multiply ?1178 ?1177) (inverse ?1177) =>= multiply ?1178 identity [1177, 1178] by Super 8 with 307 at 2,3
-Id : 42163, {_}: multiply (multiply ?33679 ?33680) (inverse ?33680) =>= ?33679 [33680, 33679] by Demod 598 with 441 at 3
-Id : 210, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound (multiply (inverse ?561) ?560) identity [560, 561] by Super 208 with 6 at 2,3
-Id : 229, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound identity (multiply (inverse ?561) ?560) [560, 561] by Demod 210 with 10 at 3
-Id : 401, {_}: inverse (least_upper_bound identity ?928) =>= greatest_lower_bound identity (inverse ?928) [928] by Super 398 with 34 at 1,3
-Id : 534, {_}: inverse (multiply (least_upper_bound identity ?1106) ?1107) =<= multiply (inverse ?1107) (greatest_lower_bound identity (inverse ?1106)) [1107, 1106] by Super 38 with 401 at 2,3
-Id : 34883, {_}: inverse (multiply (least_upper_bound identity ?27004) (inverse ?27004)) =>= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Super 229 with 534 at 2
-Id : 34945, {_}: multiply ?27004 (inverse (least_upper_bound identity ?27004)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Demod 34883 with 328 at 2
-Id : 34946, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Demod 34945 with 401 at 2,2
-Id : 34947, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =>= greatest_lower_bound identity (inverse (inverse ?27004)) [27004] by Demod 34946 with 441 at 2,3
-Id : 34948, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =>= greatest_lower_bound identity ?27004 [27004] by Demod 34947 with 36 at 2,3
-Id : 42223, {_}: multiply (greatest_lower_bound identity ?33882) (inverse (greatest_lower_bound identity (inverse ?33882))) =>= ?33882 [33882] by Super 42163 with 34948 at 1,2
-Id : 377, {_}: inverse (greatest_lower_bound ?883 (inverse ?882)) =>= least_upper_bound (inverse ?883) ?882 [882, 883] by Super 375 with 36 at 2,3
-Id : 42257, {_}: multiply (greatest_lower_bound identity ?33882) (least_upper_bound (inverse identity) ?33882) =>= ?33882 [33882] by Demod 42223 with 377 at 2,2
-Id : 118341, {_}: multiply (greatest_lower_bound identity ?85951) (least_upper_bound identity ?85951) =>= ?85951 [85951] by Demod 42257 with 34 at 1,2,2
-Id : 376, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound (inverse ?880) identity [880] by Super 375 with 34 at 2,3
-Id : 388, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound identity (inverse ?880) [880] by Demod 376 with 12 at 3
-Id : 509, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (inverse ?1077) (least_upper_bound identity (inverse ?1076)) [1076, 1077] by Super 44 with 388 at 2,3
-Id : 519, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (least_upper_bound identity (inverse ?1076)) (inverse ?1077) [1076, 1077] by Demod 509 with 12 at 3
-Id : 520, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound identity (least_upper_bound (inverse ?1076) (inverse ?1077)) [1076, 1077] by Demod 519 with 16 at 3
-Id : 521, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 520 with 44 at 2,3
-Id : 512, {_}: inverse (greatest_lower_bound ?1083 identity) =>= least_upper_bound identity (inverse ?1083) [1083] by Demod 376 with 12 at 3
-Id : 516, {_}: inverse (greatest_lower_bound ?1090 (greatest_lower_bound ?1091 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1090 ?1091)) [1091, 1090] by Super 512 with 14 at 1,2
-Id : 2150, {_}: least_upper_bound identity (inverse (greatest_lower_bound ?1077 ?1076)) =?= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 521 with 516 at 2
-Id : 30474, {_}: multiply (inverse ?22001) (greatest_lower_bound ?22001 ?22002) =>= greatest_lower_bound identity (multiply (inverse ?22001) ?22002) [22002, 22001] by Super 208 with 6 at 1,3
-Id : 337, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 40 with 10 at 2
-Id : 338, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 337 with 10 at 3
-Id : 30482, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 30474 with 338 at 2,2
-Id : 214, {_}: multiply (inverse ?576) (greatest_lower_bound ?576 ?577) =>= greatest_lower_bound identity (multiply (inverse ?576) ?577) [577, 576] by Super 208 with 6 at 1,3
-Id : 30627, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 30482 with 214 at 2
-Id : 30842, {_}: least_upper_bound identity (inverse (greatest_lower_bound (multiply (inverse c) a) identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Super 2150 with 30627 at 1,2,3
-Id : 30855, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) a))) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30842 with 2150 at 2
-Id : 378, {_}: inverse (greatest_lower_bound identity ?885) =>= least_upper_bound identity (inverse ?885) [885] by Super 375 with 34 at 1,3
-Id : 30856, {_}: least_upper_bound identity (least_upper_bound identity (inverse (multiply (inverse c) a))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30855 with 378 at 2,2
-Id : 112, {_}: least_upper_bound ?298 (least_upper_bound ?298 ?299) =>= least_upper_bound ?298 ?299 [299, 298] by Super 16 with 18 at 1,3
-Id : 30857, {_}: least_upper_bound identity (inverse (multiply (inverse c) a)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30856 with 112 at 2
-Id : 326, {_}: inverse (multiply (inverse ?827) ?828) =>= multiply (inverse ?828) ?827 [828, 827] by Super 324 with 36 at 2,3
-Id : 30858, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30857 with 326 at 2,2
-Id : 30859, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (least_upper_bound identity (inverse (multiply (inverse c) b))) [] by Demod 30858 with 378 at 2,3
-Id : 30860, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (inverse (multiply (inverse c) b)) [] by Demod 30859 with 112 at 3
-Id : 30861, {_}: least_upper_bound identity (multiply (inverse a) c) =>= least_upper_bound identity (multiply (inverse b) c) [] by Demod 30860 with 326 at 2,3
-Id : 118363, {_}: multiply (greatest_lower_bound identity (multiply (inverse a) c)) (least_upper_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 118341 with 30861 at 2,2
-Id : 399, {_}: inverse (least_upper_bound ?923 identity) =>= greatest_lower_bound (inverse ?923) identity [923] by Super 398 with 34 at 2,3
-Id : 413, {_}: inverse (least_upper_bound ?923 identity) =>= greatest_lower_bound identity (inverse ?923) [923] by Demod 399 with 10 at 3
-Id : 560, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound (inverse ?1130) (greatest_lower_bound identity (inverse ?1129)) [1129, 1130] by Super 46 with 413 at 2,3
-Id : 580, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound (greatest_lower_bound identity (inverse ?1129)) (inverse ?1130) [1129, 1130] by Demod 560 with 10 at 3
-Id : 581, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound identity (greatest_lower_bound (inverse ?1129) (inverse ?1130)) [1129, 1130] by Demod 580 with 14 at 3
-Id : 582, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound ?1129 ?1130)) [1129, 1130] by Demod 581 with 46 at 2,3
-Id : 569, {_}: inverse (least_upper_bound ?1152 identity) =>= greatest_lower_bound identity (inverse ?1152) [1152] by Demod 399 with 10 at 3
-Id : 573, {_}: inverse (least_upper_bound ?1159 (least_upper_bound ?1160 identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound ?1159 ?1160)) [1160, 1159] by Super 569 with 16 at 1,2
-Id : 2778, {_}: greatest_lower_bound identity (inverse (least_upper_bound ?1130 ?1129)) =?= greatest_lower_bound identity (inverse (least_upper_bound ?1129 ?1130)) [1129, 1130] by Demod 582 with 573 at 2
-Id : 28815, {_}: multiply (inverse ?20915) (least_upper_bound ?20915 ?20916) =>= least_upper_bound identity (multiply (inverse ?20915) ?20916) [20916, 20915] by Super 177 with 6 at 1,3
-Id : 353, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 42 with 12 at 2
-Id : 354, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 353 with 12 at 3
-Id : 28823, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 28815 with 354 at 2,2
-Id : 183, {_}: multiply (inverse ?500) (least_upper_bound ?500 ?501) =>= least_upper_bound identity (multiply (inverse ?500) ?501) [501, 500] by Super 177 with 6 at 1,3
-Id : 28958, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 28823 with 183 at 2
-Id : 29161, {_}: greatest_lower_bound identity (inverse (least_upper_bound (multiply (inverse c) a) identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Super 2778 with 28958 at 1,2,3
-Id : 29185, {_}: greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) a))) =>= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29161 with 2778 at 2
-Id : 29186, {_}: greatest_lower_bound identity (greatest_lower_bound identity (inverse (multiply (inverse c) a))) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29185 with 401 at 2,2
-Id : 124, {_}: greatest_lower_bound ?324 (greatest_lower_bound ?324 ?325) =>= greatest_lower_bound ?324 ?325 [325, 324] by Super 14 with 20 at 1,3
-Id : 29187, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) a)) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29186 with 124 at 2
-Id : 29188, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29187 with 326 at 2,2
-Id : 29189, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (greatest_lower_bound identity (inverse (multiply (inverse c) b))) [] by Demod 29188 with 401 at 2,3
-Id : 29190, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (inverse (multiply (inverse c) b)) [] by Demod 29189 with 124 at 3
-Id : 29191, {_}: greatest_lower_bound identity (multiply (inverse a) c) =>= greatest_lower_bound identity (multiply (inverse b) c) [] by Demod 29190 with 326 at 2,3
-Id : 118571, {_}: multiply (greatest_lower_bound identity (multiply (inverse b) c)) (least_upper_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 118363 with 29191 at 1,2
-Id : 42258, {_}: multiply (greatest_lower_bound identity ?33882) (least_upper_bound identity ?33882) =>= ?33882 [33882] by Demod 42257 with 34 at 1,2,2
-Id : 118572, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 118571 with 42258 at 2
-Id : 118655, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 28730 with 118572 at 1,2,3
-Id : 118658, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 118655 with 36 at 2
-Id : 118659, {_}: a =<= inverse (inverse b) [] by Demod 118658 with 28730 at 3
-Id : 118660, {_}: a =>= b [] by Demod 118659 with 36 at 3
-Id : 119303, {_}: b === b [] by Demod 2 with 118660 at 2
-Id : 2, {_}: a =>= b [] by prove_p12x
-% SZS output end CNFRefutation for GRP181-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 94
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 95
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 92
- p20x_1 is 76
- p20x_3 is 75
- prove_20x is 93
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p20x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-Last chance: 1246059266.52
-Last chance: all is indexed 1246060713.99
-Last chance: failed over 100 goal 1246060714.1
-FAILURE in 0 iterations
-% SZS status Timeout for GRP183-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21 is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-Found proof, 112.909833s
-% SZS status Unsatisfiable for GRP184-1.p
-% SZS output start CNFRefutation for GRP184-1.p
-Id : 265, {_}: multiply (greatest_lower_bound ?703 ?704) ?705 =<= greatest_lower_bound (multiply ?703 ?705) (multiply ?704 ?705) [705, 704, 703] by monotony_glb2 ?703 ?704 ?705
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 145, {_}: greatest_lower_bound ?406 (least_upper_bound ?406 ?407) =>= ?406 [407, 406] by glb_absorbtion ?406 ?407
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 127, {_}: least_upper_bound ?353 (greatest_lower_bound ?353 ?354) =>= ?353 [354, 353] by lub_absorbtion ?353 ?354
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 230, {_}: multiply (least_upper_bound ?621 ?622) ?623 =<= least_upper_bound (multiply ?621 ?623) (multiply ?622 ?623) [623, 622, 621] by monotony_lub2 ?621 ?622 ?623
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 38, {_}: multiply (multiply ?61 ?62) ?63 =?= multiply ?61 (multiply ?62 ?63) [63, 62, 61] by associativity ?61 ?62 ?63
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 2065, {_}: multiply (multiply ?3204 (inverse ?3205)) ?3205 =>= multiply ?3204 identity [3205, 3204] by Super 38 with 6 at 2,3
-Id : 2068, {_}: multiply identity ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Super 2065 with 6 at 1,2
-Id : 2091, {_}: ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Demod 2068 with 4 at 2
-Id : 2111, {_}: multiply (inverse (inverse ?3262)) (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Super 26 with 2091 at 2,3
-Id : 39, {_}: multiply (multiply ?65 identity) ?66 =>= multiply ?65 ?66 [66, 65] by Super 38 with 4 at 2,3
-Id : 2108, {_}: multiply ?3253 ?3254 =<= multiply (inverse (inverse ?3253)) ?3254 [3254, 3253] by Super 39 with 2091 at 1,2
-Id : 2129, {_}: ?3211 =<= multiply ?3211 identity [3211] by Demod 2091 with 2108 at 3
-Id : 2149, {_}: inverse (inverse ?3356) =>= multiply ?3356 identity [3356] by Super 2129 with 2108 at 3
-Id : 2156, {_}: inverse (inverse ?3356) =>= ?3356 [3356] by Demod 2149 with 2129 at 3
-Id : 9722, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Demod 2111 with 2156 at 1,2
-Id : 9764, {_}: multiply ?11921 (least_upper_bound ?11922 identity) =<= least_upper_bound (multiply ?11921 ?11922) ?11921 [11922, 11921] by Demod 9722 with 2156 at 1,1,3
-Id : 701, {_}: multiply (least_upper_bound ?1544 identity) ?1545 =<= least_upper_bound (multiply ?1544 ?1545) ?1545 [1545, 1544] by Super 230 with 4 at 2,3
-Id : 703, {_}: multiply (least_upper_bound (inverse ?1549) identity) ?1549 =>= least_upper_bound identity ?1549 [1549] by Super 701 with 6 at 1,3
-Id : 729, {_}: multiply (least_upper_bound identity (inverse ?1549)) ?1549 =>= least_upper_bound identity ?1549 [1549] by Demod 703 with 12 at 1,2
-Id : 2193, {_}: multiply (least_upper_bound identity ?3378) (inverse ?3378) =>= least_upper_bound identity (inverse ?3378) [3378] by Super 729 with 2156 at 2,1,2
-Id : 9777, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound (inverse ?11957) identity) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Super 9764 with 2193 at 1,3
-Id : 9888, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Demod 9777 with 12 at 2,2
-Id : 9889, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound identity (least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957)) [11957] by Demod 9888 with 16 at 3
-Id : 523, {_}: least_upper_bound (greatest_lower_bound ?1203 ?1204) ?1203 =>= ?1203 [1204, 1203] by Super 12 with 22 at 3
-Id : 524, {_}: least_upper_bound (greatest_lower_bound ?1207 ?1206) ?1206 =>= ?1206 [1206, 1207] by Super 523 with 10 at 1,2
-Id : 139, {_}: greatest_lower_bound (least_upper_bound ?385 ?386) ?385 =>= ?385 [386, 385] by Super 10 with 24 at 3
-Id : 40, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= multiply ?68 identity [69, 68] by Super 38 with 6 at 2,3
-Id : 2130, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= ?68 [69, 68] by Demod 40 with 2129 at 3
-Id : 231, {_}: multiply (least_upper_bound ?625 identity) ?626 =<= least_upper_bound (multiply ?625 ?626) ?626 [626, 625] by Super 230 with 4 at 2,3
-Id : 693, {_}: least_upper_bound ?1518 (multiply ?1517 ?1518) =>= multiply (least_upper_bound ?1517 identity) ?1518 [1517, 1518] by Super 12 with 231 at 3
-Id : 235, {_}: multiply (least_upper_bound identity ?641) ?642 =<= least_upper_bound ?642 (multiply ?641 ?642) [642, 641] by Super 230 with 4 at 1,3
-Id : 1616, {_}: multiply (least_upper_bound identity ?1517) ?1518 =?= multiply (least_upper_bound ?1517 identity) ?1518 [1518, 1517] by Demod 693 with 235 at 2
-Id : 1625, {_}: multiply (least_upper_bound (least_upper_bound identity ?2728) ?2730) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Super 30 with 1616 at 1,3
-Id : 1699, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Demod 1625 with 16 at 1,2
-Id : 1700, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= multiply (least_upper_bound (least_upper_bound ?2728 identity) ?2730) ?2729 [2729, 2730, 2728] by Demod 1699 with 30 at 3
-Id : 4487, {_}: multiply (multiply (least_upper_bound identity (least_upper_bound ?5822 ?5823)) (inverse ?5824)) ?5824 =>= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5824, 5823, 5822] by Super 2130 with 1700 at 1,2
-Id : 4634, {_}: least_upper_bound identity (least_upper_bound ?6053 ?6054) =<= least_upper_bound (least_upper_bound ?6053 identity) ?6054 [6054, 6053] by Demod 4487 with 2130 at 2
-Id : 122, {_}: least_upper_bound (greatest_lower_bound ?335 ?336) ?335 =>= ?335 [336, 335] by Super 12 with 22 at 3
-Id : 4738, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound identity ?6182) ?6183) =>= least_upper_bound identity ?6183 [6183, 6182] by Super 4634 with 122 at 1,3
-Id : 4751, {_}: least_upper_bound identity (least_upper_bound ?6221 (greatest_lower_bound identity ?6220)) =>= least_upper_bound identity ?6221 [6220, 6221] by Super 4738 with 12 at 2,2
-Id : 4923, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (least_upper_bound identity ?6418) (greatest_lower_bound identity ?6419) [6419, 6418] by Super 16 with 4751 at 2
-Id : 4974, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (greatest_lower_bound identity ?6419) (least_upper_bound identity ?6418) [6419, 6418] by Demod 4923 with 12 at 3
-Id : 5424, {_}: greatest_lower_bound (least_upper_bound identity ?7110) (greatest_lower_bound identity ?7111) =>= greatest_lower_bound identity ?7111 [7111, 7110] by Super 139 with 4974 at 1,2
-Id : 5471, {_}: greatest_lower_bound (greatest_lower_bound identity ?7111) (least_upper_bound identity ?7110) =>= greatest_lower_bound identity ?7111 [7110, 7111] by Demod 5424 with 10 at 2
-Id : 6383, {_}: greatest_lower_bound identity (greatest_lower_bound ?8259 (least_upper_bound identity ?8260)) =>= greatest_lower_bound identity ?8259 [8260, 8259] by Demod 5471 with 14 at 2
-Id : 605, {_}: greatest_lower_bound (least_upper_bound ?1361 ?1362) ?1361 =>= ?1361 [1362, 1361] by Super 10 with 24 at 3
-Id : 606, {_}: greatest_lower_bound (least_upper_bound ?1365 ?1364) ?1364 =>= ?1364 [1364, 1365] by Super 605 with 12 at 1,2
-Id : 6408, {_}: greatest_lower_bound identity (least_upper_bound identity ?8337) =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8336, 8337] by Super 6383 with 606 at 2,2
-Id : 6477, {_}: identity =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8337, 8336] by Demod 6408 with 24 at 2
-Id : 8574, {_}: least_upper_bound identity (least_upper_bound ?10550 (least_upper_bound identity ?10551)) =>= least_upper_bound ?10550 (least_upper_bound identity ?10551) [10551, 10550] by Super 524 with 6477 at 1,2
-Id : 9890, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957) [11957] by Demod 9889 with 8574 at 3
-Id : 382, {_}: least_upper_bound ?896 (least_upper_bound ?896 ?897) =>= least_upper_bound ?896 ?897 [897, 896] by Super 16 with 18 at 1,3
-Id : 383, {_}: least_upper_bound ?899 (least_upper_bound ?900 ?899) =>= least_upper_bound ?899 ?900 [900, 899] by Super 382 with 12 at 2,2
-Id : 9723, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply ?3262 ?3263) ?3262 [3263, 3262] by Demod 9722 with 2156 at 1,1,3
-Id : 9944, {_}: least_upper_bound ?12111 (multiply ?12111 ?12112) =>= multiply ?12111 (least_upper_bound ?12112 identity) [12112, 12111] by Super 12 with 9723 at 3
-Id : 9957, {_}: least_upper_bound (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Super 9944 with 2193 at 2,2
-Id : 10090, {_}: least_upper_bound identity (least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147))) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 9957 with 16 at 2
-Id : 10091, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 10090 with 8574 at 2
-Id : 10092, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) [12147] by Demod 10091 with 12 at 2,3
-Id : 50296, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound (inverse ?12147) (least_upper_bound identity ?12147) [12147] by Demod 10092 with 9890 at 3
-Id : 50343, {_}: least_upper_bound (least_upper_bound identity (inverse ?46312)) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Super 383 with 50296 at 2,2
-Id : 50540, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312))) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50343 with 16 at 2
-Id : 100, {_}: least_upper_bound ?287 (least_upper_bound ?287 ?288) =>= least_upper_bound ?287 ?288 [288, 287] by Super 16 with 18 at 1,3
-Id : 50541, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50540 with 100 at 2,2
-Id : 50542, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =<= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50541 with 8574 at 2
-Id : 50543, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =>= least_upper_bound identity (least_upper_bound (inverse ?46312) ?46312) [46312] by Demod 50542 with 16 at 3
-Id : 51165, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound identity (least_upper_bound (inverse ?11957) ?11957) [11957] by Demod 9890 with 50543 at 3
-Id : 51164, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 50296 with 50543 at 3
-Id : 1772, {_}: multiply (multiply ?2886 (least_upper_bound identity (inverse ?2885))) ?2885 =>= multiply ?2886 (least_upper_bound identity ?2885) [2885, 2886] by Super 8 with 729 at 2,3
-Id : 2194, {_}: multiply (multiply ?3381 ?3380) (inverse ?3380) =>= ?3381 [3380, 3381] by Super 2130 with 2156 at 2,1,2
-Id : 2142, {_}: multiply ?3332 (inverse ?3332) =>= identity [3332] by Super 6 with 2108 at 2
-Id : 2212, {_}: multiply identity ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Super 8 with 2142 at 1,2
-Id : 2238, {_}: ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Demod 2212 with 4 at 2
-Id : 4219, {_}: multiply ?5438 (inverse (multiply (inverse ?5439) ?5438)) =>= ?5439 [5439, 5438] by Super 2194 with 2238 at 1,2
-Id : 18113, {_}: inverse (multiply (inverse ?20071) (inverse ?20072)) =>= multiply ?20072 ?20071 [20072, 20071] by Super 2238 with 4219 at 2,3
-Id : 18209, {_}: inverse (multiply ?20210 ?20209) =<= multiply (inverse ?20209) (inverse ?20210) [20209, 20210] by Super 2156 with 18113 at 1,2
-Id : 18309, {_}: multiply (inverse (multiply ?20330 ?20331)) ?20330 =>= inverse ?20331 [20331, 20330] by Super 2130 with 18209 at 1,2
-Id : 20618, {_}: multiply (least_upper_bound identity (inverse (multiply ?22269 ?22270))) ?22269 =>= least_upper_bound ?22269 (inverse ?22270) [22270, 22269] by Super 235 with 18309 at 2,3
-Id : 379959, {_}: multiply (least_upper_bound ?332905 (inverse ?332906)) (inverse ?332905) =>= least_upper_bound identity (inverse (multiply ?332905 ?332906)) [332906, 332905] by Super 2194 with 20618 at 1,2
-Id : 243389, {_}: multiply (least_upper_bound identity (multiply ?228491 ?228492)) (inverse ?228492) =>= least_upper_bound (inverse ?228492) ?228491 [228492, 228491] by Super 235 with 2194 at 2,3
-Id : 177106, {_}: multiply (multiply ?175304 (least_upper_bound identity (inverse ?175305))) ?175305 =>= multiply ?175304 (least_upper_bound identity ?175305) [175305, 175304] by Super 8 with 729 at 2,3
-Id : 10132, {_}: multiply (inverse ?12250) (least_upper_bound ?12250 identity) =>= least_upper_bound identity (inverse ?12250) [12250] by Super 9764 with 6 at 1,3
-Id : 10133, {_}: multiply (inverse ?12252) (least_upper_bound identity ?12252) =>= least_upper_bound identity (inverse ?12252) [12252] by Super 10132 with 12 at 2,2
-Id : 10242, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound (least_upper_bound identity ?12325) (least_upper_bound identity (inverse ?12325)) [12325] by Super 235 with 10133 at 2,3
-Id : 10288, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound identity (least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325))) [12325] by Demod 10242 with 16 at 3
-Id : 10289, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325)) [12325] by Demod 10288 with 8574 at 3
-Id : 177160, {_}: multiply (least_upper_bound (inverse ?175487) (least_upper_bound identity (inverse (inverse ?175487)))) ?175487 =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Super 177106 with 10289 at 1,2
-Id : 236, {_}: multiply (least_upper_bound (inverse ?645) ?644) ?645 =>= least_upper_bound identity (multiply ?644 ?645) [644, 645] by Super 230 with 6 at 1,3
-Id : 177356, {_}: least_upper_bound identity (multiply (least_upper_bound identity (inverse (inverse ?175487))) ?175487) =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177160 with 236 at 2
-Id : 177357, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =<= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177356 with 2156 at 2,1,2,2
-Id : 177519, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175800) ?175800) =>= multiply (least_upper_bound identity ?175800) (least_upper_bound identity ?175800) [175800] by Demod 177357 with 2156 at 2,1,3
-Id : 177520, {_}: least_upper_bound identity (multiply (least_upper_bound ?175802 identity) ?175802) =>= multiply (least_upper_bound identity ?175802) (least_upper_bound identity ?175802) [175802] by Super 177519 with 12 at 1,2,2
-Id : 3515, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?4381) ?4382)) ?4381 =>= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4382, 4381] by Super 235 with 236 at 2,3
-Id : 1778, {_}: multiply (least_upper_bound (least_upper_bound identity (inverse ?2903)) ?2904) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Super 30 with 729 at 1,3
-Id : 1803, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Demod 1778 with 16 at 1,2
-Id : 1804, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (multiply ?2904 ?2903) (least_upper_bound identity ?2903) [2904, 2903] by Demod 1803 with 12 at 3
-Id : 102, {_}: least_upper_bound ?294 ?293 =<= least_upper_bound (least_upper_bound ?294 ?293) ?293 [293, 294] by Super 16 with 18 at 2,2
-Id : 29053, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27543 ?27544) ?27545) =<= least_upper_bound (least_upper_bound ?27543 (least_upper_bound ?27544 identity)) ?27545 [27545, 27544, 27543] by Super 4634 with 16 at 1,3
-Id : 29054, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27547 ?27548) ?27549) =<= least_upper_bound (least_upper_bound ?27547 (least_upper_bound identity ?27548)) ?27549 [27549, 27548, 27547] by Super 29053 with 12 at 2,1,3
-Id : 93172, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324)) [78324, 78323] by Super 102 with 29054 at 3
-Id : 93561, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324) [78324, 78323] by Demod 93172 with 8574 at 3
-Id : 4534, {_}: least_upper_bound identity (least_upper_bound ?5822 ?5823) =<= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5823, 5822] by Demod 4487 with 2130 at 2
-Id : 27996, {_}: least_upper_bound ?26567 (least_upper_bound identity (least_upper_bound ?26568 ?26567)) =>= least_upper_bound ?26567 (least_upper_bound ?26568 identity) [26568, 26567] by Super 383 with 4534 at 2,2
-Id : 28002, {_}: least_upper_bound ?26586 (least_upper_bound identity ?26586) =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Super 27996 with 122 at 2,2,2
-Id : 28236, {_}: least_upper_bound ?26586 identity =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Demod 28002 with 383 at 2
-Id : 8916, {_}: least_upper_bound identity (least_upper_bound ?11024 (least_upper_bound identity ?11025)) =>= least_upper_bound ?11024 (least_upper_bound identity ?11025) [11025, 11024] by Super 524 with 6477 at 1,2
-Id : 8917, {_}: least_upper_bound identity (least_upper_bound ?11027 (least_upper_bound ?11028 identity)) =>= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Super 8916 with 12 at 2,2,2
-Id : 4835, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound ?6313 identity) ?6314) =>= least_upper_bound identity ?6314 [6314, 6313] by Super 4634 with 524 at 1,3
-Id : 4847, {_}: least_upper_bound identity (greatest_lower_bound ?6349 identity) =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Super 4835 with 22 at 2,2
-Id : 128, {_}: least_upper_bound ?356 (greatest_lower_bound ?357 ?356) =>= ?356 [357, 356] by Super 127 with 10 at 2,2
-Id : 4903, {_}: identity =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Demod 4847 with 128 at 2
-Id : 5840, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631) =>= greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631 [7631, 7630] by Super 606 with 4903 at 1,2
-Id : 5845, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7645) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Super 5840 with 606 at 1,2,2
-Id : 112, {_}: greatest_lower_bound ?313 (greatest_lower_bound ?313 ?314) =>= greatest_lower_bound ?313 ?314 [314, 313] by Super 14 with 20 at 1,3
-Id : 5908, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Demod 5845 with 112 at 2
-Id : 5909, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound ?7644 identity)) ?7645 [7644, 7645] by Demod 5908 with 10 at 1,3
-Id : 7862, {_}: greatest_lower_bound identity ?10013 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound ?10014 identity) ?10013) [10014, 10013] by Demod 5909 with 14 at 3
-Id : 146, {_}: greatest_lower_bound ?409 (least_upper_bound ?410 ?409) =>= ?409 [410, 409] by Super 145 with 12 at 2,2
-Id : 7879, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= greatest_lower_bound identity (least_upper_bound ?10064 identity) [10064, 10063] by Super 7862 with 146 at 2,3
-Id : 7984, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= identity [10064, 10063] by Demod 7879 with 146 at 3
-Id : 8758, {_}: least_upper_bound identity (least_upper_bound ?10813 (least_upper_bound ?10814 identity)) =>= least_upper_bound ?10813 (least_upper_bound ?10814 identity) [10814, 10813] by Super 524 with 7984 at 1,2
-Id : 9284, {_}: least_upper_bound ?11027 (least_upper_bound ?11028 identity) =?= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Demod 8917 with 8758 at 2
-Id : 89245, {_}: least_upper_bound ?75550 identity =<= least_upper_bound ?75550 (least_upper_bound identity (greatest_lower_bound ?75550 ?75551)) [75551, 75550] by Demod 28236 with 9284 at 3
-Id : 89255, {_}: least_upper_bound (least_upper_bound ?75580 ?75581) identity =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Super 89245 with 606 at 2,2,3
-Id : 89821, {_}: least_upper_bound identity (least_upper_bound ?75580 ?75581) =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Demod 89255 with 12 at 2
-Id : 113848, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =?= least_upper_bound identity (least_upper_bound ?78323 ?78324) [78324, 78323] by Demod 93561 with 89821 at 3
-Id : 181989, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (least_upper_bound (multiply ?2904 ?2903) ?2903) [2904, 2903] by Demod 1804 with 113848 at 3
-Id : 181990, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (multiply (least_upper_bound ?2904 identity) ?2903) [2904, 2903] by Demod 181989 with 231 at 2,3
-Id : 230272, {_}: least_upper_bound identity (multiply (least_upper_bound ?4382 identity) ?4381) =?= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4381, 4382] by Demod 3515 with 181990 at 2
-Id : 230301, {_}: least_upper_bound ?219571 (least_upper_bound identity (multiply ?219571 ?219571)) =>= multiply (least_upper_bound identity ?219571) (least_upper_bound identity ?219571) [219571] by Super 177520 with 230272 at 2
-Id : 232386, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (least_upper_bound ?221067 identity) (multiply ?221067 ?221067) [221067] by Super 16 with 230301 at 2
-Id : 233006, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (multiply ?221067 ?221067) (least_upper_bound ?221067 identity) [221067] by Demod 232386 with 12 at 3
-Id : 4614, {_}: greatest_lower_bound ?5993 (least_upper_bound identity (least_upper_bound ?5992 ?5993)) =>= ?5993 [5992, 5993] by Super 146 with 4534 at 2,2
-Id : 27608, {_}: least_upper_bound ?26112 (least_upper_bound identity (least_upper_bound ?26113 ?26112)) =>= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Super 524 with 4614 at 1,2
-Id : 4631, {_}: least_upper_bound ?6045 (least_upper_bound identity (least_upper_bound ?6044 ?6045)) =>= least_upper_bound ?6045 (least_upper_bound ?6044 identity) [6044, 6045] by Super 383 with 4534 at 2,2
-Id : 83798, {_}: least_upper_bound ?26112 (least_upper_bound ?26113 identity) =?= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Demod 27608 with 4631 at 2
-Id : 233007, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound identity (least_upper_bound ?221067 (multiply ?221067 ?221067)) [221067] by Demod 233006 with 83798 at 3
-Id : 9743, {_}: least_upper_bound ?11859 (multiply ?11859 ?11860) =>= multiply ?11859 (least_upper_bound ?11860 identity) [11860, 11859] by Super 12 with 9723 at 3
-Id : 233595, {_}: multiply (least_upper_bound identity ?221617) (least_upper_bound identity ?221617) =<= least_upper_bound identity (multiply ?221617 (least_upper_bound ?221617 identity)) [221617] by Demod 233007 with 9743 at 2,3
-Id : 233596, {_}: multiply (least_upper_bound identity ?221619) (least_upper_bound identity ?221619) =<= least_upper_bound identity (multiply ?221619 (least_upper_bound identity ?221619)) [221619] by Super 233595 with 12 at 2,2,3
-Id : 243525, {_}: multiply (multiply (least_upper_bound identity ?228868) (least_upper_bound identity ?228868)) (inverse (least_upper_bound identity ?228868)) =>= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Super 243389 with 233596 at 1,2
-Id : 243950, {_}: least_upper_bound identity ?228868 =<= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Demod 243525 with 2194 at 2
-Id : 244049, {_}: least_upper_bound ?229075 (inverse (least_upper_bound identity ?229075)) =>= least_upper_bound identity ?229075 [229075] by Super 12 with 243950 at 3
-Id : 380052, {_}: multiply (least_upper_bound identity ?333235) (inverse ?333235) =<= least_upper_bound identity (inverse (multiply ?333235 (least_upper_bound identity ?333235))) [333235] by Super 379959 with 244049 at 1,2
-Id : 381402, {_}: least_upper_bound identity (inverse ?334503) =<= least_upper_bound identity (inverse (multiply ?334503 (least_upper_bound identity ?334503))) [334503] by Demod 380052 with 2193 at 2
-Id : 177358, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =>= multiply (least_upper_bound identity ?175487) (least_upper_bound identity ?175487) [175487] by Demod 177357 with 2156 at 2,1,3
-Id : 177476, {_}: multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (multiply (least_upper_bound identity ?175688) (least_upper_bound identity ?175688)) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Super 10133 with 177358 at 2,2
-Id : 177670, {_}: multiply (multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (least_upper_bound identity ?175688)) (least_upper_bound identity ?175688) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177476 with 8 at 2
-Id : 177671, {_}: multiply (inverse ?175688) (least_upper_bound identity ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177670 with 18309 at 1,2
-Id : 177672, {_}: least_upper_bound identity (inverse ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177671 with 10133 at 2
-Id : 381492, {_}: least_upper_bound identity (inverse (inverse (multiply (least_upper_bound identity ?334735) ?334735))) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Super 381402 with 177672 at 2,1,2,3
-Id : 382266, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?334735) ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 381492 with 2156 at 2,2
-Id : 382267, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 382266 with 177358 at 2
-Id : 18224, {_}: inverse (multiply (inverse ?20261) (inverse ?20262)) =>= multiply ?20262 ?20261 [20262, 20261] by Super 2238 with 4219 at 2,3
-Id : 18226, {_}: inverse (multiply (inverse ?20267) ?20266) =>= multiply (inverse ?20266) ?20267 [20266, 20267] by Super 18224 with 2156 at 2,1,2
-Id : 382268, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (inverse (least_upper_bound identity (inverse ?334735))) (multiply (least_upper_bound identity ?334735) ?334735)) [334735] by Demod 382267 with 18226 at 2,3
-Id : 382269, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (multiply (inverse (least_upper_bound identity (inverse ?334735))) (least_upper_bound identity ?334735)) ?334735) [334735] by Demod 382268 with 8 at 2,3
-Id : 18545, {_}: inverse (multiply ?20706 (inverse ?20707)) =>= multiply ?20707 (inverse ?20706) [20707, 20706] by Super 18224 with 2156 at 1,1,2
-Id : 18566, {_}: inverse (least_upper_bound identity (inverse ?20767)) =<= multiply ?20767 (inverse (least_upper_bound identity ?20767)) [20767] by Super 18545 with 2193 at 1,2
-Id : 19741, {_}: multiply (inverse (least_upper_bound identity (inverse ?21554))) (least_upper_bound identity ?21554) =>= ?21554 [21554] by Super 2130 with 18566 at 1,2
-Id : 382270, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =>= least_upper_bound identity (multiply ?334735 ?334735) [334735] by Demod 382269 with 19741 at 1,2,3
-Id : 382385, {_}: multiply (least_upper_bound identity (multiply (inverse ?334827) (inverse ?334827))) ?334827 =>= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Super 1772 with 382270 at 1,2
-Id : 2064, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 (multiply ?3201 identity) [3202, 3201] by Super 235 with 40 at 2,3
-Id : 223367, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 ?3201 [3202, 3201] by Demod 2064 with 2129 at 2,3
-Id : 382807, {_}: least_upper_bound ?334827 (inverse ?334827) =<= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Demod 382385 with 223367 at 2
-Id : 382808, {_}: least_upper_bound ?334827 (inverse ?334827) =<= least_upper_bound ?334827 (least_upper_bound identity (inverse ?334827)) [334827] by Demod 382807 with 10289 at 3
-Id : 383798, {_}: least_upper_bound ?12147 (inverse ?12147) =<= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 51164 with 382808 at 2
-Id : 383800, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 51165 with 383798 at 3
-Id : 2115, {_}: multiply (inverse (inverse ?3274)) (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Super 28 with 2091 at 2,3
-Id : 10659, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Demod 2115 with 2156 at 1,2
-Id : 10660, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply ?3274 ?3275) ?3274 [3275, 3274] by Demod 10659 with 2156 at 1,1,3
-Id : 10678, {_}: greatest_lower_bound ?12834 (multiply ?12834 ?12835) =>= multiply ?12834 (greatest_lower_bound ?12835 identity) [12835, 12834] by Super 10 with 10660 at 3
-Id : 18328, {_}: greatest_lower_bound (inverse ?20397) (inverse (multiply ?20396 ?20397)) =>= multiply (inverse ?20397) (greatest_lower_bound (inverse ?20396) identity) [20396, 20397] by Super 10678 with 18209 at 2,2
-Id : 2116, {_}: multiply (inverse (inverse ?3277)) (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Super 28 with 2091 at 1,3
-Id : 11396, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Demod 2116 with 2156 at 1,2
-Id : 11397, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply ?3277 ?3278) [3278, 3277] by Demod 11396 with 2156 at 1,2,3
-Id : 11398, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =?= multiply ?3277 (greatest_lower_bound ?3278 identity) [3278, 3277] by Demod 11397 with 10678 at 3
-Id : 78468, {_}: greatest_lower_bound (inverse ?65596) (inverse (multiply ?65597 ?65596)) =>= multiply (inverse ?65596) (greatest_lower_bound identity (inverse ?65597)) [65597, 65596] by Demod 18328 with 11398 at 3
-Id : 78507, {_}: greatest_lower_bound (inverse ?65693) (inverse (inverse ?65692)) =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Super 78468 with 18309 at 1,2,2
-Id : 78731, {_}: greatest_lower_bound (inverse ?65693) ?65692 =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Demod 78507 with 2156 at 2,2
-Id : 443714, {_}: greatest_lower_bound (inverse ?378148) ?378149 =<= multiply (inverse ?378148) (greatest_lower_bound identity (multiply ?378148 ?378149)) [378149, 378148] by Demod 78731 with 2156 at 2,2,3
-Id : 842, {_}: multiply (greatest_lower_bound ?1730 identity) ?1731 =<= greatest_lower_bound (multiply ?1730 ?1731) ?1731 [1731, 1730] by Super 265 with 4 at 2,3
-Id : 844, {_}: multiply (greatest_lower_bound (inverse ?1735) identity) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Super 842 with 6 at 1,3
-Id : 874, {_}: multiply (greatest_lower_bound identity (inverse ?1735)) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Demod 844 with 10 at 1,2
-Id : 2191, {_}: multiply (greatest_lower_bound identity ?3374) (inverse ?3374) =>= greatest_lower_bound identity (inverse ?3374) [3374] by Super 874 with 2156 at 2,1,2
-Id : 9776, {_}: multiply (greatest_lower_bound identity ?11955) (least_upper_bound (inverse ?11955) identity) =<= least_upper_bound (greatest_lower_bound identity (inverse ?11955)) (greatest_lower_bound identity ?11955) [11955] by Super 9764 with 2191 at 1,3
-Id : 47906, {_}: multiply (greatest_lower_bound identity ?45245) (least_upper_bound identity (inverse ?45245)) =<= least_upper_bound (greatest_lower_bound identity (inverse ?45245)) (greatest_lower_bound identity ?45245) [45245] by Demod 9776 with 12 at 2,2
-Id : 47957, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity (inverse (inverse ?45371))) =>= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Super 47906 with 2156 at 2,1,3
-Id : 48268, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =<= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Demod 47957 with 2156 at 2,2,2
-Id : 9956, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound (inverse ?12145) identity) [12145] by Super 9944 with 2191 at 2,2
-Id : 10089, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound identity (inverse ?12145)) [12145] by Demod 9956 with 12 at 2,3
-Id : 105582, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =?= multiply (greatest_lower_bound identity ?45371) (least_upper_bound identity (inverse ?45371)) [45371] by Demod 48268 with 10089 at 3
-Id : 443814, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?378412) (least_upper_bound identity (inverse ?378412)))) [378412] by Super 443714 with 105582 at 2,2,3
-Id : 5843, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7639) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Super 5840 with 139 at 1,2,2
-Id : 5900, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Demod 5843 with 112 at 2
-Id : 5901, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound identity ?7638)) ?7639 [7638, 7639] by Demod 5900 with 10 at 1,3
-Id : 7645, {_}: greatest_lower_bound identity ?9767 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound identity ?9768) ?9767) [9768, 9767] by Demod 5901 with 14 at 3
-Id : 270, {_}: multiply (greatest_lower_bound identity ?723) ?724 =<= greatest_lower_bound ?724 (multiply ?723 ?724) [724, 723] by Super 265 with 4 at 1,3
-Id : 7676, {_}: greatest_lower_bound identity (multiply ?9863 (least_upper_bound identity ?9864)) =<= greatest_lower_bound identity (multiply (greatest_lower_bound identity ?9863) (least_upper_bound identity ?9864)) [9864, 9863] by Super 7645 with 270 at 2,3
-Id : 444411, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply ?378412 (least_upper_bound identity (inverse ?378412)))) [378412] by Demod 443814 with 7676 at 2,3
-Id : 2215, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound (multiply ?3422 ?3423) identity [3423, 3422] by Super 26 with 2142 at 2,3
-Id : 2235, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound identity (multiply ?3422 ?3423) [3423, 3422] by Demod 2215 with 12 at 3
-Id : 444412, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?378412 identity))) [378412] by Demod 444411 with 2235 at 2,2,3
-Id : 444413, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) identity [378412] by Demod 444412 with 24 at 2,3
-Id : 444414, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= inverse (greatest_lower_bound identity (inverse ?378412)) [378412] by Demod 444413 with 2129 at 3
-Id : 761747, {_}: least_upper_bound (least_upper_bound identity ?693163) (inverse (greatest_lower_bound identity (inverse ?693163))) =>= least_upper_bound identity ?693163 [693163] by Super 128 with 444414 at 2,2
-Id : 762288, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) (least_upper_bound identity ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 761747 with 12 at 2
-Id : 1150, {_}: least_upper_bound (least_upper_bound ?2078 ?2079) ?2078 =>= least_upper_bound ?2078 ?2079 [2079, 2078] by Super 12 with 100 at 3
-Id : 158742, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?149635 ?149636) ?149637) ?149635 =>= least_upper_bound ?149635 (least_upper_bound ?149636 ?149637) [149637, 149636, 149635] by Super 1150 with 16 at 1,2
-Id : 375, {_}: least_upper_bound (least_upper_bound ?872 ?873) ?872 =>= least_upper_bound ?872 ?873 [873, 872] by Super 12 with 100 at 3
-Id : 1142, {_}: least_upper_bound (least_upper_bound ?2051 ?2052) (least_upper_bound ?2051 ?2053) =>= least_upper_bound (least_upper_bound ?2051 ?2052) ?2053 [2053, 2052, 2051] by Super 16 with 375 at 1,3
-Id : 158880, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?150190 ?150191) ?150189) ?150190 =?= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Super 158742 with 1142 at 1,2
-Id : 1152, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?2086 ?2084) ?2085) ?2086 =>= least_upper_bound ?2086 (least_upper_bound ?2084 ?2085) [2085, 2084, 2086] by Super 1150 with 16 at 1,2
-Id : 159604, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =<= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Demod 158880 with 1152 at 2
-Id : 126, {_}: least_upper_bound ?351 ?349 =<= least_upper_bound (least_upper_bound ?351 ?349) (greatest_lower_bound ?349 ?350) [350, 349, 351] by Super 16 with 22 at 2,2
-Id : 135029, {_}: least_upper_bound ?113864 ?113865 =<= least_upper_bound (greatest_lower_bound ?113865 ?113866) (least_upper_bound ?113864 ?113865) [113866, 113865, 113864] by Demod 126 with 12 at 3
-Id : 135153, {_}: least_upper_bound ?114345 (least_upper_bound ?114346 ?114344) =<= least_upper_bound ?114346 (least_upper_bound ?114345 (least_upper_bound ?114346 ?114344)) [114344, 114346, 114345] by Super 135029 with 139 at 1,3
-Id : 503059, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =?= least_upper_bound ?150191 (least_upper_bound ?150190 ?150189) [150189, 150191, 150190] by Demod 159604 with 135153 at 3
-Id : 762289, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 762288 with 503059 at 2
-Id : 2280, {_}: multiply (greatest_lower_bound identity ?3504) (inverse ?3504) =>= greatest_lower_bound identity (inverse ?3504) [3504] by Super 874 with 2156 at 2,1,2
-Id : 2286, {_}: multiply (greatest_lower_bound identity ?3514) (inverse (greatest_lower_bound identity ?3514)) =>= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Super 2280 with 112 at 1,2
-Id : 2335, {_}: identity =<= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Demod 2286 with 2142 at 2
-Id : 2422, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity ?3608)) =>= inverse (greatest_lower_bound identity ?3608) [3608] by Super 524 with 2335 at 1,2
-Id : 2722, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827) =>= least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827 [3827, 3826] by Super 16 with 2422 at 1,3
-Id : 762290, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163 =>= least_upper_bound identity ?693163 [693163] by Demod 762289 with 2722 at 2
-Id : 18327, {_}: multiply (inverse ?20394) (least_upper_bound (inverse ?20393) identity) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Super 9723 with 18209 at 1,3
-Id : 2112, {_}: multiply (inverse (inverse ?3265)) (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Super 26 with 2091 at 1,3
-Id : 10376, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Demod 2112 with 2156 at 1,2
-Id : 10377, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply ?3265 ?3266) [3266, 3265] by Demod 10376 with 2156 at 1,2,3
-Id : 10378, {_}: multiply ?3265 (least_upper_bound identity ?3266) =?= multiply ?3265 (least_upper_bound ?3266 identity) [3266, 3265] by Demod 10377 with 9743 at 3
-Id : 18347, {_}: multiply (inverse ?20394) (least_upper_bound identity (inverse ?20393)) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Demod 18327 with 10378 at 2
-Id : 2048, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 (multiply ?3142 identity) [3143, 3142] by Super 270 with 40 at 2,3
-Id : 194485, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 ?3142 [3143, 3142] by Demod 2048 with 2129 at 2,3
-Id : 194529, {_}: multiply (inverse ?186266) (least_upper_bound identity (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Super 18347 with 194485 at 1,1,3
-Id : 194632, {_}: multiply (inverse ?186266) (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266)))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Demod 194529 with 2422 at 2,2
-Id : 194633, {_}: inverse (multiply (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))) ?186266) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186266, 186265] by Demod 194632 with 18209 at 2
-Id : 195668, {_}: inverse (greatest_lower_bound ?187604 ?187605) =<= least_upper_bound (inverse (greatest_lower_bound ?187604 ?187605)) (inverse ?187604) [187605, 187604] by Demod 194633 with 194485 at 1,2
-Id : 201008, {_}: inverse (greatest_lower_bound (inverse ?193412) ?193413) =<= least_upper_bound (inverse (greatest_lower_bound (inverse ?193412) ?193413)) ?193412 [193413, 193412] by Super 195668 with 2156 at 2,3
-Id : 201035, {_}: inverse (greatest_lower_bound (inverse ?193516) ?193517) =<= least_upper_bound (inverse (greatest_lower_bound ?193517 (inverse ?193516))) ?193516 [193517, 193516] by Super 201008 with 10 at 1,1,3
-Id : 762291, {_}: inverse (greatest_lower_bound (inverse ?693163) identity) =>= least_upper_bound identity ?693163 [693163] by Demod 762290 with 201035 at 2
-Id : 18116, {_}: multiply ?20080 (inverse (multiply (inverse ?20081) ?20080)) =>= ?20081 [20081, 20080] by Super 2194 with 2238 at 1,2
-Id : 20397, {_}: multiply ?22035 (inverse (multiply ?22036 ?22035)) =>= inverse ?22036 [22036, 22035] by Super 18116 with 2156 at 1,1,2,2
-Id : 267, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound (multiply ?710 ?711) identity [711, 710] by Super 265 with 6 at 2,3
-Id : 287, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound identity (multiply ?710 ?711) [711, 710] by Demod 267 with 10 at 3
-Id : 20404, {_}: multiply ?22056 (inverse (greatest_lower_bound identity (multiply ?22055 ?22056))) =>= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Super 20397 with 287 at 1,2,2
-Id : 271, {_}: multiply (greatest_lower_bound (inverse ?727) ?726) ?727 =>= greatest_lower_bound identity (multiply ?726 ?727) [726, 727] by Super 265 with 6 at 1,3
-Id : 20403, {_}: multiply ?22053 (inverse (greatest_lower_bound identity (multiply ?22052 ?22053))) =>= inverse (greatest_lower_bound (inverse ?22053) ?22052) [22052, 22053] by Super 20397 with 271 at 1,2,2
-Id : 354211, {_}: inverse (greatest_lower_bound (inverse ?22056) ?22055) =?= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Demod 20404 with 20403 at 2
-Id : 763705, {_}: inverse (greatest_lower_bound identity (inverse ?694794)) =>= least_upper_bound identity ?694794 [694794] by Demod 762291 with 354211 at 2
-Id : 763707, {_}: inverse (greatest_lower_bound identity ?694797) =<= least_upper_bound identity (inverse ?694797) [694797] by Super 763705 with 2156 at 2,1,2
-Id : 766509, {_}: multiply (least_upper_bound identity ?11957) (inverse (greatest_lower_bound identity ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 383800 with 763707 at 2,2
-Id : 383797, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 10289 with 382808 at 3
-Id : 766508, {_}: multiply (inverse (greatest_lower_bound identity ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 383797 with 763707 at 1,2
-Id : 768092, {_}: least_upper_bound a (inverse a) === least_upper_bound a (inverse a) [] by Demod 768091 with 766508 at 3
-Id : 768091, {_}: least_upper_bound a (inverse a) =<= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 298 with 766509 at 2
-Id : 298, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 297 with 12 at 2,3
-Id : 297, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound a identity) [] by Demod 296 with 10 at 1,1,3
-Id : 296, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 295 with 10 at 1,2,2
-Id : 295, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 2 with 12 at 1,2
-Id : 2, {_}: multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by prove_p21
-% SZS output end CNFRefutation for GRP184-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21x is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-Found proof, 111.372968s
-% SZS status Unsatisfiable for GRP184-3.p
-% SZS output start CNFRefutation for GRP184-3.p
-Id : 265, {_}: multiply (greatest_lower_bound ?703 ?704) ?705 =<= greatest_lower_bound (multiply ?703 ?705) (multiply ?704 ?705) [705, 704, 703] by monotony_glb2 ?703 ?704 ?705
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 145, {_}: greatest_lower_bound ?406 (least_upper_bound ?406 ?407) =>= ?406 [407, 406] by glb_absorbtion ?406 ?407
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 127, {_}: least_upper_bound ?353 (greatest_lower_bound ?353 ?354) =>= ?353 [354, 353] by lub_absorbtion ?353 ?354
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 230, {_}: multiply (least_upper_bound ?621 ?622) ?623 =<= least_upper_bound (multiply ?621 ?623) (multiply ?622 ?623) [623, 622, 621] by monotony_lub2 ?621 ?622 ?623
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 38, {_}: multiply (multiply ?61 ?62) ?63 =?= multiply ?61 (multiply ?62 ?63) [63, 62, 61] by associativity ?61 ?62 ?63
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 2065, {_}: multiply (multiply ?3204 (inverse ?3205)) ?3205 =>= multiply ?3204 identity [3205, 3204] by Super 38 with 6 at 2,3
-Id : 2068, {_}: multiply identity ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Super 2065 with 6 at 1,2
-Id : 2091, {_}: ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Demod 2068 with 4 at 2
-Id : 2111, {_}: multiply (inverse (inverse ?3262)) (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Super 26 with 2091 at 2,3
-Id : 39, {_}: multiply (multiply ?65 identity) ?66 =>= multiply ?65 ?66 [66, 65] by Super 38 with 4 at 2,3
-Id : 2108, {_}: multiply ?3253 ?3254 =<= multiply (inverse (inverse ?3253)) ?3254 [3254, 3253] by Super 39 with 2091 at 1,2
-Id : 2129, {_}: ?3211 =<= multiply ?3211 identity [3211] by Demod 2091 with 2108 at 3
-Id : 2149, {_}: inverse (inverse ?3356) =>= multiply ?3356 identity [3356] by Super 2129 with 2108 at 3
-Id : 2156, {_}: inverse (inverse ?3356) =>= ?3356 [3356] by Demod 2149 with 2129 at 3
-Id : 9722, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Demod 2111 with 2156 at 1,2
-Id : 9764, {_}: multiply ?11921 (least_upper_bound ?11922 identity) =<= least_upper_bound (multiply ?11921 ?11922) ?11921 [11922, 11921] by Demod 9722 with 2156 at 1,1,3
-Id : 701, {_}: multiply (least_upper_bound ?1544 identity) ?1545 =<= least_upper_bound (multiply ?1544 ?1545) ?1545 [1545, 1544] by Super 230 with 4 at 2,3
-Id : 703, {_}: multiply (least_upper_bound (inverse ?1549) identity) ?1549 =>= least_upper_bound identity ?1549 [1549] by Super 701 with 6 at 1,3
-Id : 729, {_}: multiply (least_upper_bound identity (inverse ?1549)) ?1549 =>= least_upper_bound identity ?1549 [1549] by Demod 703 with 12 at 1,2
-Id : 2193, {_}: multiply (least_upper_bound identity ?3378) (inverse ?3378) =>= least_upper_bound identity (inverse ?3378) [3378] by Super 729 with 2156 at 2,1,2
-Id : 9777, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound (inverse ?11957) identity) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Super 9764 with 2193 at 1,3
-Id : 9888, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Demod 9777 with 12 at 2,2
-Id : 9889, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound identity (least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957)) [11957] by Demod 9888 with 16 at 3
-Id : 523, {_}: least_upper_bound (greatest_lower_bound ?1203 ?1204) ?1203 =>= ?1203 [1204, 1203] by Super 12 with 22 at 3
-Id : 524, {_}: least_upper_bound (greatest_lower_bound ?1207 ?1206) ?1206 =>= ?1206 [1206, 1207] by Super 523 with 10 at 1,2
-Id : 139, {_}: greatest_lower_bound (least_upper_bound ?385 ?386) ?385 =>= ?385 [386, 385] by Super 10 with 24 at 3
-Id : 40, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= multiply ?68 identity [69, 68] by Super 38 with 6 at 2,3
-Id : 2130, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= ?68 [69, 68] by Demod 40 with 2129 at 3
-Id : 231, {_}: multiply (least_upper_bound ?625 identity) ?626 =<= least_upper_bound (multiply ?625 ?626) ?626 [626, 625] by Super 230 with 4 at 2,3
-Id : 693, {_}: least_upper_bound ?1518 (multiply ?1517 ?1518) =>= multiply (least_upper_bound ?1517 identity) ?1518 [1517, 1518] by Super 12 with 231 at 3
-Id : 235, {_}: multiply (least_upper_bound identity ?641) ?642 =<= least_upper_bound ?642 (multiply ?641 ?642) [642, 641] by Super 230 with 4 at 1,3
-Id : 1616, {_}: multiply (least_upper_bound identity ?1517) ?1518 =?= multiply (least_upper_bound ?1517 identity) ?1518 [1518, 1517] by Demod 693 with 235 at 2
-Id : 1625, {_}: multiply (least_upper_bound (least_upper_bound identity ?2728) ?2730) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Super 30 with 1616 at 1,3
-Id : 1699, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Demod 1625 with 16 at 1,2
-Id : 1700, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= multiply (least_upper_bound (least_upper_bound ?2728 identity) ?2730) ?2729 [2729, 2730, 2728] by Demod 1699 with 30 at 3
-Id : 4487, {_}: multiply (multiply (least_upper_bound identity (least_upper_bound ?5822 ?5823)) (inverse ?5824)) ?5824 =>= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5824, 5823, 5822] by Super 2130 with 1700 at 1,2
-Id : 4634, {_}: least_upper_bound identity (least_upper_bound ?6053 ?6054) =<= least_upper_bound (least_upper_bound ?6053 identity) ?6054 [6054, 6053] by Demod 4487 with 2130 at 2
-Id : 122, {_}: least_upper_bound (greatest_lower_bound ?335 ?336) ?335 =>= ?335 [336, 335] by Super 12 with 22 at 3
-Id : 4738, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound identity ?6182) ?6183) =>= least_upper_bound identity ?6183 [6183, 6182] by Super 4634 with 122 at 1,3
-Id : 4751, {_}: least_upper_bound identity (least_upper_bound ?6221 (greatest_lower_bound identity ?6220)) =>= least_upper_bound identity ?6221 [6220, 6221] by Super 4738 with 12 at 2,2
-Id : 4923, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (least_upper_bound identity ?6418) (greatest_lower_bound identity ?6419) [6419, 6418] by Super 16 with 4751 at 2
-Id : 4974, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (greatest_lower_bound identity ?6419) (least_upper_bound identity ?6418) [6419, 6418] by Demod 4923 with 12 at 3
-Id : 5424, {_}: greatest_lower_bound (least_upper_bound identity ?7110) (greatest_lower_bound identity ?7111) =>= greatest_lower_bound identity ?7111 [7111, 7110] by Super 139 with 4974 at 1,2
-Id : 5471, {_}: greatest_lower_bound (greatest_lower_bound identity ?7111) (least_upper_bound identity ?7110) =>= greatest_lower_bound identity ?7111 [7110, 7111] by Demod 5424 with 10 at 2
-Id : 6383, {_}: greatest_lower_bound identity (greatest_lower_bound ?8259 (least_upper_bound identity ?8260)) =>= greatest_lower_bound identity ?8259 [8260, 8259] by Demod 5471 with 14 at 2
-Id : 605, {_}: greatest_lower_bound (least_upper_bound ?1361 ?1362) ?1361 =>= ?1361 [1362, 1361] by Super 10 with 24 at 3
-Id : 606, {_}: greatest_lower_bound (least_upper_bound ?1365 ?1364) ?1364 =>= ?1364 [1364, 1365] by Super 605 with 12 at 1,2
-Id : 6408, {_}: greatest_lower_bound identity (least_upper_bound identity ?8337) =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8336, 8337] by Super 6383 with 606 at 2,2
-Id : 6477, {_}: identity =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8337, 8336] by Demod 6408 with 24 at 2
-Id : 8574, {_}: least_upper_bound identity (least_upper_bound ?10550 (least_upper_bound identity ?10551)) =>= least_upper_bound ?10550 (least_upper_bound identity ?10551) [10551, 10550] by Super 524 with 6477 at 1,2
-Id : 9890, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957) [11957] by Demod 9889 with 8574 at 3
-Id : 382, {_}: least_upper_bound ?896 (least_upper_bound ?896 ?897) =>= least_upper_bound ?896 ?897 [897, 896] by Super 16 with 18 at 1,3
-Id : 383, {_}: least_upper_bound ?899 (least_upper_bound ?900 ?899) =>= least_upper_bound ?899 ?900 [900, 899] by Super 382 with 12 at 2,2
-Id : 9723, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply ?3262 ?3263) ?3262 [3263, 3262] by Demod 9722 with 2156 at 1,1,3
-Id : 9944, {_}: least_upper_bound ?12111 (multiply ?12111 ?12112) =>= multiply ?12111 (least_upper_bound ?12112 identity) [12112, 12111] by Super 12 with 9723 at 3
-Id : 9957, {_}: least_upper_bound (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Super 9944 with 2193 at 2,2
-Id : 10090, {_}: least_upper_bound identity (least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147))) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 9957 with 16 at 2
-Id : 10091, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 10090 with 8574 at 2
-Id : 10092, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) [12147] by Demod 10091 with 12 at 2,3
-Id : 50296, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound (inverse ?12147) (least_upper_bound identity ?12147) [12147] by Demod 10092 with 9890 at 3
-Id : 50343, {_}: least_upper_bound (least_upper_bound identity (inverse ?46312)) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Super 383 with 50296 at 2,2
-Id : 50540, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312))) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50343 with 16 at 2
-Id : 100, {_}: least_upper_bound ?287 (least_upper_bound ?287 ?288) =>= least_upper_bound ?287 ?288 [288, 287] by Super 16 with 18 at 1,3
-Id : 50541, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50540 with 100 at 2,2
-Id : 50542, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =<= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50541 with 8574 at 2
-Id : 50543, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =>= least_upper_bound identity (least_upper_bound (inverse ?46312) ?46312) [46312] by Demod 50542 with 16 at 3
-Id : 51165, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound identity (least_upper_bound (inverse ?11957) ?11957) [11957] by Demod 9890 with 50543 at 3
-Id : 51164, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 50296 with 50543 at 3
-Id : 1772, {_}: multiply (multiply ?2886 (least_upper_bound identity (inverse ?2885))) ?2885 =>= multiply ?2886 (least_upper_bound identity ?2885) [2885, 2886] by Super 8 with 729 at 2,3
-Id : 2194, {_}: multiply (multiply ?3381 ?3380) (inverse ?3380) =>= ?3381 [3380, 3381] by Super 2130 with 2156 at 2,1,2
-Id : 2142, {_}: multiply ?3332 (inverse ?3332) =>= identity [3332] by Super 6 with 2108 at 2
-Id : 2212, {_}: multiply identity ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Super 8 with 2142 at 1,2
-Id : 2238, {_}: ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Demod 2212 with 4 at 2
-Id : 4219, {_}: multiply ?5438 (inverse (multiply (inverse ?5439) ?5438)) =>= ?5439 [5439, 5438] by Super 2194 with 2238 at 1,2
-Id : 18113, {_}: inverse (multiply (inverse ?20071) (inverse ?20072)) =>= multiply ?20072 ?20071 [20072, 20071] by Super 2238 with 4219 at 2,3
-Id : 18209, {_}: inverse (multiply ?20210 ?20209) =<= multiply (inverse ?20209) (inverse ?20210) [20209, 20210] by Super 2156 with 18113 at 1,2
-Id : 18309, {_}: multiply (inverse (multiply ?20330 ?20331)) ?20330 =>= inverse ?20331 [20331, 20330] by Super 2130 with 18209 at 1,2
-Id : 20618, {_}: multiply (least_upper_bound identity (inverse (multiply ?22269 ?22270))) ?22269 =>= least_upper_bound ?22269 (inverse ?22270) [22270, 22269] by Super 235 with 18309 at 2,3
-Id : 379959, {_}: multiply (least_upper_bound ?332905 (inverse ?332906)) (inverse ?332905) =>= least_upper_bound identity (inverse (multiply ?332905 ?332906)) [332906, 332905] by Super 2194 with 20618 at 1,2
-Id : 243389, {_}: multiply (least_upper_bound identity (multiply ?228491 ?228492)) (inverse ?228492) =>= least_upper_bound (inverse ?228492) ?228491 [228492, 228491] by Super 235 with 2194 at 2,3
-Id : 177106, {_}: multiply (multiply ?175304 (least_upper_bound identity (inverse ?175305))) ?175305 =>= multiply ?175304 (least_upper_bound identity ?175305) [175305, 175304] by Super 8 with 729 at 2,3
-Id : 10132, {_}: multiply (inverse ?12250) (least_upper_bound ?12250 identity) =>= least_upper_bound identity (inverse ?12250) [12250] by Super 9764 with 6 at 1,3
-Id : 10133, {_}: multiply (inverse ?12252) (least_upper_bound identity ?12252) =>= least_upper_bound identity (inverse ?12252) [12252] by Super 10132 with 12 at 2,2
-Id : 10242, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound (least_upper_bound identity ?12325) (least_upper_bound identity (inverse ?12325)) [12325] by Super 235 with 10133 at 2,3
-Id : 10288, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound identity (least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325))) [12325] by Demod 10242 with 16 at 3
-Id : 10289, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325)) [12325] by Demod 10288 with 8574 at 3
-Id : 177160, {_}: multiply (least_upper_bound (inverse ?175487) (least_upper_bound identity (inverse (inverse ?175487)))) ?175487 =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Super 177106 with 10289 at 1,2
-Id : 236, {_}: multiply (least_upper_bound (inverse ?645) ?644) ?645 =>= least_upper_bound identity (multiply ?644 ?645) [644, 645] by Super 230 with 6 at 1,3
-Id : 177356, {_}: least_upper_bound identity (multiply (least_upper_bound identity (inverse (inverse ?175487))) ?175487) =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177160 with 236 at 2
-Id : 177357, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =<= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177356 with 2156 at 2,1,2,2
-Id : 177519, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175800) ?175800) =>= multiply (least_upper_bound identity ?175800) (least_upper_bound identity ?175800) [175800] by Demod 177357 with 2156 at 2,1,3
-Id : 177520, {_}: least_upper_bound identity (multiply (least_upper_bound ?175802 identity) ?175802) =>= multiply (least_upper_bound identity ?175802) (least_upper_bound identity ?175802) [175802] by Super 177519 with 12 at 1,2,2
-Id : 3515, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?4381) ?4382)) ?4381 =>= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4382, 4381] by Super 235 with 236 at 2,3
-Id : 1778, {_}: multiply (least_upper_bound (least_upper_bound identity (inverse ?2903)) ?2904) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Super 30 with 729 at 1,3
-Id : 1803, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Demod 1778 with 16 at 1,2
-Id : 1804, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (multiply ?2904 ?2903) (least_upper_bound identity ?2903) [2904, 2903] by Demod 1803 with 12 at 3
-Id : 102, {_}: least_upper_bound ?294 ?293 =<= least_upper_bound (least_upper_bound ?294 ?293) ?293 [293, 294] by Super 16 with 18 at 2,2
-Id : 29053, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27543 ?27544) ?27545) =<= least_upper_bound (least_upper_bound ?27543 (least_upper_bound ?27544 identity)) ?27545 [27545, 27544, 27543] by Super 4634 with 16 at 1,3
-Id : 29054, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27547 ?27548) ?27549) =<= least_upper_bound (least_upper_bound ?27547 (least_upper_bound identity ?27548)) ?27549 [27549, 27548, 27547] by Super 29053 with 12 at 2,1,3
-Id : 93172, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324)) [78324, 78323] by Super 102 with 29054 at 3
-Id : 93561, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324) [78324, 78323] by Demod 93172 with 8574 at 3
-Id : 4534, {_}: least_upper_bound identity (least_upper_bound ?5822 ?5823) =<= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5823, 5822] by Demod 4487 with 2130 at 2
-Id : 27996, {_}: least_upper_bound ?26567 (least_upper_bound identity (least_upper_bound ?26568 ?26567)) =>= least_upper_bound ?26567 (least_upper_bound ?26568 identity) [26568, 26567] by Super 383 with 4534 at 2,2
-Id : 28002, {_}: least_upper_bound ?26586 (least_upper_bound identity ?26586) =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Super 27996 with 122 at 2,2,2
-Id : 28236, {_}: least_upper_bound ?26586 identity =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Demod 28002 with 383 at 2
-Id : 8916, {_}: least_upper_bound identity (least_upper_bound ?11024 (least_upper_bound identity ?11025)) =>= least_upper_bound ?11024 (least_upper_bound identity ?11025) [11025, 11024] by Super 524 with 6477 at 1,2
-Id : 8917, {_}: least_upper_bound identity (least_upper_bound ?11027 (least_upper_bound ?11028 identity)) =>= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Super 8916 with 12 at 2,2,2
-Id : 4835, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound ?6313 identity) ?6314) =>= least_upper_bound identity ?6314 [6314, 6313] by Super 4634 with 524 at 1,3
-Id : 4847, {_}: least_upper_bound identity (greatest_lower_bound ?6349 identity) =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Super 4835 with 22 at 2,2
-Id : 128, {_}: least_upper_bound ?356 (greatest_lower_bound ?357 ?356) =>= ?356 [357, 356] by Super 127 with 10 at 2,2
-Id : 4903, {_}: identity =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Demod 4847 with 128 at 2
-Id : 5840, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631) =>= greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631 [7631, 7630] by Super 606 with 4903 at 1,2
-Id : 5845, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7645) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Super 5840 with 606 at 1,2,2
-Id : 112, {_}: greatest_lower_bound ?313 (greatest_lower_bound ?313 ?314) =>= greatest_lower_bound ?313 ?314 [314, 313] by Super 14 with 20 at 1,3
-Id : 5908, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Demod 5845 with 112 at 2
-Id : 5909, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound ?7644 identity)) ?7645 [7644, 7645] by Demod 5908 with 10 at 1,3
-Id : 7862, {_}: greatest_lower_bound identity ?10013 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound ?10014 identity) ?10013) [10014, 10013] by Demod 5909 with 14 at 3
-Id : 146, {_}: greatest_lower_bound ?409 (least_upper_bound ?410 ?409) =>= ?409 [410, 409] by Super 145 with 12 at 2,2
-Id : 7879, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= greatest_lower_bound identity (least_upper_bound ?10064 identity) [10064, 10063] by Super 7862 with 146 at 2,3
-Id : 7984, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= identity [10064, 10063] by Demod 7879 with 146 at 3
-Id : 8758, {_}: least_upper_bound identity (least_upper_bound ?10813 (least_upper_bound ?10814 identity)) =>= least_upper_bound ?10813 (least_upper_bound ?10814 identity) [10814, 10813] by Super 524 with 7984 at 1,2
-Id : 9284, {_}: least_upper_bound ?11027 (least_upper_bound ?11028 identity) =?= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Demod 8917 with 8758 at 2
-Id : 89245, {_}: least_upper_bound ?75550 identity =<= least_upper_bound ?75550 (least_upper_bound identity (greatest_lower_bound ?75550 ?75551)) [75551, 75550] by Demod 28236 with 9284 at 3
-Id : 89255, {_}: least_upper_bound (least_upper_bound ?75580 ?75581) identity =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Super 89245 with 606 at 2,2,3
-Id : 89821, {_}: least_upper_bound identity (least_upper_bound ?75580 ?75581) =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Demod 89255 with 12 at 2
-Id : 113848, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =?= least_upper_bound identity (least_upper_bound ?78323 ?78324) [78324, 78323] by Demod 93561 with 89821 at 3
-Id : 181989, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (least_upper_bound (multiply ?2904 ?2903) ?2903) [2904, 2903] by Demod 1804 with 113848 at 3
-Id : 181990, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (multiply (least_upper_bound ?2904 identity) ?2903) [2904, 2903] by Demod 181989 with 231 at 2,3
-Id : 230272, {_}: least_upper_bound identity (multiply (least_upper_bound ?4382 identity) ?4381) =?= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4381, 4382] by Demod 3515 with 181990 at 2
-Id : 230301, {_}: least_upper_bound ?219571 (least_upper_bound identity (multiply ?219571 ?219571)) =>= multiply (least_upper_bound identity ?219571) (least_upper_bound identity ?219571) [219571] by Super 177520 with 230272 at 2
-Id : 232386, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (least_upper_bound ?221067 identity) (multiply ?221067 ?221067) [221067] by Super 16 with 230301 at 2
-Id : 233006, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (multiply ?221067 ?221067) (least_upper_bound ?221067 identity) [221067] by Demod 232386 with 12 at 3
-Id : 4614, {_}: greatest_lower_bound ?5993 (least_upper_bound identity (least_upper_bound ?5992 ?5993)) =>= ?5993 [5992, 5993] by Super 146 with 4534 at 2,2
-Id : 27608, {_}: least_upper_bound ?26112 (least_upper_bound identity (least_upper_bound ?26113 ?26112)) =>= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Super 524 with 4614 at 1,2
-Id : 4631, {_}: least_upper_bound ?6045 (least_upper_bound identity (least_upper_bound ?6044 ?6045)) =>= least_upper_bound ?6045 (least_upper_bound ?6044 identity) [6044, 6045] by Super 383 with 4534 at 2,2
-Id : 83798, {_}: least_upper_bound ?26112 (least_upper_bound ?26113 identity) =?= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Demod 27608 with 4631 at 2
-Id : 233007, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound identity (least_upper_bound ?221067 (multiply ?221067 ?221067)) [221067] by Demod 233006 with 83798 at 3
-Id : 9743, {_}: least_upper_bound ?11859 (multiply ?11859 ?11860) =>= multiply ?11859 (least_upper_bound ?11860 identity) [11860, 11859] by Super 12 with 9723 at 3
-Id : 233595, {_}: multiply (least_upper_bound identity ?221617) (least_upper_bound identity ?221617) =<= least_upper_bound identity (multiply ?221617 (least_upper_bound ?221617 identity)) [221617] by Demod 233007 with 9743 at 2,3
-Id : 233596, {_}: multiply (least_upper_bound identity ?221619) (least_upper_bound identity ?221619) =<= least_upper_bound identity (multiply ?221619 (least_upper_bound identity ?221619)) [221619] by Super 233595 with 12 at 2,2,3
-Id : 243525, {_}: multiply (multiply (least_upper_bound identity ?228868) (least_upper_bound identity ?228868)) (inverse (least_upper_bound identity ?228868)) =>= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Super 243389 with 233596 at 1,2
-Id : 243950, {_}: least_upper_bound identity ?228868 =<= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Demod 243525 with 2194 at 2
-Id : 244049, {_}: least_upper_bound ?229075 (inverse (least_upper_bound identity ?229075)) =>= least_upper_bound identity ?229075 [229075] by Super 12 with 243950 at 3
-Id : 380052, {_}: multiply (least_upper_bound identity ?333235) (inverse ?333235) =<= least_upper_bound identity (inverse (multiply ?333235 (least_upper_bound identity ?333235))) [333235] by Super 379959 with 244049 at 1,2
-Id : 381402, {_}: least_upper_bound identity (inverse ?334503) =<= least_upper_bound identity (inverse (multiply ?334503 (least_upper_bound identity ?334503))) [334503] by Demod 380052 with 2193 at 2
-Id : 177358, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =>= multiply (least_upper_bound identity ?175487) (least_upper_bound identity ?175487) [175487] by Demod 177357 with 2156 at 2,1,3
-Id : 177476, {_}: multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (multiply (least_upper_bound identity ?175688) (least_upper_bound identity ?175688)) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Super 10133 with 177358 at 2,2
-Id : 177670, {_}: multiply (multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (least_upper_bound identity ?175688)) (least_upper_bound identity ?175688) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177476 with 8 at 2
-Id : 177671, {_}: multiply (inverse ?175688) (least_upper_bound identity ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177670 with 18309 at 1,2
-Id : 177672, {_}: least_upper_bound identity (inverse ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177671 with 10133 at 2
-Id : 381492, {_}: least_upper_bound identity (inverse (inverse (multiply (least_upper_bound identity ?334735) ?334735))) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Super 381402 with 177672 at 2,1,2,3
-Id : 382266, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?334735) ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 381492 with 2156 at 2,2
-Id : 382267, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 382266 with 177358 at 2
-Id : 18224, {_}: inverse (multiply (inverse ?20261) (inverse ?20262)) =>= multiply ?20262 ?20261 [20262, 20261] by Super 2238 with 4219 at 2,3
-Id : 18226, {_}: inverse (multiply (inverse ?20267) ?20266) =>= multiply (inverse ?20266) ?20267 [20266, 20267] by Super 18224 with 2156 at 2,1,2
-Id : 382268, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (inverse (least_upper_bound identity (inverse ?334735))) (multiply (least_upper_bound identity ?334735) ?334735)) [334735] by Demod 382267 with 18226 at 2,3
-Id : 382269, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (multiply (inverse (least_upper_bound identity (inverse ?334735))) (least_upper_bound identity ?334735)) ?334735) [334735] by Demod 382268 with 8 at 2,3
-Id : 18545, {_}: inverse (multiply ?20706 (inverse ?20707)) =>= multiply ?20707 (inverse ?20706) [20707, 20706] by Super 18224 with 2156 at 1,1,2
-Id : 18566, {_}: inverse (least_upper_bound identity (inverse ?20767)) =<= multiply ?20767 (inverse (least_upper_bound identity ?20767)) [20767] by Super 18545 with 2193 at 1,2
-Id : 19741, {_}: multiply (inverse (least_upper_bound identity (inverse ?21554))) (least_upper_bound identity ?21554) =>= ?21554 [21554] by Super 2130 with 18566 at 1,2
-Id : 382270, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =>= least_upper_bound identity (multiply ?334735 ?334735) [334735] by Demod 382269 with 19741 at 1,2,3
-Id : 382385, {_}: multiply (least_upper_bound identity (multiply (inverse ?334827) (inverse ?334827))) ?334827 =>= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Super 1772 with 382270 at 1,2
-Id : 2064, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 (multiply ?3201 identity) [3202, 3201] by Super 235 with 40 at 2,3
-Id : 223367, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 ?3201 [3202, 3201] by Demod 2064 with 2129 at 2,3
-Id : 382807, {_}: least_upper_bound ?334827 (inverse ?334827) =<= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Demod 382385 with 223367 at 2
-Id : 382808, {_}: least_upper_bound ?334827 (inverse ?334827) =<= least_upper_bound ?334827 (least_upper_bound identity (inverse ?334827)) [334827] by Demod 382807 with 10289 at 3
-Id : 383798, {_}: least_upper_bound ?12147 (inverse ?12147) =<= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 51164 with 382808 at 2
-Id : 383800, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 51165 with 383798 at 3
-Id : 2115, {_}: multiply (inverse (inverse ?3274)) (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Super 28 with 2091 at 2,3
-Id : 10659, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Demod 2115 with 2156 at 1,2
-Id : 10660, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply ?3274 ?3275) ?3274 [3275, 3274] by Demod 10659 with 2156 at 1,1,3
-Id : 10678, {_}: greatest_lower_bound ?12834 (multiply ?12834 ?12835) =>= multiply ?12834 (greatest_lower_bound ?12835 identity) [12835, 12834] by Super 10 with 10660 at 3
-Id : 18328, {_}: greatest_lower_bound (inverse ?20397) (inverse (multiply ?20396 ?20397)) =>= multiply (inverse ?20397) (greatest_lower_bound (inverse ?20396) identity) [20396, 20397] by Super 10678 with 18209 at 2,2
-Id : 2116, {_}: multiply (inverse (inverse ?3277)) (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Super 28 with 2091 at 1,3
-Id : 11396, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Demod 2116 with 2156 at 1,2
-Id : 11397, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply ?3277 ?3278) [3278, 3277] by Demod 11396 with 2156 at 1,2,3
-Id : 11398, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =?= multiply ?3277 (greatest_lower_bound ?3278 identity) [3278, 3277] by Demod 11397 with 10678 at 3
-Id : 78468, {_}: greatest_lower_bound (inverse ?65596) (inverse (multiply ?65597 ?65596)) =>= multiply (inverse ?65596) (greatest_lower_bound identity (inverse ?65597)) [65597, 65596] by Demod 18328 with 11398 at 3
-Id : 78507, {_}: greatest_lower_bound (inverse ?65693) (inverse (inverse ?65692)) =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Super 78468 with 18309 at 1,2,2
-Id : 78731, {_}: greatest_lower_bound (inverse ?65693) ?65692 =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Demod 78507 with 2156 at 2,2
-Id : 443714, {_}: greatest_lower_bound (inverse ?378148) ?378149 =<= multiply (inverse ?378148) (greatest_lower_bound identity (multiply ?378148 ?378149)) [378149, 378148] by Demod 78731 with 2156 at 2,2,3
-Id : 842, {_}: multiply (greatest_lower_bound ?1730 identity) ?1731 =<= greatest_lower_bound (multiply ?1730 ?1731) ?1731 [1731, 1730] by Super 265 with 4 at 2,3
-Id : 844, {_}: multiply (greatest_lower_bound (inverse ?1735) identity) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Super 842 with 6 at 1,3
-Id : 874, {_}: multiply (greatest_lower_bound identity (inverse ?1735)) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Demod 844 with 10 at 1,2
-Id : 2191, {_}: multiply (greatest_lower_bound identity ?3374) (inverse ?3374) =>= greatest_lower_bound identity (inverse ?3374) [3374] by Super 874 with 2156 at 2,1,2
-Id : 9776, {_}: multiply (greatest_lower_bound identity ?11955) (least_upper_bound (inverse ?11955) identity) =<= least_upper_bound (greatest_lower_bound identity (inverse ?11955)) (greatest_lower_bound identity ?11955) [11955] by Super 9764 with 2191 at 1,3
-Id : 47906, {_}: multiply (greatest_lower_bound identity ?45245) (least_upper_bound identity (inverse ?45245)) =<= least_upper_bound (greatest_lower_bound identity (inverse ?45245)) (greatest_lower_bound identity ?45245) [45245] by Demod 9776 with 12 at 2,2
-Id : 47957, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity (inverse (inverse ?45371))) =>= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Super 47906 with 2156 at 2,1,3
-Id : 48268, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =<= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Demod 47957 with 2156 at 2,2,2
-Id : 9956, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound (inverse ?12145) identity) [12145] by Super 9944 with 2191 at 2,2
-Id : 10089, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound identity (inverse ?12145)) [12145] by Demod 9956 with 12 at 2,3
-Id : 105582, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =?= multiply (greatest_lower_bound identity ?45371) (least_upper_bound identity (inverse ?45371)) [45371] by Demod 48268 with 10089 at 3
-Id : 443814, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?378412) (least_upper_bound identity (inverse ?378412)))) [378412] by Super 443714 with 105582 at 2,2,3
-Id : 5843, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7639) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Super 5840 with 139 at 1,2,2
-Id : 5900, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Demod 5843 with 112 at 2
-Id : 5901, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound identity ?7638)) ?7639 [7638, 7639] by Demod 5900 with 10 at 1,3
-Id : 7645, {_}: greatest_lower_bound identity ?9767 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound identity ?9768) ?9767) [9768, 9767] by Demod 5901 with 14 at 3
-Id : 270, {_}: multiply (greatest_lower_bound identity ?723) ?724 =<= greatest_lower_bound ?724 (multiply ?723 ?724) [724, 723] by Super 265 with 4 at 1,3
-Id : 7676, {_}: greatest_lower_bound identity (multiply ?9863 (least_upper_bound identity ?9864)) =<= greatest_lower_bound identity (multiply (greatest_lower_bound identity ?9863) (least_upper_bound identity ?9864)) [9864, 9863] by Super 7645 with 270 at 2,3
-Id : 444411, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply ?378412 (least_upper_bound identity (inverse ?378412)))) [378412] by Demod 443814 with 7676 at 2,3
-Id : 2215, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound (multiply ?3422 ?3423) identity [3423, 3422] by Super 26 with 2142 at 2,3
-Id : 2235, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound identity (multiply ?3422 ?3423) [3423, 3422] by Demod 2215 with 12 at 3
-Id : 444412, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?378412 identity))) [378412] by Demod 444411 with 2235 at 2,2,3
-Id : 444413, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) identity [378412] by Demod 444412 with 24 at 2,3
-Id : 444414, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= inverse (greatest_lower_bound identity (inverse ?378412)) [378412] by Demod 444413 with 2129 at 3
-Id : 761747, {_}: least_upper_bound (least_upper_bound identity ?693163) (inverse (greatest_lower_bound identity (inverse ?693163))) =>= least_upper_bound identity ?693163 [693163] by Super 128 with 444414 at 2,2
-Id : 762288, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) (least_upper_bound identity ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 761747 with 12 at 2
-Id : 1150, {_}: least_upper_bound (least_upper_bound ?2078 ?2079) ?2078 =>= least_upper_bound ?2078 ?2079 [2079, 2078] by Super 12 with 100 at 3
-Id : 158742, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?149635 ?149636) ?149637) ?149635 =>= least_upper_bound ?149635 (least_upper_bound ?149636 ?149637) [149637, 149636, 149635] by Super 1150 with 16 at 1,2
-Id : 375, {_}: least_upper_bound (least_upper_bound ?872 ?873) ?872 =>= least_upper_bound ?872 ?873 [873, 872] by Super 12 with 100 at 3
-Id : 1142, {_}: least_upper_bound (least_upper_bound ?2051 ?2052) (least_upper_bound ?2051 ?2053) =>= least_upper_bound (least_upper_bound ?2051 ?2052) ?2053 [2053, 2052, 2051] by Super 16 with 375 at 1,3
-Id : 158880, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?150190 ?150191) ?150189) ?150190 =?= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Super 158742 with 1142 at 1,2
-Id : 1152, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?2086 ?2084) ?2085) ?2086 =>= least_upper_bound ?2086 (least_upper_bound ?2084 ?2085) [2085, 2084, 2086] by Super 1150 with 16 at 1,2
-Id : 159604, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =<= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Demod 158880 with 1152 at 2
-Id : 126, {_}: least_upper_bound ?351 ?349 =<= least_upper_bound (least_upper_bound ?351 ?349) (greatest_lower_bound ?349 ?350) [350, 349, 351] by Super 16 with 22 at 2,2
-Id : 135029, {_}: least_upper_bound ?113864 ?113865 =<= least_upper_bound (greatest_lower_bound ?113865 ?113866) (least_upper_bound ?113864 ?113865) [113866, 113865, 113864] by Demod 126 with 12 at 3
-Id : 135153, {_}: least_upper_bound ?114345 (least_upper_bound ?114346 ?114344) =<= least_upper_bound ?114346 (least_upper_bound ?114345 (least_upper_bound ?114346 ?114344)) [114344, 114346, 114345] by Super 135029 with 139 at 1,3
-Id : 503059, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =?= least_upper_bound ?150191 (least_upper_bound ?150190 ?150189) [150189, 150191, 150190] by Demod 159604 with 135153 at 3
-Id : 762289, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 762288 with 503059 at 2
-Id : 2280, {_}: multiply (greatest_lower_bound identity ?3504) (inverse ?3504) =>= greatest_lower_bound identity (inverse ?3504) [3504] by Super 874 with 2156 at 2,1,2
-Id : 2286, {_}: multiply (greatest_lower_bound identity ?3514) (inverse (greatest_lower_bound identity ?3514)) =>= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Super 2280 with 112 at 1,2
-Id : 2335, {_}: identity =<= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Demod 2286 with 2142 at 2
-Id : 2422, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity ?3608)) =>= inverse (greatest_lower_bound identity ?3608) [3608] by Super 524 with 2335 at 1,2
-Id : 2722, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827) =>= least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827 [3827, 3826] by Super 16 with 2422 at 1,3
-Id : 762290, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163 =>= least_upper_bound identity ?693163 [693163] by Demod 762289 with 2722 at 2
-Id : 18327, {_}: multiply (inverse ?20394) (least_upper_bound (inverse ?20393) identity) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Super 9723 with 18209 at 1,3
-Id : 2112, {_}: multiply (inverse (inverse ?3265)) (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Super 26 with 2091 at 1,3
-Id : 10376, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Demod 2112 with 2156 at 1,2
-Id : 10377, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply ?3265 ?3266) [3266, 3265] by Demod 10376 with 2156 at 1,2,3
-Id : 10378, {_}: multiply ?3265 (least_upper_bound identity ?3266) =?= multiply ?3265 (least_upper_bound ?3266 identity) [3266, 3265] by Demod 10377 with 9743 at 3
-Id : 18347, {_}: multiply (inverse ?20394) (least_upper_bound identity (inverse ?20393)) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Demod 18327 with 10378 at 2
-Id : 2048, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 (multiply ?3142 identity) [3143, 3142] by Super 270 with 40 at 2,3
-Id : 194485, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 ?3142 [3143, 3142] by Demod 2048 with 2129 at 2,3
-Id : 194529, {_}: multiply (inverse ?186266) (least_upper_bound identity (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Super 18347 with 194485 at 1,1,3
-Id : 194632, {_}: multiply (inverse ?186266) (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266)))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Demod 194529 with 2422 at 2,2
-Id : 194633, {_}: inverse (multiply (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))) ?186266) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186266, 186265] by Demod 194632 with 18209 at 2
-Id : 195668, {_}: inverse (greatest_lower_bound ?187604 ?187605) =<= least_upper_bound (inverse (greatest_lower_bound ?187604 ?187605)) (inverse ?187604) [187605, 187604] by Demod 194633 with 194485 at 1,2
-Id : 201008, {_}: inverse (greatest_lower_bound (inverse ?193412) ?193413) =<= least_upper_bound (inverse (greatest_lower_bound (inverse ?193412) ?193413)) ?193412 [193413, 193412] by Super 195668 with 2156 at 2,3
-Id : 201035, {_}: inverse (greatest_lower_bound (inverse ?193516) ?193517) =<= least_upper_bound (inverse (greatest_lower_bound ?193517 (inverse ?193516))) ?193516 [193517, 193516] by Super 201008 with 10 at 1,1,3
-Id : 762291, {_}: inverse (greatest_lower_bound (inverse ?693163) identity) =>= least_upper_bound identity ?693163 [693163] by Demod 762290 with 201035 at 2
-Id : 18116, {_}: multiply ?20080 (inverse (multiply (inverse ?20081) ?20080)) =>= ?20081 [20081, 20080] by Super 2194 with 2238 at 1,2
-Id : 20397, {_}: multiply ?22035 (inverse (multiply ?22036 ?22035)) =>= inverse ?22036 [22036, 22035] by Super 18116 with 2156 at 1,1,2,2
-Id : 267, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound (multiply ?710 ?711) identity [711, 710] by Super 265 with 6 at 2,3
-Id : 287, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound identity (multiply ?710 ?711) [711, 710] by Demod 267 with 10 at 3
-Id : 20404, {_}: multiply ?22056 (inverse (greatest_lower_bound identity (multiply ?22055 ?22056))) =>= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Super 20397 with 287 at 1,2,2
-Id : 271, {_}: multiply (greatest_lower_bound (inverse ?727) ?726) ?727 =>= greatest_lower_bound identity (multiply ?726 ?727) [726, 727] by Super 265 with 6 at 1,3
-Id : 20403, {_}: multiply ?22053 (inverse (greatest_lower_bound identity (multiply ?22052 ?22053))) =>= inverse (greatest_lower_bound (inverse ?22053) ?22052) [22052, 22053] by Super 20397 with 271 at 1,2,2
-Id : 354211, {_}: inverse (greatest_lower_bound (inverse ?22056) ?22055) =?= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Demod 20404 with 20403 at 2
-Id : 763705, {_}: inverse (greatest_lower_bound identity (inverse ?694794)) =>= least_upper_bound identity ?694794 [694794] by Demod 762291 with 354211 at 2
-Id : 763707, {_}: inverse (greatest_lower_bound identity ?694797) =<= least_upper_bound identity (inverse ?694797) [694797] by Super 763705 with 2156 at 2,1,2
-Id : 766509, {_}: multiply (least_upper_bound identity ?11957) (inverse (greatest_lower_bound identity ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 383800 with 763707 at 2,2
-Id : 383797, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 10289 with 382808 at 3
-Id : 766508, {_}: multiply (inverse (greatest_lower_bound identity ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 383797 with 763707 at 1,2
-Id : 768092, {_}: least_upper_bound a (inverse a) === least_upper_bound a (inverse a) [] by Demod 768091 with 766508 at 3
-Id : 768091, {_}: least_upper_bound a (inverse a) =<= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 298 with 766509 at 2
-Id : 298, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 297 with 12 at 2,3
-Id : 297, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound a identity) [] by Demod 296 with 10 at 1,1,3
-Id : 296, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 295 with 10 at 1,2,2
-Id : 295, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 2 with 12 at 1,2
-Id : 2, {_}: multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by prove_p21x
-% SZS output end CNFRefutation for GRP184-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 88
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 91
- least_upper_bound is 94
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p22a_1 is 75
- p22a_2 is 74
- p22a_3 is 73
- prove_p22a is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p22a_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-Last chance: 1246061240.31
-Last chance: all is indexed 1246062610.72
-Last chance: failed over 100 goal 1246062611.07
-FAILURE in 0 iterations
-% SZS status Timeout for GRP185-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 93
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 90
- least_upper_bound is 94
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p22b is 92
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-Last chance: 1246062912.35
-Last chance: all is indexed 1246064177.36
-Last chance: failed over 100 goal 1246064177.45
-FAILURE in 0 iterations
-% SZS status Timeout for GRP185-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Found proof, 54.277350s
-% SZS status Unsatisfiable for GRP186-1.p
-% SZS output start CNFRefutation for GRP186-1.p
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 194, {_}: multiply ?539 (greatest_lower_bound ?540 ?541) =<= greatest_lower_bound (multiply ?539 ?540) (multiply ?539 ?541) [541, 540, 539] by monotony_glb1 ?539 ?540 ?541
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 125, {_}: least_upper_bound ?350 (greatest_lower_bound ?350 ?351) =>= ?350 [351, 350] by lub_absorbtion ?350 ?351
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 143, {_}: greatest_lower_bound ?403 (least_upper_bound ?403 ?404) =>= ?403 [404, 403] by glb_absorbtion ?403 ?404
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 228, {_}: multiply (least_upper_bound ?618 ?619) ?620 =<= least_upper_bound (multiply ?618 ?620) (multiply ?619 ?620) [620, 619, 618] by monotony_lub2 ?618 ?619 ?620
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 37, {_}: multiply (multiply ?58 ?59) ?60 =?= multiply ?58 (multiply ?59 ?60) [60, 59, 58] by associativity ?58 ?59 ?60
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 163, {_}: multiply ?463 (least_upper_bound ?464 ?465) =<= least_upper_bound (multiply ?463 ?464) (multiply ?463 ?465) [465, 464, 463] by monotony_lub1 ?463 ?464 ?465
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 1397, {_}: multiply (inverse ?2611) (least_upper_bound ?2611 ?2612) =>= least_upper_bound identity (multiply (inverse ?2611) ?2612) [2612, 2611] by Super 163 with 6 at 1,3
-Id : 120, {_}: least_upper_bound (greatest_lower_bound ?332 ?333) ?332 =>= ?332 [333, 332] by Super 12 with 22 at 3
-Id : 1403, {_}: multiply (inverse (greatest_lower_bound ?2630 ?2629)) ?2630 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2630 ?2629)) ?2630) [2629, 2630] by Super 1397 with 120 at 2,2
-Id : 137, {_}: greatest_lower_bound (least_upper_bound ?382 ?383) ?382 =>= ?382 [383, 382] by Super 10 with 24 at 3
-Id : 39, {_}: multiply (multiply ?65 (inverse ?66)) ?66 =>= multiply ?65 identity [66, 65] by Super 37 with 6 at 2,3
-Id : 1222, {_}: multiply (multiply ?2303 (inverse ?2304)) ?2304 =>= multiply ?2303 identity [2304, 2303] by Super 37 with 6 at 2,3
-Id : 1225, {_}: multiply identity ?2310 =<= multiply (inverse (inverse ?2310)) identity [2310] by Super 1222 with 6 at 1,2
-Id : 1240, {_}: ?2310 =<= multiply (inverse (inverse ?2310)) identity [2310] by Demod 1225 with 4 at 2
-Id : 38, {_}: multiply (multiply ?62 identity) ?63 =>= multiply ?62 ?63 [63, 62] by Super 37 with 4 at 2,3
-Id : 1245, {_}: multiply ?2332 ?2333 =<= multiply (inverse (inverse ?2332)) ?2333 [2333, 2332] by Super 38 with 1240 at 1,2
-Id : 1261, {_}: ?2310 =<= multiply ?2310 identity [2310] by Demod 1240 with 1245 at 3
-Id : 1262, {_}: multiply (multiply ?65 (inverse ?66)) ?66 =>= ?65 [66, 65] by Demod 39 with 1261 at 3
-Id : 234, {_}: multiply (least_upper_bound (inverse ?642) ?641) ?642 =>= least_upper_bound identity (multiply ?641 ?642) [641, 642] by Super 228 with 6 at 1,3
-Id : 1630, {_}: multiply (least_upper_bound identity (multiply ?2984 (inverse ?2985))) ?2985 =>= least_upper_bound (inverse (inverse ?2985)) ?2984 [2985, 2984] by Super 1262 with 234 at 1,2
-Id : 1277, {_}: inverse (inverse ?2419) =<= multiply ?2419 identity [2419] by Super 1261 with 1245 at 3
-Id : 1283, {_}: inverse (inverse ?2419) =>= ?2419 [2419] by Demod 1277 with 1261 at 3
-Id : 59624, {_}: multiply (least_upper_bound identity (multiply ?78799 (inverse ?78800))) ?78800 =>= least_upper_bound ?78800 ?78799 [78800, 78799] by Demod 1630 with 1283 at 1,3
-Id : 59667, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?78935) ?78934)) (inverse ?78935)) ?78935 =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Super 59624 with 1403 at 1,2
-Id : 59764, {_}: multiply (inverse (greatest_lower_bound (inverse ?78935) ?78934)) (multiply (inverse ?78935) ?78935) =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59667 with 8 at 2
-Id : 1311, {_}: multiply (multiply ?2436 ?2435) (inverse ?2435) =>= ?2436 [2435, 2436] by Super 1262 with 1283 at 2,1,2
-Id : 46, {_}: multiply identity ?93 =<= multiply (inverse ?92) (multiply ?92 ?93) [92, 93] by Super 37 with 6 at 1,2
-Id : 55, {_}: ?93 =<= multiply (inverse ?92) (multiply ?92 ?93) [92, 93] by Demod 46 with 4 at 2
-Id : 1907, {_}: inverse ?3391 =<= multiply (inverse (multiply ?3390 ?3391)) ?3390 [3390, 3391] by Super 55 with 1311 at 2,3
-Id : 2602, {_}: multiply (inverse ?4415) (inverse ?4416) =>= inverse (multiply ?4416 ?4415) [4416, 4415] by Super 1311 with 1907 at 1,2
-Id : 2683, {_}: multiply (inverse (multiply ?4589 ?4588)) ?4590 =<= multiply (inverse ?4588) (multiply (inverse ?4589) ?4590) [4590, 4588, 4589] by Super 8 with 2602 at 1,2
-Id : 59765, {_}: multiply (inverse (multiply ?78935 (greatest_lower_bound (inverse ?78935) ?78934))) ?78935 =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59764 with 2683 at 2
-Id : 59766, {_}: inverse (greatest_lower_bound (inverse ?78935) ?78934) =<= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59765 with 1907 at 2
-Id : 75243, {_}: greatest_lower_bound (inverse (greatest_lower_bound (inverse ?90061) ?90062)) ?90061 =>= ?90061 [90062, 90061] by Super 137 with 59766 at 1,2
-Id : 75245, {_}: greatest_lower_bound (inverse (greatest_lower_bound ?90066 ?90067)) (inverse ?90066) =>= inverse ?90066 [90067, 90066] by Super 75243 with 1283 at 1,1,1,2
-Id : 90405, {_}: multiply (inverse (greatest_lower_bound (inverse (greatest_lower_bound ?103908 ?103909)) (inverse ?103908))) (inverse (greatest_lower_bound ?103908 ?103909)) =>= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Super 1403 with 75245 at 1,1,2,3
-Id : 90576, {_}: inverse (multiply (greatest_lower_bound ?103908 ?103909) (greatest_lower_bound (inverse (greatest_lower_bound ?103908 ?103909)) (inverse ?103908))) =>= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Demod 90405 with 2602 at 2
-Id : 1272, {_}: multiply ?2401 (inverse ?2401) =>= identity [2401] by Super 6 with 1245 at 2
-Id : 1323, {_}: multiply ?2456 (greatest_lower_bound (inverse ?2456) ?2457) =>= greatest_lower_bound identity (multiply ?2456 ?2457) [2457, 2456] by Super 28 with 1272 at 1,3
-Id : 90577, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound ?103908 ?103909) (inverse ?103908))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Demod 90576 with 1323 at 1,2
-Id : 1321, {_}: multiply (greatest_lower_bound ?2450 ?2451) (inverse ?2450) =>= greatest_lower_bound identity (multiply ?2451 (inverse ?2450)) [2451, 2450] by Super 32 with 1272 at 1,3
-Id : 90578, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply ?103909 (inverse ?103908)))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90577 with 1321 at 2,1,2
-Id : 110, {_}: greatest_lower_bound ?310 (greatest_lower_bound ?310 ?311) =>= greatest_lower_bound ?310 ?311 [311, 310] by Super 14 with 20 at 1,3
-Id : 90579, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90578 with 110 at 1,2
-Id : 90580, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound ?103908 ?103909) (inverse ?103908))) [103908, 103909] by Demod 90579 with 2602 at 2,3
-Id : 2693, {_}: multiply (inverse ?4622) (inverse ?4623) =>= inverse (multiply ?4623 ?4622) [4623, 4622] by Super 1311 with 1907 at 1,2
-Id : 2697, {_}: multiply ?4632 (inverse ?4633) =<= inverse (multiply ?4633 (inverse ?4632)) [4633, 4632] by Super 2693 with 1283 at 1,2
-Id : 90581, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (multiply ?103908 (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90580 with 2697 at 2,3
-Id : 2159, {_}: multiply (least_upper_bound ?3809 ?3810) (inverse ?3809) =>= least_upper_bound identity (multiply ?3810 (inverse ?3809)) [3810, 3809] by Super 30 with 1272 at 1,3
-Id : 2167, {_}: multiply ?3833 (inverse (greatest_lower_bound ?3833 ?3832)) =<= least_upper_bound identity (multiply ?3833 (inverse (greatest_lower_bound ?3833 ?3832))) [3832, 3833] by Super 2159 with 120 at 1,2
-Id : 241130, {_}: inverse (greatest_lower_bound identity (multiply ?281248 (inverse ?281249))) =?= multiply ?281249 (inverse (greatest_lower_bound ?281249 ?281248)) [281249, 281248] by Demod 90581 with 2167 at 3
-Id : 241323, {_}: inverse (greatest_lower_bound identity (inverse (multiply ?281886 ?281885))) =<= multiply ?281886 (inverse (greatest_lower_bound ?281886 (inverse ?281885))) [281885, 281886] by Super 241130 with 2602 at 2,1,2
-Id : 1908, {_}: multiply (multiply ?3393 ?3394) (inverse ?3394) =>= ?3393 [3394, 3393] by Super 1262 with 1283 at 2,1,2
-Id : 1918, {_}: multiply (least_upper_bound identity (multiply ?3421 ?3422)) (inverse ?3422) =>= least_upper_bound (inverse ?3422) ?3421 [3422, 3421] by Super 1908 with 234 at 1,2
-Id : 169, {_}: multiply (inverse ?486) (least_upper_bound ?486 ?487) =>= least_upper_bound identity (multiply (inverse ?486) ?487) [487, 486] by Super 163 with 6 at 1,3
-Id : 1396, {_}: least_upper_bound ?2608 ?2609 =<= multiply (inverse (inverse ?2608)) (least_upper_bound identity (multiply (inverse ?2608) ?2609)) [2609, 2608] by Super 55 with 169 at 2,3
-Id : 1416, {_}: least_upper_bound ?2608 ?2609 =<= multiply ?2608 (least_upper_bound identity (multiply (inverse ?2608) ?2609)) [2609, 2608] by Demod 1396 with 1283 at 1,3
-Id : 512, {_}: least_upper_bound (greatest_lower_bound ?1197 ?1198) ?1197 =>= ?1197 [1198, 1197] by Super 12 with 22 at 3
-Id : 513, {_}: least_upper_bound (greatest_lower_bound ?1201 ?1200) ?1200 =>= ?1200 [1200, 1201] by Super 512 with 10 at 1,2
-Id : 1407, {_}: multiply (inverse (greatest_lower_bound ?2641 ?2642)) ?2642 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2641 ?2642)) ?2642) [2642, 2641] by Super 1397 with 513 at 2,2
-Id : 144, {_}: greatest_lower_bound ?406 (least_upper_bound ?407 ?406) =>= ?406 [407, 406] by Super 143 with 12 at 2,2
-Id : 12520, {_}: multiply (inverse (greatest_lower_bound ?25685 ?25686)) ?25685 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?25685 ?25686)) ?25685) [25686, 25685] by Super 1397 with 120 at 2,2
-Id : 12560, {_}: multiply (inverse (greatest_lower_bound identity ?25830)) identity =>= least_upper_bound identity (inverse (greatest_lower_bound identity ?25830)) [25830] by Super 12520 with 1261 at 2,3
-Id : 12795, {_}: inverse (greatest_lower_bound identity ?25965) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?25965)) [25965] by Demod 12560 with 1261 at 2
-Id : 12796, {_}: inverse (greatest_lower_bound identity ?25967) =<= least_upper_bound identity (inverse (greatest_lower_bound ?25967 identity)) [25967] by Super 12795 with 10 at 1,2,3
-Id : 20061, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound ?34946 identity)) ?34947) =>= least_upper_bound (inverse (greatest_lower_bound identity ?34946)) ?34947 [34947, 34946] by Super 16 with 12796 at 1,3
-Id : 20078, {_}: least_upper_bound identity (least_upper_bound ?35005 (inverse (greatest_lower_bound ?35004 identity))) =>= least_upper_bound (inverse (greatest_lower_bound identity ?35004)) ?35005 [35004, 35005] by Super 20061 with 12 at 2,2
-Id : 126, {_}: least_upper_bound ?353 (greatest_lower_bound ?354 ?353) =>= ?353 [354, 353] by Super 125 with 10 at 2,2
-Id : 547, {_}: least_upper_bound ?1258 ?1256 =<= least_upper_bound (least_upper_bound ?1258 ?1256) (greatest_lower_bound ?1257 ?1256) [1257, 1256, 1258] by Super 16 with 126 at 2,2
-Id : 570, {_}: least_upper_bound ?1258 ?1256 =<= least_upper_bound (greatest_lower_bound ?1257 ?1256) (least_upper_bound ?1258 ?1256) [1257, 1256, 1258] by Demod 547 with 12 at 3
-Id : 12745, {_}: inverse (greatest_lower_bound identity ?25830) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?25830)) [25830] by Demod 12560 with 1261 at 2
-Id : 12983, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound identity ?26133)) =>= identity [26133] by Super 24 with 12745 at 2,2
-Id : 12984, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound ?26135 identity)) =>= identity [26135] by Super 12983 with 10 at 1,2,2
-Id : 13334, {_}: least_upper_bound ?26447 (inverse (greatest_lower_bound ?26446 identity)) =<= least_upper_bound identity (least_upper_bound ?26447 (inverse (greatest_lower_bound ?26446 identity))) [26446, 26447] by Super 570 with 12984 at 1,3
-Id : 33938, {_}: least_upper_bound ?35005 (inverse (greatest_lower_bound ?35004 identity)) =?= least_upper_bound (inverse (greatest_lower_bound identity ?35004)) ?35005 [35004, 35005] by Demod 20078 with 13334 at 2
-Id : 59877, {_}: inverse (greatest_lower_bound (inverse ?79280) identity) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?79280))) ?79280 [79280] by Super 33938 with 59766 at 2
-Id : 13166, {_}: inverse (greatest_lower_bound identity ?26300) =<= least_upper_bound identity (inverse (greatest_lower_bound ?26300 identity)) [26300] by Super 12795 with 10 at 1,2,3
-Id : 588, {_}: greatest_lower_bound ?1337 ?1335 =<= greatest_lower_bound (greatest_lower_bound ?1337 (least_upper_bound ?1335 ?1336)) ?1335 [1336, 1335, 1337] by Super 14 with 137 at 2,2
-Id : 13179, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?26330 (least_upper_bound identity ?26331))) =>= least_upper_bound identity (inverse (greatest_lower_bound ?26330 identity)) [26331, 26330] by Super 13166 with 588 at 1,2,3
-Id : 13288, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?26330 (least_upper_bound identity ?26331))) =>= inverse (greatest_lower_bound identity ?26330) [26331, 26330] by Demod 13179 with 12796 at 3
-Id : 508, {_}: least_upper_bound ?1185 ?1183 =<= least_upper_bound (least_upper_bound ?1185 (greatest_lower_bound ?1183 ?1184)) ?1183 [1184, 1183, 1185] by Super 16 with 120 at 2,2
-Id : 139, {_}: greatest_lower_bound ?388 (greatest_lower_bound (least_upper_bound ?388 ?389) ?390) =>= greatest_lower_bound ?388 ?390 [390, 389, 388] by Super 14 with 24 at 1,3
-Id : 12760, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse (greatest_lower_bound identity ?25876)) ?25877) =>= greatest_lower_bound identity ?25877 [25877, 25876] by Super 139 with 12745 at 1,2,2
-Id : 13743, {_}: least_upper_bound ?26971 identity =<= least_upper_bound (least_upper_bound ?26971 (greatest_lower_bound identity ?26970)) identity [26970, 26971] by Super 508 with 12760 at 2,1,3
-Id : 13824, {_}: least_upper_bound ?26971 identity =<= least_upper_bound identity (least_upper_bound ?26971 (greatest_lower_bound identity ?26970)) [26970, 26971] by Demod 13743 with 12 at 3
-Id : 14000, {_}: greatest_lower_bound ?27303 identity =<= greatest_lower_bound (greatest_lower_bound ?27303 (least_upper_bound ?27301 identity)) identity [27301, 27303] by Super 588 with 13824 at 2,1,3
-Id : 15451, {_}: greatest_lower_bound ?29213 identity =<= greatest_lower_bound identity (greatest_lower_bound ?29213 (least_upper_bound ?29214 identity)) [29214, 29213] by Demod 14000 with 10 at 3
-Id : 15452, {_}: greatest_lower_bound ?29216 identity =<= greatest_lower_bound identity (greatest_lower_bound ?29216 (least_upper_bound identity ?29217)) [29217, 29216] by Super 15451 with 12 at 2,2,3
-Id : 21667, {_}: inverse (greatest_lower_bound ?26330 identity) =?= inverse (greatest_lower_bound identity ?26330) [26330] by Demod 13288 with 15452 at 1,2
-Id : 60032, {_}: inverse (greatest_lower_bound identity (inverse ?79280)) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?79280))) ?79280 [79280] by Demod 59877 with 21667 at 2
-Id : 61973, {_}: greatest_lower_bound ?80555 (inverse (greatest_lower_bound identity (inverse ?80555))) =>= ?80555 [80555] by Super 144 with 60032 at 2,2
-Id : 61975, {_}: greatest_lower_bound (inverse ?80558) (inverse (greatest_lower_bound identity ?80558)) =>= inverse ?80558 [80558] by Super 61973 with 1283 at 2,1,2,2
-Id : 64087, {_}: multiply (inverse (greatest_lower_bound (inverse ?81915) (inverse (greatest_lower_bound identity ?81915)))) (inverse (greatest_lower_bound identity ?81915)) =>= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Super 1407 with 61975 at 1,1,2,3
-Id : 64168, {_}: inverse (multiply (greatest_lower_bound identity ?81915) (greatest_lower_bound (inverse ?81915) (inverse (greatest_lower_bound identity ?81915)))) =>= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64087 with 2602 at 2
-Id : 1322, {_}: multiply ?2453 (greatest_lower_bound ?2454 (inverse ?2453)) =>= greatest_lower_bound (multiply ?2453 ?2454) identity [2454, 2453] by Super 28 with 1272 at 2,3
-Id : 1343, {_}: multiply ?2453 (greatest_lower_bound ?2454 (inverse ?2453)) =>= greatest_lower_bound identity (multiply ?2453 ?2454) [2454, 2453] by Demod 1322 with 10 at 3
-Id : 64169, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?81915) (inverse ?81915))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64168 with 1343 at 1,2
-Id : 1320, {_}: multiply (greatest_lower_bound ?2448 ?2447) (inverse ?2447) =>= greatest_lower_bound (multiply ?2448 (inverse ?2447)) identity [2447, 2448] by Super 32 with 1272 at 2,3
-Id : 1344, {_}: multiply (greatest_lower_bound ?2448 ?2447) (inverse ?2447) =>= greatest_lower_bound identity (multiply ?2448 (inverse ?2447)) [2447, 2448] by Demod 1320 with 10 at 3
-Id : 64170, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply identity (inverse ?81915)))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64169 with 1344 at 2,1,2
-Id : 64171, {_}: inverse (greatest_lower_bound identity (multiply identity (inverse ?81915))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64170 with 110 at 1,2
-Id : 64172, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64171 with 4 at 2,1,2
-Id : 64173, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?81915) (inverse ?81915))) [81915] by Demod 64172 with 2602 at 2,3
-Id : 64174, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (multiply ?81915 (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64173 with 2697 at 2,3
-Id : 1328, {_}: multiply ?2469 (least_upper_bound ?2470 (inverse ?2469)) =>= least_upper_bound (multiply ?2469 ?2470) identity [2470, 2469] by Super 26 with 1272 at 2,3
-Id : 1339, {_}: multiply ?2469 (least_upper_bound ?2470 (inverse ?2469)) =>= least_upper_bound identity (multiply ?2469 ?2470) [2470, 2469] by Demod 1328 with 12 at 3
-Id : 60418, {_}: multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661)))) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661))))) [79661] by Super 1339 with 60032 at 2,2
-Id : 60787, {_}: multiply ?79661 (inverse (greatest_lower_bound identity ?79661)) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661))))) [79661] by Demod 60418 with 1283 at 2,1,2,2
-Id : 60788, {_}: multiply ?79661 (inverse (greatest_lower_bound identity ?79661)) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity ?79661))) [79661] by Demod 60787 with 1283 at 2,1,2,2,3
-Id : 79553, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= multiply ?81915 (inverse (greatest_lower_bound identity ?81915)) [81915] by Demod 64174 with 60788 at 3
-Id : 79566, {_}: multiply (inverse (greatest_lower_bound identity (inverse ?93969))) (greatest_lower_bound identity ?93969) =>= ?93969 [93969] by Super 1262 with 79553 at 1,2
-Id : 210019, {_}: least_upper_bound (greatest_lower_bound identity (inverse ?259211)) (greatest_lower_bound identity ?259211) =<= multiply (greatest_lower_bound identity (inverse ?259211)) (least_upper_bound identity ?259211) [259211] by Super 1416 with 79566 at 2,2,3
-Id : 210576, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound identity (inverse ?259634)) (greatest_lower_bound identity ?259634))) (inverse (least_upper_bound identity ?259634)) =>= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Super 1918 with 210019 at 2,1,2
-Id : 122, {_}: least_upper_bound ?338 (least_upper_bound (greatest_lower_bound ?338 ?339) ?340) =>= least_upper_bound ?338 ?340 [340, 339, 338] by Super 16 with 22 at 1,3
-Id : 210728, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity ?259634)) (inverse (least_upper_bound identity ?259634)) =>= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210576 with 122 at 1,2
-Id : 210729, {_}: multiply identity (inverse (least_upper_bound identity ?259634)) =<= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210728 with 22 at 1,2
-Id : 210730, {_}: inverse (least_upper_bound identity ?259634) =<= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210729 with 4 at 2
-Id : 210731, {_}: inverse (least_upper_bound identity ?259634) =<= least_upper_bound (greatest_lower_bound identity (inverse ?259634)) (inverse (least_upper_bound identity ?259634)) [259634] by Demod 210730 with 12 at 3
-Id : 425033, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?443021)) (greatest_lower_bound identity (inverse ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Super 137 with 210731 at 1,2
-Id : 425426, {_}: greatest_lower_bound (greatest_lower_bound identity (inverse ?443021)) (inverse (least_upper_bound identity ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425033 with 10 at 2
-Id : 425427, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse ?443021) (inverse (least_upper_bound identity ?443021))) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425426 with 14 at 2
-Id : 441, {_}: greatest_lower_bound ?1042 (greatest_lower_bound ?1042 ?1043) =>= greatest_lower_bound ?1042 ?1043 [1043, 1042] by Super 14 with 20 at 1,3
-Id : 997, {_}: greatest_lower_bound ?1977 (greatest_lower_bound ?1978 ?1977) =>= greatest_lower_bound ?1977 ?1978 [1978, 1977] by Super 441 with 10 at 2,2
-Id : 1008, {_}: greatest_lower_bound ?2012 (greatest_lower_bound ?2010 (greatest_lower_bound ?2011 ?2012)) =>= greatest_lower_bound ?2012 (greatest_lower_bound ?2010 ?2011) [2011, 2010, 2012] by Super 997 with 14 at 2,2
-Id : 196, {_}: multiply (inverse ?547) (greatest_lower_bound ?546 ?547) =>= greatest_lower_bound (multiply (inverse ?547) ?546) identity [546, 547] by Super 194 with 6 at 2,3
-Id : 215, {_}: multiply (inverse ?547) (greatest_lower_bound ?546 ?547) =>= greatest_lower_bound identity (multiply (inverse ?547) ?546) [546, 547] by Demod 196 with 10 at 3
-Id : 145, {_}: greatest_lower_bound ?411 (least_upper_bound (least_upper_bound ?411 ?409) ?410) =>= ?411 [410, 409, 411] by Super 143 with 16 at 2,2
-Id : 13972, {_}: greatest_lower_bound identity (least_upper_bound (least_upper_bound ?27209 identity) ?27211) =>= identity [27211, 27209] by Super 145 with 13824 at 1,2,2
-Id : 14608, {_}: multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity =<= greatest_lower_bound identity (multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity) [27966, 27965] by Super 215 with 13972 at 2,2
-Id : 14746, {_}: inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966) =<= greatest_lower_bound identity (multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity) [27966, 27965] by Demod 14608 with 1261 at 2
-Id : 14747, {_}: inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966) =<= greatest_lower_bound identity (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) [27966, 27965] by Demod 14746 with 1261 at 2,3
-Id : 14621, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?28005 identity) ?28006) =>= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Super 513 with 13972 at 1,2
-Id : 371, {_}: least_upper_bound ?890 (least_upper_bound ?890 ?891) =>= least_upper_bound ?890 ?891 [891, 890] by Super 16 with 18 at 1,3
-Id : 372, {_}: least_upper_bound ?893 (least_upper_bound ?894 ?893) =>= least_upper_bound ?893 ?894 [894, 893] by Super 371 with 12 at 2,2
-Id : 846, {_}: least_upper_bound ?1742 (least_upper_bound (least_upper_bound ?1743 ?1742) ?1744) =>= least_upper_bound (least_upper_bound ?1742 ?1743) ?1744 [1744, 1743, 1742] by Super 16 with 372 at 1,3
-Id : 14731, {_}: least_upper_bound (least_upper_bound identity ?28005) ?28006 =?= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Demod 14621 with 846 at 2
-Id : 14732, {_}: least_upper_bound identity (least_upper_bound ?28005 ?28006) =<= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Demod 14731 with 16 at 2
-Id : 26166, {_}: inverse (least_upper_bound identity (least_upper_bound ?27965 ?27966)) =<= greatest_lower_bound identity (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) [27966, 27965] by Demod 14747 with 14732 at 1,2
-Id : 26240, {_}: inverse (least_upper_bound identity (least_upper_bound ?42502 ?42503)) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (least_upper_bound ?42502 ?42503))) [42503, 42502] by Demod 26166 with 14732 at 1,2,3
-Id : 26243, {_}: inverse (least_upper_bound identity (least_upper_bound ?42512 ?42512)) =>= greatest_lower_bound identity (inverse (least_upper_bound identity ?42512)) [42512] by Super 26240 with 18 at 2,1,2,3
-Id : 26484, {_}: inverse (least_upper_bound identity ?42512) =<= greatest_lower_bound identity (inverse (least_upper_bound identity ?42512)) [42512] by Demod 26243 with 18 at 2,1,2
-Id : 26733, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) =>= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42902, 42901] by Super 1008 with 26484 at 2,2,2
-Id : 26831, {_}: greatest_lower_bound (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) (inverse (least_upper_bound identity ?42901)) =>= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42901, 42902] by Demod 26733 with 10 at 2
-Id : 112, {_}: greatest_lower_bound ?317 ?316 =<= greatest_lower_bound (greatest_lower_bound ?317 ?316) ?316 [316, 317] by Super 14 with 20 at 2,2
-Id : 26832, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42901, 42902] by Demod 26831 with 112 at 2
-Id : 26833, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound (greatest_lower_bound ?42902 identity) (inverse (least_upper_bound identity ?42901)) [42901, 42902] by Demod 26832 with 10 at 3
-Id : 594, {_}: greatest_lower_bound (least_upper_bound ?1355 ?1356) ?1355 =>= ?1355 [1356, 1355] by Super 10 with 24 at 3
-Id : 595, {_}: greatest_lower_bound (least_upper_bound ?1359 ?1358) ?1358 =>= ?1358 [1358, 1359] by Super 594 with 12 at 1,2
-Id : 14013, {_}: least_upper_bound ?27351 identity =<= least_upper_bound identity (least_upper_bound ?27351 (greatest_lower_bound identity ?27352)) [27352, 27351] by Demod 13743 with 12 at 3
-Id : 15143, {_}: least_upper_bound ?28845 identity =<= least_upper_bound identity (least_upper_bound ?28845 (greatest_lower_bound ?28846 identity)) [28846, 28845] by Super 14013 with 10 at 2,2,3
-Id : 15162, {_}: least_upper_bound (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) identity =>= least_upper_bound identity (greatest_lower_bound ?28908 identity) [28907, 28908] by Super 15143 with 120 at 2,3
-Id : 15331, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) =>= least_upper_bound identity (greatest_lower_bound ?28908 identity) [28907, 28908] by Demod 15162 with 12 at 2
-Id : 15332, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) =>= identity [28907, 28908] by Demod 15331 with 126 at 3
-Id : 16566, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607) =>= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Super 595 with 15332 at 1,2
-Id : 442, {_}: greatest_lower_bound ?1045 (greatest_lower_bound ?1046 ?1045) =>= greatest_lower_bound ?1045 ?1046 [1046, 1045] by Super 441 with 10 at 2,2
-Id : 988, {_}: greatest_lower_bound ?1947 (greatest_lower_bound (greatest_lower_bound ?1948 ?1947) ?1949) =>= greatest_lower_bound (greatest_lower_bound ?1947 ?1948) ?1949 [1949, 1948, 1947] by Super 14 with 442 at 1,3
-Id : 16667, {_}: greatest_lower_bound (greatest_lower_bound identity ?30606) ?30607 =?= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Demod 16566 with 988 at 2
-Id : 16668, {_}: greatest_lower_bound identity (greatest_lower_bound ?30606 ?30607) =<= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Demod 16667 with 14 at 2
-Id : 26834, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound identity (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) [42901, 42902] by Demod 26833 with 16668 at 3
-Id : 425428, {_}: greatest_lower_bound (inverse ?443021) (inverse (least_upper_bound identity ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425427 with 26834 at 2
-Id : 100, {_}: least_upper_bound ?291 ?290 =<= least_upper_bound (least_upper_bound ?291 ?290) ?290 [290, 291] by Super 16 with 18 at 2,2
-Id : 1412, {_}: multiply (inverse (least_upper_bound ?2659 ?2660)) (least_upper_bound ?2659 ?2660) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2659 ?2660)) ?2660) [2660, 2659] by Super 1397 with 100 at 2,2
-Id : 1437, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2659 ?2660)) ?2660) [2660, 2659] by Demod 1412 with 6 at 2
-Id : 59670, {_}: multiply identity ?78944 =<= least_upper_bound ?78944 (inverse (least_upper_bound ?78943 (inverse ?78944))) [78943, 78944] by Super 59624 with 1437 at 1,2
-Id : 59771, {_}: ?78944 =<= least_upper_bound ?78944 (inverse (least_upper_bound ?78943 (inverse ?78944))) [78943, 78944] by Demod 59670 with 4 at 2
-Id : 89100, {_}: greatest_lower_bound ?102689 (inverse (least_upper_bound ?102690 (inverse ?102689))) =>= inverse (least_upper_bound ?102690 (inverse ?102689)) [102690, 102689] by Super 595 with 59771 at 1,2
-Id : 89102, {_}: greatest_lower_bound (inverse ?102694) (inverse (least_upper_bound ?102695 ?102694)) =>= inverse (least_upper_bound ?102695 (inverse (inverse ?102694))) [102695, 102694] by Super 89100 with 1283 at 2,1,2,2
-Id : 89528, {_}: greatest_lower_bound (inverse ?102694) (inverse (least_upper_bound ?102695 ?102694)) =>= inverse (least_upper_bound ?102695 ?102694) [102695, 102694] by Demod 89102 with 1283 at 2,1,3
-Id : 425429, {_}: inverse (least_upper_bound identity ?443021) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425428 with 89528 at 2
-Id : 426630, {_}: inverse (greatest_lower_bound identity (inverse ?443891)) =>= least_upper_bound identity ?443891 [443891] by Super 1283 with 425429 at 1,2
-Id : 428479, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 243250 with 426630 at 3
-Id : 243250, {_}: least_upper_bound identity (multiply a b) =<= inverse (greatest_lower_bound identity (inverse (multiply a b))) [] by Demod 289 with 241323 at 3
-Id : 289, {_}: least_upper_bound identity (multiply a b) =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by Demod 2 with 12 at 2
-Id : 2, {_}: least_upper_bound (multiply a b) identity =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by prove_p23
-% SZS output end CNFRefutation for GRP186-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p23_1 is 75
- p23_2 is 74
- p23_3 is 73
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p23_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Found proof, 98.278709s
-% SZS status Unsatisfiable for GRP186-2.p
-% SZS output start CNFRefutation for GRP186-2.p
-Id : 131, {_}: least_upper_bound ?356 (greatest_lower_bound ?356 ?357) =>= ?356 [357, 356] by lub_absorbtion ?356 ?357
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p23_3 ?53 ?54
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 234, {_}: multiply (least_upper_bound ?624 ?625) ?626 =<= least_upper_bound (multiply ?624 ?626) (multiply ?625 ?626) [626, 625, 624] by monotony_lub2 ?624 ?625 ?626
-Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 34, {_}: inverse identity =>= identity [] by p23_1
-Id : 316, {_}: inverse (multiply ?814 ?815) =<= multiply (inverse ?815) (inverse ?814) [815, 814] by p23_3 ?814 ?815
-Id : 43, {_}: multiply (multiply ?64 ?65) ?66 =?= multiply ?64 (multiply ?65 ?66) [66, 65, 64] by associativity ?64 ?65 ?66
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 169, {_}: multiply ?469 (least_upper_bound ?470 ?471) =<= least_upper_bound (multiply ?469 ?470) (multiply ?469 ?471) [471, 470, 469] by monotony_lub1 ?469 ?470 ?471
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 1363, {_}: multiply (inverse ?2558) (least_upper_bound ?2558 ?2559) =>= least_upper_bound identity (multiply (inverse ?2558) ?2559) [2559, 2558] by Super 169 with 6 at 1,3
-Id : 650, {_}: least_upper_bound (greatest_lower_bound ?1395 ?1396) ?1395 =>= ?1395 [1396, 1395] by Super 12 with 22 at 3
-Id : 651, {_}: least_upper_bound (greatest_lower_bound ?1399 ?1398) ?1398 =>= ?1398 [1398, 1399] by Super 650 with 10 at 1,2
-Id : 1373, {_}: multiply (inverse (greatest_lower_bound ?2588 ?2589)) ?2589 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2588 ?2589)) ?2589) [2589, 2588] by Super 1363 with 651 at 2,2
-Id : 45, {_}: multiply (multiply ?71 (inverse ?72)) ?72 =>= multiply ?71 identity [72, 71] by Super 43 with 6 at 2,3
-Id : 317, {_}: inverse (multiply identity ?817) =<= multiply (inverse ?817) identity [817] by Super 316 with 34 at 2,3
-Id : 341, {_}: inverse ?863 =<= multiply (inverse ?863) identity [863] by Demod 317 with 4 at 1,2
-Id : 343, {_}: inverse (inverse ?866) =<= multiply ?866 identity [866] by Super 341 with 36 at 1,3
-Id : 354, {_}: ?866 =<= multiply ?866 identity [866] by Demod 343 with 36 at 2
-Id : 1260, {_}: multiply (multiply ?71 (inverse ?72)) ?72 =>= ?71 [72, 71] by Demod 45 with 354 at 3
-Id : 240, {_}: multiply (least_upper_bound (inverse ?648) ?647) ?648 =>= least_upper_bound identity (multiply ?647 ?648) [647, 648] by Super 234 with 6 at 1,3
-Id : 1623, {_}: multiply (least_upper_bound identity (multiply ?2972 (inverse ?2973))) ?2973 =>= least_upper_bound (inverse (inverse ?2973)) ?2972 [2973, 2972] by Super 1260 with 240 at 1,2
-Id : 139882, {_}: multiply (least_upper_bound identity (multiply ?153893 (inverse ?153894))) ?153894 =>= least_upper_bound ?153894 ?153893 [153894, 153893] by Demod 1623 with 36 at 1,3
-Id : 126, {_}: least_upper_bound (greatest_lower_bound ?338 ?339) ?338 =>= ?338 [339, 338] by Super 12 with 22 at 3
-Id : 1369, {_}: multiply (inverse (greatest_lower_bound ?2577 ?2576)) ?2577 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2577 ?2576)) ?2577) [2576, 2577] by Super 1363 with 126 at 2,2
-Id : 139933, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?154061) ?154060)) (inverse ?154061)) ?154061 =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Super 139882 with 1369 at 1,2
-Id : 140037, {_}: multiply (inverse (greatest_lower_bound (inverse ?154061) ?154060)) (multiply (inverse ?154061) ?154061) =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 139933 with 8 at 2
-Id : 311, {_}: multiply (inverse (multiply ?794 ?795)) ?796 =<= multiply (inverse ?795) (multiply (inverse ?794) ?796) [796, 795, 794] by Super 8 with 38 at 1,2
-Id : 140038, {_}: multiply (inverse (multiply ?154061 (greatest_lower_bound (inverse ?154061) ?154060))) ?154061 =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 140037 with 311 at 2
-Id : 1275, {_}: multiply (multiply ?2378 (inverse ?2379)) ?2379 =>= ?2378 [2379, 2378] by Demod 45 with 354 at 3
-Id : 1285, {_}: multiply (inverse (multiply ?2408 ?2407)) ?2408 =>= inverse ?2407 [2407, 2408] by Super 1275 with 38 at 1,2
-Id : 140039, {_}: inverse (greatest_lower_bound (inverse ?154061) ?154060) =<= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 140038 with 1285 at 2
-Id : 160759, {_}: greatest_lower_bound ?168171 (inverse (greatest_lower_bound (inverse ?168171) ?168172)) =>= ?168171 [168172, 168171] by Super 24 with 140039 at 2,2
-Id : 160761, {_}: greatest_lower_bound (inverse ?168176) (inverse (greatest_lower_bound ?168176 ?168177)) =>= inverse ?168176 [168177, 168176] by Super 160759 with 36 at 1,1,2,2
-Id : 178590, {_}: multiply (inverse (greatest_lower_bound (inverse ?184996) (inverse (greatest_lower_bound ?184996 ?184997)))) (inverse (greatest_lower_bound ?184996 ?184997)) =>= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Super 1373 with 160761 at 1,1,2,3
-Id : 178788, {_}: inverse (multiply (greatest_lower_bound ?184996 ?184997) (greatest_lower_bound (inverse ?184996) (inverse (greatest_lower_bound ?184996 ?184997)))) =>= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Demod 178590 with 38 at 2
-Id : 299, {_}: multiply ?763 (inverse ?763) =>= identity [763] by Super 6 with 36 at 1,2
-Id : 392, {_}: multiply ?921 (greatest_lower_bound ?922 (inverse ?921)) =>= greatest_lower_bound (multiply ?921 ?922) identity [922, 921] by Super 28 with 299 at 2,3
-Id : 417, {_}: multiply ?921 (greatest_lower_bound ?922 (inverse ?921)) =>= greatest_lower_bound identity (multiply ?921 ?922) [922, 921] by Demod 392 with 10 at 3
-Id : 178789, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound ?184996 ?184997) (inverse ?184996))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Demod 178788 with 417 at 1,2
-Id : 391, {_}: multiply (greatest_lower_bound ?918 ?919) (inverse ?918) =>= greatest_lower_bound identity (multiply ?919 (inverse ?918)) [919, 918] by Super 32 with 299 at 1,3
-Id : 178790, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply ?184997 (inverse ?184996)))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178789 with 391 at 2,1,2
-Id : 116, {_}: greatest_lower_bound ?316 (greatest_lower_bound ?316 ?317) =>= greatest_lower_bound ?316 ?317 [317, 316] by Super 14 with 20 at 1,3
-Id : 178791, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178790 with 116 at 1,2
-Id : 178792, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound ?184996 ?184997) (inverse ?184996))) [184996, 184997] by Demod 178791 with 38 at 2,3
-Id : 320, {_}: inverse (multiply ?825 (inverse ?824)) =>= multiply ?824 (inverse ?825) [824, 825] by Super 316 with 36 at 1,3
-Id : 178793, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (multiply ?184996 (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178792 with 320 at 2,3
-Id : 2114, {_}: multiply (least_upper_bound ?3753 ?3754) (inverse ?3753) =>= least_upper_bound identity (multiply ?3754 (inverse ?3753)) [3754, 3753] by Super 30 with 299 at 1,3
-Id : 2124, {_}: multiply ?3785 (inverse (greatest_lower_bound ?3785 ?3784)) =<= least_upper_bound identity (multiply ?3785 (inverse (greatest_lower_bound ?3785 ?3784))) [3784, 3785] by Super 2114 with 126 at 1,2
-Id : 517036, {_}: inverse (greatest_lower_bound identity (multiply ?520378 (inverse ?520379))) =?= multiply ?520379 (inverse (greatest_lower_bound ?520379 ?520378)) [520379, 520378] by Demod 178793 with 2124 at 3
-Id : 517346, {_}: inverse (greatest_lower_bound identity (inverse (multiply ?521360 ?521359))) =<= multiply ?521360 (inverse (greatest_lower_bound ?521360 (inverse ?521359))) [521359, 521360] by Super 517036 with 38 at 2,1,2
-Id : 143, {_}: greatest_lower_bound (least_upper_bound ?388 ?389) ?388 =>= ?388 [389, 388] by Super 10 with 24 at 3
-Id : 394, {_}: multiply (multiply ?928 ?927) (inverse ?927) =>= multiply ?928 identity [927, 928] by Super 8 with 299 at 2,3
-Id : 2350, {_}: multiply (multiply ?4107 ?4108) (inverse ?4108) =>= ?4107 [4108, 4107] by Demod 394 with 354 at 3
-Id : 2362, {_}: multiply (least_upper_bound identity (multiply ?4143 ?4144)) (inverse ?4144) =>= least_upper_bound (inverse ?4144) ?4143 [4144, 4143] by Super 2350 with 240 at 1,2
-Id : 52, {_}: multiply identity ?99 =<= multiply (inverse ?98) (multiply ?98 ?99) [98, 99] by Super 43 with 6 at 1,2
-Id : 61, {_}: ?99 =<= multiply (inverse ?98) (multiply ?98 ?99) [98, 99] by Demod 52 with 4 at 2
-Id : 175, {_}: multiply (inverse ?492) (least_upper_bound ?492 ?493) =>= least_upper_bound identity (multiply (inverse ?492) ?493) [493, 492] by Super 169 with 6 at 1,3
-Id : 1362, {_}: least_upper_bound ?2555 ?2556 =<= multiply (inverse (inverse ?2555)) (least_upper_bound identity (multiply (inverse ?2555) ?2556)) [2556, 2555] by Super 61 with 175 at 2,3
-Id : 1384, {_}: least_upper_bound ?2555 ?2556 =<= multiply ?2555 (least_upper_bound identity (multiply (inverse ?2555) ?2556)) [2556, 2555] by Demod 1362 with 36 at 1,3
-Id : 327, {_}: inverse ?817 =<= multiply (inverse ?817) identity [817] by Demod 317 with 4 at 1,2
-Id : 338, {_}: multiply (inverse ?854) (least_upper_bound identity ?855) =<= least_upper_bound (inverse ?854) (multiply (inverse ?854) ?855) [855, 854] by Super 26 with 327 at 1,3
-Id : 332, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =<= greatest_lower_bound (multiply (inverse ?838) ?839) (inverse ?838) [839, 838] by Super 28 with 327 at 2,3
-Id : 350, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =<= greatest_lower_bound (inverse ?838) (multiply (inverse ?838) ?839) [839, 838] by Demod 332 with 10 at 3
-Id : 333, {_}: multiply (inverse ?841) (greatest_lower_bound identity ?842) =<= greatest_lower_bound (inverse ?841) (multiply (inverse ?841) ?842) [842, 841] by Super 28 with 327 at 1,3
-Id : 3646, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =?= multiply (inverse ?838) (greatest_lower_bound identity ?839) [839, 838] by Demod 350 with 333 at 3
-Id : 3670, {_}: multiply (inverse (greatest_lower_bound ?5927 identity)) (greatest_lower_bound identity ?5927) =>= identity [5927] by Super 6 with 3646 at 2
-Id : 5362, {_}: multiply (inverse (greatest_lower_bound ?8279 identity)) (least_upper_bound identity (greatest_lower_bound identity ?8279)) =>= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Super 338 with 3670 at 2,3
-Id : 5430, {_}: multiply (inverse (greatest_lower_bound ?8279 identity)) identity =>= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Demod 5362 with 22 at 2,2
-Id : 5431, {_}: inverse (greatest_lower_bound ?8279 identity) =<= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Demod 5430 with 354 at 2
-Id : 5432, {_}: inverse (greatest_lower_bound ?8279 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound ?8279 identity)) [8279] by Demod 5431 with 12 at 3
-Id : 5579, {_}: least_upper_bound ?8466 (inverse (greatest_lower_bound ?8465 identity)) =<= least_upper_bound (least_upper_bound ?8466 identity) (inverse (greatest_lower_bound ?8465 identity)) [8465, 8466] by Super 16 with 5432 at 2,2
-Id : 5622, {_}: least_upper_bound ?8466 (inverse (greatest_lower_bound ?8465 identity)) =<= least_upper_bound (inverse (greatest_lower_bound ?8465 identity)) (least_upper_bound ?8466 identity) [8465, 8466] by Demod 5579 with 12 at 3
-Id : 400, {_}: multiply (least_upper_bound ?944 ?943) (inverse ?943) =>= least_upper_bound (multiply ?944 (inverse ?943)) identity [943, 944] by Super 30 with 299 at 2,3
-Id : 412, {_}: multiply (least_upper_bound ?944 ?943) (inverse ?943) =>= least_upper_bound identity (multiply ?944 (inverse ?943)) [943, 944] by Demod 400 with 12 at 3
-Id : 337, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =<= least_upper_bound (multiply (inverse ?851) ?852) (inverse ?851) [852, 851] by Super 26 with 327 at 2,3
-Id : 347, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =<= least_upper_bound (inverse ?851) (multiply (inverse ?851) ?852) [852, 851] by Demod 337 with 12 at 3
-Id : 3431, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =?= multiply (inverse ?851) (least_upper_bound identity ?852) [852, 851] by Demod 347 with 338 at 3
-Id : 3454, {_}: multiply (inverse (least_upper_bound ?5686 identity)) (least_upper_bound identity ?5686) =>= identity [5686] by Super 6 with 3431 at 2
-Id : 4555, {_}: multiply (inverse (least_upper_bound ?7520 identity)) (least_upper_bound identity (least_upper_bound identity ?7520)) =>= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Super 338 with 3454 at 2,3
-Id : 104, {_}: least_upper_bound ?290 (least_upper_bound ?290 ?291) =>= least_upper_bound ?290 ?291 [291, 290] by Super 16 with 18 at 1,3
-Id : 4621, {_}: multiply (inverse (least_upper_bound ?7520 identity)) (least_upper_bound identity ?7520) =>= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Demod 4555 with 104 at 2,2
-Id : 4622, {_}: identity =<= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Demod 4621 with 3454 at 2
-Id : 4773, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?7713 identity)) [7713] by Demod 4622 with 12 at 3
-Id : 4780, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?7726 (least_upper_bound ?7727 identity))) [7727, 7726] by Super 4773 with 16 at 1,2,3
-Id : 6791, {_}: multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity)))) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Super 412 with 4780 at 1,2
-Id : 6824, {_}: inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Demod 6791 with 4 at 2
-Id : 6825, {_}: least_upper_bound ?9674 (least_upper_bound ?9675 identity) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Demod 6824 with 36 at 2
-Id : 6826, {_}: least_upper_bound ?9674 (least_upper_bound ?9675 identity) =<= least_upper_bound identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity)))) [9675, 9674] by Demod 6825 with 4 at 2,3
-Id : 6913, {_}: least_upper_bound ?9827 (least_upper_bound ?9828 identity) =<= least_upper_bound identity (least_upper_bound ?9827 (least_upper_bound ?9828 identity)) [9828, 9827] by Demod 6826 with 36 at 2,3
-Id : 6922, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?9855 identity) ?9854) [9855, 9854] by Super 6913 with 12 at 2,3
-Id : 502, {_}: least_upper_bound (least_upper_bound ?1064 ?1065) ?1064 =>= least_upper_bound ?1064 ?1065 [1065, 1064] by Super 12 with 104 at 3
-Id : 6917, {_}: least_upper_bound ?9839 (least_upper_bound (least_upper_bound identity ?9838) identity) =?= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Super 6913 with 502 at 2,2,3
-Id : 6992, {_}: least_upper_bound ?9839 (least_upper_bound identity (least_upper_bound identity ?9838)) =?= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Demod 6917 with 12 at 2,2
-Id : 6993, {_}: least_upper_bound ?9839 (least_upper_bound identity ?9838) =<= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Demod 6992 with 104 at 2,2
-Id : 6914, {_}: least_upper_bound ?9830 (least_upper_bound ?9831 identity) =<= least_upper_bound identity (least_upper_bound ?9830 (least_upper_bound identity ?9831)) [9831, 9830] by Super 6913 with 12 at 2,2,3
-Id : 7479, {_}: least_upper_bound ?9839 (least_upper_bound identity ?9838) =?= least_upper_bound ?9839 (least_upper_bound ?9838 identity) [9838, 9839] by Demod 6993 with 6914 at 3
-Id : 7163, {_}: least_upper_bound ?10110 (least_upper_bound ?10111 identity) =<= least_upper_bound identity (least_upper_bound ?10110 (least_upper_bound identity ?10111)) [10111, 10110] by Super 6913 with 12 at 2,2,3
-Id : 7180, {_}: least_upper_bound ?10164 (least_upper_bound ?10165 identity) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?10164 identity) ?10165) [10165, 10164] by Super 7163 with 16 at 2,3
-Id : 8147, {_}: least_upper_bound ?11328 (least_upper_bound ?11329 identity) =?= least_upper_bound ?11329 (least_upper_bound ?11328 identity) [11329, 11328] by Demod 7180 with 6922 at 3
-Id : 8150, {_}: least_upper_bound (greatest_lower_bound identity ?11336) (least_upper_bound ?11337 identity) =>= least_upper_bound ?11337 identity [11337, 11336] by Super 8147 with 126 at 2,3
-Id : 8900, {_}: least_upper_bound (greatest_lower_bound identity ?11839) (least_upper_bound identity ?11840) =>= least_upper_bound ?11840 identity [11840, 11839] by Super 7479 with 8150 at 3
-Id : 10250, {_}: least_upper_bound (greatest_lower_bound identity ?13083) (least_upper_bound (least_upper_bound identity ?13084) ?13085) =>= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084, 13083] by Super 16 with 8900 at 1,3
-Id : 10334, {_}: least_upper_bound (greatest_lower_bound identity ?13083) (least_upper_bound identity (least_upper_bound ?13084 ?13085)) =>= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084, 13083] by Demod 10250 with 16 at 2,2
-Id : 10335, {_}: least_upper_bound (least_upper_bound ?13084 ?13085) identity =?= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084] by Demod 10334 with 8900 at 2
-Id : 10336, {_}: least_upper_bound identity (least_upper_bound ?13084 ?13085) =<= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084] by Demod 10335 with 12 at 2
-Id : 10485, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =<= least_upper_bound identity (least_upper_bound identity (least_upper_bound ?9855 ?9854)) [9855, 9854] by Demod 6922 with 10336 at 2,3
-Id : 10492, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =?= least_upper_bound identity (least_upper_bound ?9855 ?9854) [9855, 9854] by Demod 10485 with 104 at 3
-Id : 18158, {_}: least_upper_bound ?21052 (inverse (greatest_lower_bound ?21053 identity)) =<= least_upper_bound identity (least_upper_bound ?21052 (inverse (greatest_lower_bound ?21053 identity))) [21053, 21052] by Demod 5622 with 10492 at 3
-Id : 577, {_}: greatest_lower_bound (greatest_lower_bound ?1234 ?1235) ?1234 =>= greatest_lower_bound ?1234 ?1235 [1235, 1234] by Super 10 with 116 at 3
-Id : 18162, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound (greatest_lower_bound identity ?21063) identity)) =?= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Super 18158 with 577 at 1,2,2,3
-Id : 5589, {_}: inverse (greatest_lower_bound ?8486 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound ?8486 identity)) [8486] by Demod 5431 with 12 at 3
-Id : 5593, {_}: inverse (greatest_lower_bound (greatest_lower_bound identity ?8493) identity) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Super 5589 with 577 at 1,2,3
-Id : 5675, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity ?8493)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Demod 5593 with 10 at 1,2
-Id : 5676, {_}: inverse (greatest_lower_bound identity ?8493) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Demod 5675 with 116 at 1,2
-Id : 5590, {_}: inverse (greatest_lower_bound ?8488 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8488)) [8488] by Super 5589 with 10 at 1,2,3
-Id : 5940, {_}: inverse (greatest_lower_bound identity ?8493) =?= inverse (greatest_lower_bound ?8493 identity) [8493] by Demod 5676 with 5590 at 3
-Id : 18288, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity (greatest_lower_bound identity ?21063))) =?= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Demod 18162 with 5940 at 2,2
-Id : 18289, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063)) =<= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Demod 18288 with 116 at 1,2,2
-Id : 5804, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound (least_upper_bound ?8608 identity) (inverse (greatest_lower_bound identity ?8607)) [8607, 8608] by Super 16 with 5590 at 2,2
-Id : 5849, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound (inverse (greatest_lower_bound identity ?8607)) (least_upper_bound ?8608 identity) [8607, 8608] by Demod 5804 with 12 at 3
-Id : 19653, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound identity (least_upper_bound ?8608 (inverse (greatest_lower_bound identity ?8607))) [8607, 8608] by Demod 5849 with 10492 at 3
-Id : 50221, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063)) =?= least_upper_bound ?21064 (inverse (greatest_lower_bound ?21063 identity)) [21063, 21064] by Demod 18289 with 19653 at 3
-Id : 140157, {_}: least_upper_bound ?154397 (inverse (greatest_lower_bound identity (inverse ?154397))) =>= inverse (greatest_lower_bound (inverse ?154397) identity) [154397] by Super 50221 with 140039 at 3
-Id : 140328, {_}: least_upper_bound ?154397 (inverse (greatest_lower_bound identity (inverse ?154397))) =>= inverse (greatest_lower_bound identity (inverse ?154397)) [154397] by Demod 140157 with 5940 at 3
-Id : 141908, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?155586))) ?155586 =>= ?155586 [155586] by Super 143 with 140328 at 1,2
-Id : 141910, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity ?155589)) (inverse ?155589) =>= inverse ?155589 [155589] by Super 141908 with 36 at 2,1,1,2
-Id : 144996, {_}: multiply (inverse (greatest_lower_bound (inverse (greatest_lower_bound identity ?157076)) (inverse ?157076))) (inverse (greatest_lower_bound identity ?157076)) =>= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Super 1369 with 141910 at 1,1,2,3
-Id : 145323, {_}: inverse (multiply (greatest_lower_bound identity ?157076) (greatest_lower_bound (inverse (greatest_lower_bound identity ?157076)) (inverse ?157076))) =>= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 144996 with 38 at 2
-Id : 393, {_}: multiply ?924 (greatest_lower_bound (inverse ?924) ?925) =>= greatest_lower_bound identity (multiply ?924 ?925) [925, 924] by Super 28 with 299 at 1,3
-Id : 145324, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?157076) (inverse ?157076))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145323 with 393 at 1,2
-Id : 390, {_}: multiply (greatest_lower_bound ?916 ?915) (inverse ?915) =>= greatest_lower_bound (multiply ?916 (inverse ?915)) identity [915, 916] by Super 32 with 299 at 2,3
-Id : 418, {_}: multiply (greatest_lower_bound ?916 ?915) (inverse ?915) =>= greatest_lower_bound identity (multiply ?916 (inverse ?915)) [915, 916] by Demod 390 with 10 at 3
-Id : 145325, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply identity (inverse ?157076)))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145324 with 418 at 2,1,2
-Id : 145326, {_}: inverse (greatest_lower_bound identity (multiply identity (inverse ?157076))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145325 with 116 at 1,2
-Id : 145327, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145326 with 4 at 2,1,2
-Id : 145328, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?157076) (inverse ?157076))) [157076] by Demod 145327 with 38 at 2,3
-Id : 145329, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (multiply ?157076 (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145328 with 320 at 2,3
-Id : 399, {_}: multiply ?940 (least_upper_bound (inverse ?940) ?941) =>= least_upper_bound identity (multiply ?940 ?941) [941, 940] by Super 26 with 299 at 1,3
-Id : 140842, {_}: multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994)))) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994))))) [154994] by Super 399 with 140328 at 2,2
-Id : 141158, {_}: multiply ?154994 (inverse (greatest_lower_bound identity ?154994)) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994))))) [154994] by Demod 140842 with 36 at 2,1,2,2
-Id : 141159, {_}: multiply ?154994 (inverse (greatest_lower_bound identity ?154994)) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity ?154994))) [154994] by Demod 141158 with 36 at 2,1,2,2,3
-Id : 165997, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= multiply ?157076 (inverse (greatest_lower_bound identity ?157076)) [157076] by Demod 145329 with 141159 at 3
-Id : 166015, {_}: multiply (inverse (greatest_lower_bound identity (inverse ?173131))) (greatest_lower_bound identity ?173131) =>= ?173131 [173131] by Super 1260 with 165997 at 1,2
-Id : 396771, {_}: least_upper_bound (greatest_lower_bound identity (inverse ?441901)) (greatest_lower_bound identity ?441901) =<= multiply (greatest_lower_bound identity (inverse ?441901)) (least_upper_bound identity ?441901) [441901] by Super 1384 with 166015 at 2,2,3
-Id : 397621, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound identity (inverse ?442410)) (greatest_lower_bound identity ?442410))) (inverse (least_upper_bound identity ?442410)) =>= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Super 2362 with 396771 at 2,1,2
-Id : 128, {_}: least_upper_bound ?344 (least_upper_bound (greatest_lower_bound ?344 ?345) ?346) =>= least_upper_bound ?344 ?346 [346, 345, 344] by Super 16 with 22 at 1,3
-Id : 397861, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity ?442410)) (inverse (least_upper_bound identity ?442410)) =>= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397621 with 128 at 1,2
-Id : 397862, {_}: multiply identity (inverse (least_upper_bound identity ?442410)) =<= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397861 with 22 at 1,2
-Id : 397863, {_}: inverse (least_upper_bound identity ?442410) =<= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397862 with 4 at 2
-Id : 397864, {_}: inverse (least_upper_bound identity ?442410) =<= least_upper_bound (greatest_lower_bound identity (inverse ?442410)) (inverse (least_upper_bound identity ?442410)) [442410] by Demod 397863 with 12 at 3
-Id : 697689, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?666285)) (greatest_lower_bound identity (inverse ?666285)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Super 143 with 397864 at 1,2
-Id : 698150, {_}: greatest_lower_bound (greatest_lower_bound identity (inverse ?666285)) (inverse (least_upper_bound identity ?666285)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 697689 with 10 at 2
-Id : 698151, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse ?666285) (inverse (least_upper_bound identity ?666285))) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698150 with 14 at 2
-Id : 4574, {_}: multiply (inverse (least_upper_bound ?7568 identity)) (greatest_lower_bound identity (least_upper_bound identity ?7568)) =>= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Super 333 with 3454 at 2,3
-Id : 4596, {_}: multiply (inverse (least_upper_bound ?7568 identity)) identity =>= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Demod 4574 with 24 at 2,2
-Id : 4597, {_}: inverse (least_upper_bound ?7568 identity) =<= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Demod 4596 with 354 at 2
-Id : 4680, {_}: inverse (least_upper_bound ?7650 identity) =<= greatest_lower_bound identity (inverse (least_upper_bound ?7650 identity)) [7650] by Demod 4597 with 10 at 3
-Id : 4681, {_}: inverse (least_upper_bound ?7652 identity) =<= greatest_lower_bound identity (inverse (least_upper_bound identity ?7652)) [7652] by Super 4680 with 12 at 1,2,3
-Id : 4945, {_}: greatest_lower_bound ?7822 (inverse (least_upper_bound ?7821 identity)) =<= greatest_lower_bound (greatest_lower_bound ?7822 identity) (inverse (least_upper_bound identity ?7821)) [7821, 7822] by Super 14 with 4681 at 2,2
-Id : 732, {_}: greatest_lower_bound (least_upper_bound ?1553 ?1554) ?1553 =>= ?1553 [1554, 1553] by Super 10 with 24 at 3
-Id : 733, {_}: greatest_lower_bound (least_upper_bound ?1557 ?1556) ?1556 =>= ?1556 [1556, 1557] by Super 732 with 12 at 1,2
-Id : 8152, {_}: least_upper_bound (greatest_lower_bound ?11342 identity) (least_upper_bound ?11343 identity) =>= least_upper_bound ?11343 identity [11343, 11342] by Super 8147 with 651 at 2,3
-Id : 9033, {_}: least_upper_bound ?11999 identity =<= least_upper_bound (least_upper_bound (greatest_lower_bound ?11998 identity) ?11999) identity [11998, 11999] by Super 16 with 8152 at 2
-Id : 11655, {_}: least_upper_bound ?14440 identity =<= least_upper_bound identity (least_upper_bound (greatest_lower_bound ?14441 identity) ?14440) [14441, 14440] by Demod 9033 with 12 at 3
-Id : 11666, {_}: least_upper_bound (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) identity =>= least_upper_bound identity (greatest_lower_bound ?14473 identity) [14472, 14473] by Super 11655 with 22 at 2,3
-Id : 11846, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) =>= least_upper_bound identity (greatest_lower_bound ?14473 identity) [14472, 14473] by Demod 11666 with 12 at 2
-Id : 132, {_}: least_upper_bound ?359 (greatest_lower_bound ?360 ?359) =>= ?359 [360, 359] by Super 131 with 10 at 2,2
-Id : 11847, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) =>= identity [14472, 14473] by Demod 11846 with 132 at 3
-Id : 13334, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?16294 identity) ?16295) =>= greatest_lower_bound (greatest_lower_bound ?16294 identity) ?16295 [16295, 16294] by Super 733 with 11847 at 1,2
-Id : 13335, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound identity ?16297) ?16298) =>= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Super 13334 with 10 at 1,2,2
-Id : 13417, {_}: greatest_lower_bound identity (greatest_lower_bound identity (greatest_lower_bound ?16297 ?16298)) =>= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Demod 13335 with 14 at 2,2
-Id : 13418, {_}: greatest_lower_bound identity (greatest_lower_bound ?16297 ?16298) =<= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Demod 13417 with 116 at 2
-Id : 16433, {_}: greatest_lower_bound ?7822 (inverse (least_upper_bound ?7821 identity)) =<= greatest_lower_bound identity (greatest_lower_bound ?7822 (inverse (least_upper_bound identity ?7821))) [7821, 7822] by Demod 4945 with 13418 at 3
-Id : 698152, {_}: greatest_lower_bound (inverse ?666285) (inverse (least_upper_bound ?666285 identity)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698151 with 16433 at 2
-Id : 1371, {_}: multiply (inverse (least_upper_bound ?2583 ?2582)) (least_upper_bound ?2583 ?2582) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2583 ?2582)) ?2583) [2582, 2583] by Super 1363 with 502 at 2,2
-Id : 1403, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2583 ?2582)) ?2583) [2582, 2583] by Demod 1371 with 6 at 2
-Id : 139935, {_}: multiply identity ?154067 =<= least_upper_bound ?154067 (inverse (least_upper_bound (inverse ?154067) ?154066)) [154066, 154067] by Super 139882 with 1403 at 1,2
-Id : 140043, {_}: ?154067 =<= least_upper_bound ?154067 (inverse (least_upper_bound (inverse ?154067) ?154066)) [154066, 154067] by Demod 139935 with 4 at 2
-Id : 171519, {_}: greatest_lower_bound ?178895 (inverse (least_upper_bound (inverse ?178895) ?178896)) =>= inverse (least_upper_bound (inverse ?178895) ?178896) [178896, 178895] by Super 733 with 140043 at 1,2
-Id : 171521, {_}: greatest_lower_bound (inverse ?178900) (inverse (least_upper_bound ?178900 ?178901)) =>= inverse (least_upper_bound (inverse (inverse ?178900)) ?178901) [178901, 178900] by Super 171519 with 36 at 1,1,2,2
-Id : 172001, {_}: greatest_lower_bound (inverse ?178900) (inverse (least_upper_bound ?178900 ?178901)) =>= inverse (least_upper_bound ?178900 ?178901) [178901, 178900] by Demod 171521 with 36 at 1,1,3
-Id : 698153, {_}: inverse (least_upper_bound ?666285 identity) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698152 with 172001 at 2
-Id : 699473, {_}: inverse (greatest_lower_bound identity (inverse ?667289)) =>= least_upper_bound ?667289 identity [667289] by Super 36 with 698153 at 1,2
-Id : 702706, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 702705 with 12 at 3
-Id : 702705, {_}: least_upper_bound identity (multiply a b) =<= least_upper_bound (multiply a b) identity [] by Demod 520020 with 699473 at 3
-Id : 520020, {_}: least_upper_bound identity (multiply a b) =<= inverse (greatest_lower_bound identity (inverse (multiply a b))) [] by Demod 329 with 517346 at 3
-Id : 329, {_}: least_upper_bound identity (multiply a b) =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by Demod 2 with 12 at 2
-Id : 2, {_}: least_upper_bound (multiply a b) identity =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by prove_p23
-% SZS output end CNFRefutation for GRP186-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 94
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p33_1 is 75
- prove_p33 is 95
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_p33
-Last chance: 1246064633.01
-Last chance: all is indexed 1246065282.69
-Last chance: failed over 100 goal 1246065282.71
-FAILURE in 0 iterations
-% SZS status Timeout for GRP187-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 95
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang1 is 82
- multiply is 96
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang2 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-Last chance: 1246065587.09
-Last chance: all is indexed 1246067443.39
-Goal subsumed
-Found proof, 2161.793582s
-% SZS status Unsatisfiable for GRP200-1.p
-% SZS output start CNFRefutation for GRP200-1.p
-Id : 8, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 43, {_}: right_division (multiply ?78 ?79) ?79 =>= ?78 [79, 78] by right_division_multiply ?78 ?79
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 16, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 12, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 18, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 66, {_}: multiply (multiply ?133 (multiply ?134 ?135)) ?133 =?= multiply (multiply ?133 ?134) (multiply ?135 ?133) [135, 134, 133] by moufang1 ?133 ?134 ?135
-Id : 14, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 10, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 20, {_}: multiply (multiply ?22 (multiply ?23 ?24)) ?22 =?= multiply (multiply ?22 ?23) (multiply ?24 ?22) [24, 23, 22] by moufang1 ?22 ?23 ?24
-Id : 72, {_}: multiply (multiply ?154 (multiply ?155 (left_inverse ?154))) ?154 =>= multiply (multiply ?154 ?155) identity [155, 154] by Super 66 with 18 at 2,3
-Id : 105, {_}: multiply (multiply ?154 (multiply ?155 (left_inverse ?154))) ?154 =>= multiply ?154 ?155 [155, 154] by Demod 72 with 6 at 3
-Id : 251, {_}: right_division (multiply ?379 ?380) ?379 =<= multiply ?379 (multiply ?380 (left_inverse ?379)) [380, 379] by Super 14 with 105 at 1,2
-Id : 348, {_}: left_division ?485 (right_division (multiply ?485 ?486) ?485) =>= multiply ?486 (left_inverse ?485) [486, 485] by Super 10 with 251 at 2,2
-Id : 259, {_}: multiply (multiply ?406 (multiply ?407 (left_inverse ?406))) ?406 =>= multiply ?406 ?407 [407, 406] by Demod 72 with 6 at 3
-Id : 263, {_}: multiply (multiply ?417 ?416) ?417 =<= multiply ?417 (right_division ?416 (left_inverse ?417)) [416, 417] by Super 259 with 12 at 2,1,2
-Id : 354, {_}: right_division (multiply ?505 ?506) ?505 =<= multiply ?505 (multiply ?506 (left_inverse ?505)) [506, 505] by Super 14 with 105 at 1,2
-Id : 264, {_}: multiply (multiply ?419 identity) ?419 =?= multiply ?419 (left_inverse (left_inverse ?419)) [419] by Super 259 with 18 at 2,1,2
-Id : 282, {_}: multiply ?419 ?419 =<= multiply ?419 (left_inverse (left_inverse ?419)) [419] by Demod 264 with 6 at 1,2
-Id : 299, {_}: left_division ?448 (multiply ?448 ?448) =>= left_inverse (left_inverse ?448) [448] by Super 10 with 282 at 2,2
-Id : 308, {_}: ?448 =<= left_inverse (left_inverse ?448) [448] by Demod 299 with 10 at 2
-Id : 356, {_}: right_division (multiply (left_inverse ?510) ?511) (left_inverse ?510) =>= multiply (left_inverse ?510) (multiply ?511 ?510) [511, 510] by Super 354 with 308 at 2,2,3
-Id : 429, {_}: multiply (multiply ?579 (multiply (left_inverse ?579) ?580)) ?579 =?= multiply ?579 (multiply (left_inverse ?579) (multiply ?580 ?579)) [580, 579] by Super 263 with 356 at 2,3
-Id : 443, {_}: multiply (multiply ?579 (left_inverse ?579)) (multiply ?580 ?579) =?= multiply ?579 (multiply (left_inverse ?579) (multiply ?580 ?579)) [580, 579] by Demod 429 with 20 at 2
-Id : 56, {_}: left_division (left_inverse ?106) identity =>= ?106 [106] by Super 10 with 18 at 2,2
-Id : 50, {_}: left_division ?95 identity =>= right_inverse ?95 [95] by Super 10 with 16 at 2,2
-Id : 202, {_}: right_inverse (left_inverse ?106) =>= ?106 [106] by Demod 56 with 50 at 2
-Id : 323, {_}: right_inverse ?467 =>= left_inverse ?467 [467] by Super 202 with 308 at 1,2
-Id : 332, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 16 with 323 at 2,2
-Id : 444, {_}: multiply identity (multiply ?580 ?579) =<= multiply ?579 (multiply (left_inverse ?579) (multiply ?580 ?579)) [579, 580] by Demod 443 with 332 at 1,2
-Id : 445, {_}: multiply ?580 ?579 =<= multiply ?579 (multiply (left_inverse ?579) (multiply ?580 ?579)) [579, 580] by Demod 444 with 4 at 2
-Id : 1799, {_}: left_division ?1898 (right_division (multiply ?1897 ?1898) ?1898) =<= multiply (multiply (left_inverse ?1898) (multiply ?1897 ?1898)) (left_inverse ?1898) [1897, 1898] by Super 348 with 445 at 1,2,2
-Id : 1864, {_}: left_division ?1898 ?1897 =<= multiply (multiply (left_inverse ?1898) (multiply ?1897 ?1898)) (left_inverse ?1898) [1897, 1898] by Demod 1799 with 14 at 2,2
-Id : 393, {_}: multiply (multiply ?551 ?552) ?551 =<= multiply ?551 (right_division ?552 (left_inverse ?551)) [552, 551] by Super 259 with 12 at 2,1,2
-Id : 395, {_}: multiply (multiply (left_inverse ?556) ?557) (left_inverse ?556) =>= multiply (left_inverse ?556) (right_division ?557 ?556) [557, 556] by Super 393 with 308 at 2,2,3
-Id : 1865, {_}: left_division ?1898 ?1897 =<= multiply (left_inverse ?1898) (right_division (multiply ?1897 ?1898) ?1898) [1897, 1898] by Demod 1864 with 395 at 3
-Id : 1866, {_}: left_division ?1898 ?1897 =<= multiply (left_inverse ?1898) ?1897 [1897, 1898] by Demod 1865 with 14 at 2,3
-Id : 1942, {_}: multiply (multiply ?2034 (multiply ?2035 (left_inverse ?2033))) ?2034 =>= multiply (multiply ?2034 ?2035) (left_division ?2033 ?2034) [2033, 2035, 2034] by Super 20 with 1866 at 2,3
-Id : 1961, {_}: left_division ?2091 ?2092 =<= multiply (left_inverse ?2091) ?2092 [2092, 2091] by Demod 1865 with 14 at 2,3
-Id : 1963, {_}: left_division (left_inverse ?2096) ?2097 =>= multiply ?2096 ?2097 [2097, 2096] by Super 1961 with 308 at 1,3
-Id : 391, {_}: left_division ?545 (multiply (multiply ?545 ?546) ?545) =>= right_division ?546 (left_inverse ?545) [546, 545] by Super 10 with 263 at 2,2
-Id : 8162, {_}: multiply (multiply ?7520 (multiply ?7521 (left_inverse ?7522))) ?7520 =>= multiply (multiply ?7520 ?7521) (left_division ?7522 ?7520) [7522, 7521, 7520] by Super 20 with 1866 at 2,3
-Id : 8170, {_}: multiply (multiply ?7554 (left_inverse ?7555)) ?7554 =<= multiply (multiply ?7554 identity) (left_division ?7555 ?7554) [7555, 7554] by Super 8162 with 4 at 2,1,2
-Id : 8237, {_}: multiply (multiply ?7554 (left_inverse ?7555)) ?7554 =>= multiply ?7554 (left_division ?7555 ?7554) [7555, 7554] by Demod 8170 with 6 at 1,3
-Id : 46, {_}: right_division ?85 (left_division ?86 ?85) =>= ?86 [86, 85] by Super 43 with 8 at 1,2
-Id : 87, {_}: multiply (multiply ?211 identity) ?211 =<= multiply (multiply ?211 ?212) (multiply (right_inverse ?212) ?211) [212, 211] by Super 66 with 16 at 2,1,2
-Id : 120, {_}: multiply ?211 ?211 =<= multiply (multiply ?211 ?212) (multiply (right_inverse ?212) ?211) [212, 211] by Demod 87 with 6 at 1,2
-Id : 1158, {_}: multiply ?211 ?211 =<= multiply (multiply ?211 ?212) (multiply (left_inverse ?212) ?211) [212, 211] by Demod 120 with 323 at 1,2,3
-Id : 1253, {_}: left_division (multiply ?1294 ?1295) (multiply ?1294 ?1294) =>= multiply (left_inverse ?1295) ?1294 [1295, 1294] by Super 10 with 1158 at 2,2
-Id : 1260, {_}: left_division ?1311 (multiply ?1312 ?1312) =<= multiply (left_inverse (left_division ?1312 ?1311)) ?1312 [1312, 1311] by Super 1253 with 8 at 1,2
-Id : 1310, {_}: right_division (left_division ?1373 (multiply ?1374 ?1374)) ?1374 =>= left_inverse (left_division ?1374 ?1373) [1374, 1373] by Super 14 with 1260 at 1,2
-Id : 2751, {_}: right_division (multiply ?3003 (multiply ?3004 ?3004)) ?3004 =>= left_inverse (left_division ?3004 (left_inverse ?3003)) [3004, 3003] by Super 1310 with 1963 at 1,2
-Id : 2759, {_}: right_division (multiply (multiply ?3027 (multiply ?3026 ?3027)) ?3027) ?3027 =>= left_inverse (left_division ?3027 (left_inverse (multiply ?3027 ?3026))) [3026, 3027] by Super 2751 with 20 at 1,2
-Id : 2904, {_}: multiply ?3141 (multiply ?3142 ?3141) =<= left_inverse (left_division ?3141 (left_inverse (multiply ?3141 ?3142))) [3142, 3141] by Demod 2759 with 14 at 2
-Id : 2907, {_}: multiply ?3149 (multiply (left_division ?3149 ?3148) ?3149) =>= left_inverse (left_division ?3149 (left_inverse ?3148)) [3148, 3149] by Super 2904 with 8 at 1,2,1,3
-Id : 4946, {_}: left_division ?4933 (left_inverse (left_division ?4933 (left_inverse ?4934))) =>= multiply (left_division ?4933 ?4934) ?4933 [4934, 4933] by Super 10 with 2907 at 2,2
-Id : 5074, {_}: left_division ?5067 (left_inverse (left_division ?5067 ?5068)) =<= multiply (left_division ?5067 (left_inverse ?5068)) ?5067 [5068, 5067] by Super 4946 with 308 at 2,1,2,2
-Id : 2787, {_}: multiply ?3027 (multiply ?3026 ?3027) =<= left_inverse (left_division ?3027 (left_inverse (multiply ?3027 ?3026))) [3026, 3027] by Demod 2759 with 14 at 2
-Id : 2896, {_}: left_division ?3111 (left_inverse (multiply ?3111 ?3112)) =>= left_inverse (multiply ?3111 (multiply ?3112 ?3111)) [3112, 3111] by Super 308 with 2787 at 1,3
-Id : 5085, {_}: left_division ?5102 (left_inverse (left_division ?5102 (multiply ?5102 ?5101))) =<= multiply (left_inverse (multiply ?5102 (multiply ?5101 ?5102))) ?5102 [5101, 5102] by Super 5074 with 2896 at 1,3
-Id : 5138, {_}: left_division ?5102 (left_inverse ?5101) =<= multiply (left_inverse (multiply ?5102 (multiply ?5101 ?5102))) ?5102 [5101, 5102] by Demod 5085 with 10 at 1,2,2
-Id : 5139, {_}: left_division ?5102 (left_inverse ?5101) =<= left_division (multiply ?5102 (multiply ?5101 ?5102)) ?5102 [5101, 5102] by Demod 5138 with 1866 at 3
-Id : 6213, {_}: right_division ?5851 (left_division ?5851 (left_inverse ?5852)) =>= multiply ?5851 (multiply ?5852 ?5851) [5852, 5851] by Super 46 with 5139 at 2,2
-Id : 6217, {_}: right_division ?5864 (left_division ?5864 ?5863) =<= multiply ?5864 (multiply (left_inverse ?5863) ?5864) [5863, 5864] by Super 6213 with 308 at 2,2,2
-Id : 6264, {_}: right_division ?5864 (left_division ?5864 ?5863) =<= multiply ?5864 (left_division ?5863 ?5864) [5863, 5864] by Demod 6217 with 1866 at 2,3
-Id : 8238, {_}: multiply (multiply ?7554 (left_inverse ?7555)) ?7554 =>= right_division ?7554 (left_division ?7554 ?7555) [7555, 7554] by Demod 8237 with 6264 at 3
-Id : 8310, {_}: left_division ?7723 (right_division ?7723 (left_division ?7723 ?7724)) =>= right_division (left_inverse ?7724) (left_inverse ?7723) [7724, 7723] by Super 391 with 8238 at 2,2
-Id : 6327, {_}: left_division ?5945 (right_division ?5945 (left_division ?5945 ?5946)) =>= left_division ?5946 ?5945 [5946, 5945] by Super 10 with 6264 at 2,2
-Id : 8507, {_}: left_division ?7882 ?7883 =<= right_division (left_inverse ?7882) (left_inverse ?7883) [7883, 7882] by Demod 8310 with 6327 at 2
-Id : 8511, {_}: left_division ?7895 (left_inverse ?7894) =>= right_division (left_inverse ?7895) ?7894 [7894, 7895] by Super 8507 with 308 at 2,3
-Id : 8660, {_}: right_division (left_inverse (left_inverse ?7973)) ?7972 =>= multiply ?7973 (left_inverse ?7972) [7972, 7973] by Super 1963 with 8511 at 2
-Id : 8725, {_}: right_division ?7973 ?7972 =<= multiply ?7973 (left_inverse ?7972) [7972, 7973] by Demod 8660 with 308 at 1,2
-Id : 9105, {_}: multiply (multiply ?2034 (right_division ?2035 ?2033)) ?2034 =?= multiply (multiply ?2034 ?2035) (left_division ?2033 ?2034) [2033, 2035, 2034] by Demod 1942 with 8725 at 2,1,2
-Id : 2111, {_}: right_division (left_division ?2205 ?2206) ?2206 =>= left_inverse ?2205 [2206, 2205] by Super 14 with 1866 at 1,2
-Id : 38, {_}: left_division (right_division ?64 ?65) ?64 =>= ?65 [65, 64] by Super 10 with 12 at 2,2
-Id : 2114, {_}: right_division ?2213 ?2214 =<= left_inverse (right_division ?2214 ?2213) [2214, 2213] by Super 2111 with 38 at 1,2
-Id : 8385, {_}: left_division ?7724 ?7723 =<= right_division (left_inverse ?7724) (left_inverse ?7723) [7723, 7724] by Demod 8310 with 6327 at 2
-Id : 8499, {_}: right_division (left_inverse ?7861) (left_inverse ?7860) =>= left_inverse (left_division ?7860 ?7861) [7860, 7861] by Super 2114 with 8385 at 1,3
-Id : 8852, {_}: left_division ?8187 ?8188 =<= left_inverse (left_division ?8188 ?8187) [8188, 8187] by Demod 8499 with 8385 at 2
-Id : 8853, {_}: left_division (multiply ?8191 ?8190) ?8191 =>= left_inverse ?8190 [8190, 8191] by Super 8852 with 10 at 1,3
-Id : 9898, {_}: multiply (multiply ?9062 (right_division ?9064 (multiply ?9062 ?9063))) ?9062 =>= multiply (multiply ?9062 ?9064) (left_inverse ?9063) [9063, 9064, 9062] by Super 9105 with 8853 at 2,3
-Id : 9970, {_}: multiply (multiply ?9062 (right_division ?9064 (multiply ?9062 ?9063))) ?9062 =>= right_division (multiply ?9062 ?9064) ?9063 [9063, 9064, 9062] by Demod 9898 with 8725 at 3
-Id : 8518, {_}: left_division (left_inverse ?7917) ?7918 =>= right_division ?7917 (left_inverse ?7918) [7918, 7917] by Super 8507 with 308 at 1,3
-Id : 8952, {_}: multiply ?8332 ?8333 =<= right_division ?8332 (left_inverse ?8333) [8333, 8332] by Demod 8518 with 1963 at 2
-Id : 8956, {_}: multiply ?8345 (right_division ?8344 ?8343) =>= right_division ?8345 (right_division ?8343 ?8344) [8343, 8344, 8345] by Super 8952 with 2114 at 2,3
-Id : 95690, {_}: multiply (right_division ?9062 (right_division (multiply ?9062 ?9063) ?9064)) ?9062 =>= right_division (multiply ?9062 ?9064) ?9063 [9064, 9063, 9062] by Demod 9970 with 8956 at 1,2
-Id : 2150, {_}: left_division (right_division ?2249 ?2250) ?2251 =<= multiply (right_division ?2250 ?2249) ?2251 [2251, 2250, 2249] by Super 1963 with 2114 at 1,2
-Id : 95691, {_}: left_division (right_division (right_division (multiply ?9062 ?9063) ?9064) ?9062) ?9062 =>= right_division (multiply ?9062 ?9064) ?9063 [9064, 9063, 9062] by Demod 95690 with 2150 at 2
-Id : 9121, {_}: multiply (right_division ?7554 ?7555) ?7554 =>= right_division ?7554 (left_division ?7554 ?7555) [7555, 7554] by Demod 8238 with 8725 at 1,2
-Id : 9127, {_}: left_division (right_division ?7555 ?7554) ?7554 =>= right_division ?7554 (left_division ?7554 ?7555) [7554, 7555] by Demod 9121 with 2150 at 2
-Id : 95777, {_}: right_division ?99014 (left_division ?99014 (right_division (multiply ?99014 ?99015) ?99016)) =>= right_division (multiply ?99014 ?99016) ?99015 [99016, 99015, 99014] by Demod 95691 with 9127 at 2
-Id : 95822, {_}: right_division ?99197 (left_division ?99197 ?99196) =<= right_division (multiply ?99197 (left_division ?99196 (multiply ?99197 ?99198))) ?99198 [99198, 99196, 99197] by Super 95777 with 46 at 2,2,2
-Id : 8545, {_}: left_division ?7861 ?7860 =<= left_inverse (left_division ?7860 ?7861) [7860, 7861] by Demod 8499 with 8385 at 2
-Id : 8958, {_}: multiply ?8352 (left_division ?8351 ?8350) =>= right_division ?8352 (left_division ?8350 ?8351) [8350, 8351, 8352] by Super 8952 with 8545 at 2,3
-Id : 392711, {_}: right_division ?377317 (left_division ?377317 ?377318) =<= right_division (right_division ?377317 (left_division (multiply ?377317 ?377319) ?377318)) ?377319 [377319, 377318, 377317] by Demod 95822 with 8958 at 1,3
-Id : 85, {_}: multiply (multiply ?204 ?203) ?204 =<= multiply (multiply ?204 ?205) (multiply (left_division ?205 ?203) ?204) [205, 203, 204] by Super 66 with 8 at 2,1,2
-Id : 8498, {_}: left_division (right_division (left_inverse ?7857) (left_inverse ?7856)) ?7858 =>= multiply (left_division ?7856 ?7857) ?7858 [7858, 7856, 7857] by Super 2150 with 8385 at 1,3
-Id : 8546, {_}: left_division (left_division ?7857 ?7856) ?7858 =<= multiply (left_division ?7856 ?7857) ?7858 [7858, 7856, 7857] by Demod 8498 with 8385 at 1,2
-Id : 60291, {_}: multiply (multiply ?204 ?203) ?204 =<= multiply (multiply ?204 ?205) (left_division (left_division ?203 ?205) ?204) [205, 203, 204] by Demod 85 with 8546 at 2,3
-Id : 60292, {_}: multiply (multiply ?204 ?203) ?204 =<= right_division (multiply ?204 ?205) (left_division ?204 (left_division ?203 ?205)) [205, 203, 204] by Demod 60291 with 8958 at 3
-Id : 60311, {_}: left_division (multiply (multiply ?63053 ?63054) ?63053) (multiply ?63053 ?63055) =>= left_division ?63053 (left_division ?63054 ?63055) [63055, 63054, 63053] by Super 38 with 60292 at 1,2
-Id : 392811, {_}: right_division (multiply ?377704 ?377702) (left_division (multiply ?377704 ?377702) (multiply ?377704 ?377703)) =>= right_division (right_division (multiply ?377704 ?377702) (left_division ?377704 (left_division ?377702 ?377703))) ?377704 [377703, 377702, 377704] by Super 392711 with 60311 at 2,1,3
-Id : 8860, {_}: left_division ?8210 (left_inverse ?8209) =>= left_inverse (multiply ?8209 ?8210) [8209, 8210] by Super 8852 with 1963 at 1,3
-Id : 8887, {_}: right_division (left_inverse ?8210) ?8209 =>= left_inverse (multiply ?8209 ?8210) [8209, 8210] by Demod 8860 with 8511 at 2
-Id : 9474, {_}: multiply (multiply ?8644 (left_inverse (multiply ?8643 ?8642))) ?8644 =?= multiply (multiply ?8644 (left_inverse ?8642)) (left_division ?8643 ?8644) [8642, 8643, 8644] by Super 9105 with 8887 at 2,1,2
-Id : 9504, {_}: multiply (right_division ?8644 (multiply ?8643 ?8642)) ?8644 =<= multiply (multiply ?8644 (left_inverse ?8642)) (left_division ?8643 ?8644) [8642, 8643, 8644] by Demod 9474 with 8725 at 1,2
-Id : 9505, {_}: left_division (right_division (multiply ?8643 ?8642) ?8644) ?8644 =<= multiply (multiply ?8644 (left_inverse ?8642)) (left_division ?8643 ?8644) [8644, 8642, 8643] by Demod 9504 with 2150 at 2
-Id : 9506, {_}: right_division ?8644 (left_division ?8644 (multiply ?8643 ?8642)) =<= multiply (multiply ?8644 (left_inverse ?8642)) (left_division ?8643 ?8644) [8642, 8643, 8644] by Demod 9505 with 9127 at 2
-Id : 9507, {_}: right_division ?8644 (left_division ?8644 (multiply ?8643 ?8642)) =<= multiply (right_division ?8644 ?8642) (left_division ?8643 ?8644) [8642, 8643, 8644] by Demod 9506 with 8725 at 1,3
-Id : 9508, {_}: right_division ?8644 (left_division ?8644 (multiply ?8643 ?8642)) =<= left_division (right_division ?8642 ?8644) (left_division ?8643 ?8644) [8642, 8643, 8644] by Demod 9507 with 2150 at 3
-Id : 10427, {_}: left_division (right_division ?9734 ?9735) (left_division ?9732 ?9733) =>= right_division (right_division ?9735 ?9734) (left_division ?9733 ?9732) [9733, 9732, 9735, 9734] by Super 2150 with 8958 at 3
-Id : 16292, {_}: right_division ?8644 (left_division ?8644 (multiply ?8643 ?8642)) =?= right_division (right_division ?8644 ?8642) (left_division ?8644 ?8643) [8642, 8643, 8644] by Demod 9508 with 10427 at 3
-Id : 393302, {_}: right_division (right_division (multiply ?377704 ?377702) ?377703) (left_division (multiply ?377704 ?377702) ?377704) =?= right_division (right_division (multiply ?377704 ?377702) (left_division ?377704 (left_division ?377702 ?377703))) ?377704 [377703, 377702, 377704] by Demod 392811 with 16292 at 2
-Id : 393303, {_}: right_division (right_division (multiply ?377704 ?377702) ?377703) (left_inverse ?377702) =<= right_division (right_division (multiply ?377704 ?377702) (left_division ?377704 (left_division ?377702 ?377703))) ?377704 [377703, 377702, 377704] by Demod 393302 with 8853 at 2,2
-Id : 8584, {_}: multiply ?7917 ?7918 =<= right_division ?7917 (left_inverse ?7918) [7918, 7917] by Demod 8518 with 1963 at 2
-Id : 393304, {_}: multiply (right_division (multiply ?377704 ?377702) ?377703) ?377702 =<= right_division (right_division (multiply ?377704 ?377702) (left_division ?377704 (left_division ?377702 ?377703))) ?377704 [377703, 377702, 377704] by Demod 393303 with 8584 at 2
-Id : 393305, {_}: left_division (right_division ?377703 (multiply ?377704 ?377702)) ?377702 =<= right_division (right_division (multiply ?377704 ?377702) (left_division ?377704 (left_division ?377702 ?377703))) ?377704 [377702, 377704, 377703] by Demod 393304 with 2150 at 2
-Id : 8144, {_}: right_division (multiply (multiply ?7446 ?7447) (left_division ?7448 ?7446)) ?7446 =>= multiply ?7446 (multiply ?7447 (left_inverse ?7448)) [7448, 7447, 7446] by Super 14 with 1942 at 1,2
-Id : 82754, {_}: right_division (right_division (multiply ?7446 ?7447) (left_division ?7446 ?7448)) ?7446 =>= multiply ?7446 (multiply ?7447 (left_inverse ?7448)) [7448, 7447, 7446] by Demod 8144 with 8958 at 1,2
-Id : 82755, {_}: right_division (right_division (multiply ?7446 ?7447) (left_division ?7446 ?7448)) ?7446 =>= multiply ?7446 (right_division ?7447 ?7448) [7448, 7447, 7446] by Demod 82754 with 8725 at 2,3
-Id : 82756, {_}: right_division (right_division (multiply ?7446 ?7447) (left_division ?7446 ?7448)) ?7446 =>= right_division ?7446 (right_division ?7448 ?7447) [7448, 7447, 7446] by Demod 82755 with 8956 at 3
-Id : 393655, {_}: left_division (right_division ?378971 (multiply ?378972 ?378973)) ?378973 =>= right_division ?378972 (right_division (left_division ?378973 ?378971) ?378973) [378973, 378972, 378971] by Demod 393305 with 82756 at 3
-Id : 393708, {_}: left_division (left_inverse (multiply (multiply ?379185 ?379186) ?379184)) ?379186 =>= right_division ?379185 (right_division (left_division ?379186 (left_inverse ?379184)) ?379186) [379184, 379186, 379185] by Super 393655 with 8887 at 1,2
-Id : 394347, {_}: multiply (multiply (multiply ?379185 ?379186) ?379184) ?379186 =<= right_division ?379185 (right_division (left_division ?379186 (left_inverse ?379184)) ?379186) [379184, 379186, 379185] by Demod 393708 with 1963 at 2
-Id : 9439, {_}: left_division ?7895 (left_inverse ?7894) =>= left_inverse (multiply ?7894 ?7895) [7894, 7895] by Demod 8511 with 8887 at 3
-Id : 394348, {_}: multiply (multiply (multiply ?379185 ?379186) ?379184) ?379186 =<= right_division ?379185 (right_division (left_inverse (multiply ?379184 ?379186)) ?379186) [379184, 379186, 379185] by Demod 394347 with 9439 at 1,2,3
-Id : 394349, {_}: multiply (multiply (multiply ?379185 ?379186) ?379184) ?379186 =<= right_division ?379185 (left_inverse (multiply ?379186 (multiply ?379184 ?379186))) [379184, 379186, 379185] by Demod 394348 with 8887 at 2,3
-Id : 394350, {_}: multiply (multiply (multiply ?379185 ?379186) ?379184) ?379186 =?= multiply ?379185 (multiply ?379186 (multiply ?379184 ?379186)) [379184, 379186, 379185] by Demod 394349 with 8584 at 3
-Id : 992665, {_}: multiply a (multiply b (multiply c b)) === multiply a (multiply b (multiply c b)) [] by Super 2 with 394350 at 2
-Id : 2, {_}: multiply (multiply (multiply a b) c) b =>= multiply a (multiply b (multiply c b)) [] by prove_moufang2
-% SZS output end CNFRefutation for GRP200-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang3 is 82
- multiply is 95
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang1 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-Last chance: 1246067751.11
-Last chance: all is indexed 1246069777.56
-Goal subsumed
-Found proof, 2330.385313s
-% SZS status Unsatisfiable for GRP202-1.p
-% SZS output start CNFRefutation for GRP202-1.p
-Id : 43, {_}: right_division (multiply ?78 ?79) ?79 =>= ?78 [79, 78] by right_division_multiply ?78 ?79
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 18, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 8, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 16, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 68, {_}: multiply (multiply (multiply ?140 ?141) ?140) ?142 =?= multiply ?140 (multiply ?141 (multiply ?140 ?142)) [142, 141, 140] by moufang3 ?140 ?141 ?142
-Id : 14, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 20, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =?= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
-Id : 12, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 10, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 38, {_}: left_division (right_division ?64 ?65) ?64 =>= ?65 [65, 64] by Super 10 with 12 at 2,2
-Id : 73, {_}: multiply (multiply (multiply ?158 ?159) ?158) (right_inverse ?158) =>= multiply ?158 (multiply ?159 identity) [159, 158] by Super 68 with 16 at 2,2,3
-Id : 106, {_}: multiply (multiply (multiply ?158 ?159) ?158) (right_inverse ?158) =>= multiply ?158 ?159 [159, 158] by Demod 73 with 6 at 2,3
-Id : 302, {_}: right_division (multiply ?452 ?453) (right_inverse ?452) =>= multiply (multiply ?452 ?453) ?452 [453, 452] by Super 14 with 106 at 1,2
-Id : 307, {_}: right_division ?464 (right_inverse ?465) =<= multiply (multiply ?465 (left_division ?465 ?464)) ?465 [465, 464] by Super 302 with 8 at 1,2
-Id : 362, {_}: right_division ?516 (right_inverse ?517) =>= multiply ?516 ?517 [517, 516] by Demod 307 with 8 at 1,3
-Id : 56, {_}: left_division (left_inverse ?106) identity =>= ?106 [106] by Super 10 with 18 at 2,2
-Id : 50, {_}: left_division ?95 identity =>= right_inverse ?95 [95] by Super 10 with 16 at 2,2
-Id : 200, {_}: right_inverse (left_inverse ?106) =>= ?106 [106] by Demod 56 with 50 at 2
-Id : 363, {_}: right_division ?520 ?519 =<= multiply ?520 (left_inverse ?519) [519, 520] by Super 362 with 200 at 2,2
-Id : 421, {_}: multiply (multiply (multiply ?562 ?564) ?562) (left_inverse ?563) =>= multiply ?562 (multiply ?564 (right_division ?562 ?563)) [563, 564, 562] by Super 20 with 363 at 2,2,3
-Id : 650, {_}: right_division (multiply (multiply ?862 ?863) ?862) ?864 =<= multiply ?862 (multiply ?863 (right_division ?862 ?864)) [864, 863, 862] by Demod 421 with 363 at 2
-Id : 657, {_}: right_division (multiply (multiply ?887 identity) ?887) ?888 =>= multiply ?887 (right_division ?887 ?888) [888, 887] by Super 650 with 4 at 2,3
-Id : 692, {_}: right_division (multiply ?940 ?940) ?941 =<= multiply ?940 (right_division ?940 ?941) [941, 940] by Demod 657 with 6 at 1,1,2
-Id : 46, {_}: right_division ?85 (left_division ?86 ?85) =>= ?86 [86, 85] by Super 43 with 8 at 1,2
-Id : 695, {_}: right_division (multiply ?949 ?949) (left_division ?948 ?949) =>= multiply ?949 ?948 [948, 949] by Super 692 with 46 at 2,3
-Id : 1572, {_}: left_division (multiply ?1757 ?1758) (multiply ?1757 ?1757) =>= left_division ?1758 ?1757 [1758, 1757] by Super 38 with 695 at 1,2
-Id : 1580, {_}: left_division ?1779 (multiply (right_division ?1779 ?1780) (right_division ?1779 ?1780)) =>= left_division ?1780 (right_division ?1779 ?1780) [1780, 1779] by Super 1572 with 12 at 1,2
-Id : 88, {_}: multiply (multiply identity ?215) ?216 =<= multiply ?215 (multiply (right_inverse ?215) (multiply ?215 ?216)) [216, 215] by Super 68 with 16 at 1,1,2
-Id : 121, {_}: multiply ?215 ?216 =<= multiply ?215 (multiply (right_inverse ?215) (multiply ?215 ?216)) [216, 215] by Demod 88 with 4 at 1,2
-Id : 44, {_}: right_division ?81 ?81 =>= identity [81] by Super 43 with 4 at 1,2
-Id : 328, {_}: right_division ?464 (right_inverse ?465) =>= multiply ?464 ?465 [465, 464] by Demod 307 with 8 at 1,3
-Id : 357, {_}: multiply (right_inverse ?503) ?503 =>= identity [503] by Super 44 with 328 at 2
-Id : 376, {_}: right_division identity ?536 =>= right_inverse ?536 [536] by Super 14 with 357 at 1,2
-Id : 55, {_}: right_division identity ?104 =>= left_inverse ?104 [104] by Super 14 with 18 at 1,2
-Id : 395, {_}: left_inverse ?536 =<= right_inverse ?536 [536] by Demod 376 with 55 at 2
-Id : 2631, {_}: multiply ?215 ?216 =<= multiply ?215 (multiply (left_inverse ?215) (multiply ?215 ?216)) [216, 215] by Demod 121 with 395 at 1,2,3
-Id : 2643, {_}: left_division ?2950 (multiply ?2950 ?2951) =<= multiply (left_inverse ?2950) (multiply ?2950 ?2951) [2951, 2950] by Super 10 with 2631 at 2,2
-Id : 2675, {_}: ?2951 =<= multiply (left_inverse ?2950) (multiply ?2950 ?2951) [2950, 2951] by Demod 2643 with 10 at 2
-Id : 2822, {_}: left_division (left_inverse ?3188) ?3189 =>= multiply ?3188 ?3189 [3189, 3188] by Super 10 with 2675 at 2,2
-Id : 407, {_}: left_inverse (left_inverse ?106) =>= ?106 [106] by Demod 200 with 395 at 2
-Id : 2823, {_}: left_division ?3191 ?3192 =<= multiply (left_inverse ?3191) ?3192 [3192, 3191] by Super 2822 with 407 at 1,2
-Id : 2737, {_}: left_division (left_inverse ?3048) ?3047 =>= multiply ?3048 ?3047 [3047, 3048] by Super 10 with 2675 at 2,2
-Id : 361, {_}: left_division (multiply ?513 ?514) ?513 =>= right_inverse ?514 [514, 513] by Super 38 with 328 at 1,2
-Id : 487, {_}: left_division (multiply ?513 ?514) ?513 =>= left_inverse ?514 [514, 513] by Demod 361 with 395 at 3
-Id : 2742, {_}: left_division ?3064 (left_inverse ?3065) =>= left_inverse (multiply ?3065 ?3064) [3065, 3064] by Super 487 with 2675 at 1,2
-Id : 2875, {_}: left_inverse (multiply ?3221 (left_inverse ?3222)) =>= multiply ?3222 (left_inverse ?3221) [3222, 3221] by Super 2737 with 2742 at 2
-Id : 2943, {_}: left_inverse (right_division ?3221 ?3222) =<= multiply ?3222 (left_inverse ?3221) [3222, 3221] by Demod 2875 with 363 at 1,2
-Id : 2944, {_}: left_inverse (right_division ?3221 ?3222) =>= right_division ?3222 ?3221 [3222, 3221] by Demod 2943 with 363 at 3
-Id : 3156, {_}: left_division (right_division ?3443 ?3444) ?3445 =<= multiply (right_division ?3444 ?3443) ?3445 [3445, 3444, 3443] by Super 2823 with 2944 at 1,3
-Id : 23022, {_}: left_division ?1779 (left_division (right_division ?1780 ?1779) (right_division ?1779 ?1780)) =>= left_division ?1780 (right_division ?1779 ?1780) [1780, 1779] by Demod 1580 with 3156 at 2,2
-Id : 3157, {_}: right_division ?3449 (right_division ?3447 ?3448) =<= multiply ?3449 (right_division ?3448 ?3447) [3448, 3447, 3449] by Super 363 with 2944 at 2,3
-Id : 3956, {_}: left_division (right_division ?4457 ?4458) (right_division ?4456 ?4455) =>= right_division (right_division ?4458 ?4457) (right_division ?4455 ?4456) [4455, 4456, 4458, 4457] by Super 3156 with 3157 at 3
-Id : 23023, {_}: left_division ?1779 (right_division (right_division ?1779 ?1780) (right_division ?1780 ?1779)) =>= left_division ?1780 (right_division ?1779 ?1780) [1780, 1779] by Demod 23022 with 3956 at 2,2
-Id : 492, {_}: left_division (multiply ?638 ?639) ?638 =>= left_inverse ?639 [639, 638] by Demod 361 with 395 at 3
-Id : 495, {_}: left_division ?645 ?646 =<= left_inverse (left_division ?646 ?645) [646, 645] by Super 492 with 8 at 1,2
-Id : 403, {_}: left_division ?95 identity =>= left_inverse ?95 [95] by Demod 50 with 395 at 3
-Id : 2980, {_}: multiply (multiply (multiply ?3354 (left_inverse ?3353)) ?3354) ?3355 =>= multiply ?3354 (left_division ?3353 (multiply ?3354 ?3355)) [3355, 3353, 3354] by Super 20 with 2823 at 2,3
-Id : 3069, {_}: multiply (multiply (right_division ?3354 ?3353) ?3354) ?3355 =?= multiply ?3354 (left_division ?3353 (multiply ?3354 ?3355)) [3355, 3353, 3354] by Demod 2980 with 363 at 1,1,2
-Id : 408, {_}: right_division ?464 (left_inverse ?465) =>= multiply ?464 ?465 [465, 464] by Demod 328 with 395 at 2,2
-Id : 514, {_}: right_division ?671 (left_division ?669 ?670) =<= multiply ?671 (left_division ?670 ?669) [670, 669, 671] by Super 408 with 495 at 2,2
-Id : 3070, {_}: multiply (multiply (right_division ?3354 ?3353) ?3354) ?3355 =>= right_division ?3354 (left_division (multiply ?3354 ?3355) ?3353) [3355, 3353, 3354] by Demod 3069 with 514 at 3
-Id : 4877, {_}: multiply (left_division (right_division ?3353 ?3354) ?3354) ?3355 =>= right_division ?3354 (left_division (multiply ?3354 ?3355) ?3353) [3355, 3354, 3353] by Demod 3070 with 3156 at 1,2
-Id : 2825, {_}: left_division (left_division ?3196 ?3197) ?3198 =<= multiply (left_division ?3197 ?3196) ?3198 [3198, 3197, 3196] by Super 2822 with 495 at 1,2
-Id : 4878, {_}: left_division (left_division ?3354 (right_division ?3353 ?3354)) ?3355 =>= right_division ?3354 (left_division (multiply ?3354 ?3355) ?3353) [3355, 3353, 3354] by Demod 4877 with 2825 at 2
-Id : 4885, {_}: right_division ?5383 (left_division (multiply ?5383 identity) ?5384) =>= left_inverse (left_division ?5383 (right_division ?5384 ?5383)) [5384, 5383] by Super 403 with 4878 at 2
-Id : 4962, {_}: right_division ?5383 (left_division ?5383 ?5384) =<= left_inverse (left_division ?5383 (right_division ?5384 ?5383)) [5384, 5383] by Demod 4885 with 6 at 1,2,2
-Id : 4963, {_}: right_division ?5383 (left_division ?5383 ?5384) =<= left_division (right_division ?5384 ?5383) ?5383 [5384, 5383] by Demod 4962 with 495 at 3
-Id : 5068, {_}: left_division ?5634 (right_division ?5635 ?5634) =<= left_inverse (right_division ?5634 (left_division ?5634 ?5635)) [5635, 5634] by Super 495 with 4963 at 1,3
-Id : 5126, {_}: left_division ?5634 (right_division ?5635 ?5634) =>= right_division (left_division ?5634 ?5635) ?5634 [5635, 5634] by Demod 5068 with 2944 at 3
-Id : 23066, {_}: left_division ?25029 (right_division (right_division ?25029 ?25030) (right_division ?25030 ?25029)) =>= right_division (left_division ?25030 ?25029) ?25030 [25030, 25029] by Demod 23023 with 5126 at 3
-Id : 2978, {_}: right_division (left_inverse ?3346) ?3347 =<= left_division ?3346 (left_inverse ?3347) [3347, 3346] by Super 363 with 2823 at 3
-Id : 3081, {_}: right_division (left_inverse ?3346) ?3347 =>= left_inverse (multiply ?3347 ?3346) [3347, 3346] by Demod 2978 with 2742 at 3
-Id : 23086, {_}: left_division ?25090 (right_division (right_division ?25090 (left_inverse ?25089)) (left_inverse (multiply ?25090 ?25089))) =>= right_division (left_division (left_inverse ?25089) ?25090) (left_inverse ?25089) [25089, 25090] by Super 23066 with 3081 at 2,2,2
-Id : 23342, {_}: left_division ?25090 (multiply (right_division ?25090 (left_inverse ?25089)) (multiply ?25090 ?25089)) =>= right_division (left_division (left_inverse ?25089) ?25090) (left_inverse ?25089) [25089, 25090] by Demod 23086 with 408 at 2,2
-Id : 23343, {_}: left_division ?25090 (left_division (right_division (left_inverse ?25089) ?25090) (multiply ?25090 ?25089)) =>= right_division (left_division (left_inverse ?25089) ?25090) (left_inverse ?25089) [25089, 25090] by Demod 23342 with 3156 at 2,2
-Id : 23344, {_}: left_division ?25090 (left_division (left_inverse (multiply ?25090 ?25089)) (multiply ?25090 ?25089)) =>= right_division (left_division (left_inverse ?25089) ?25090) (left_inverse ?25089) [25089, 25090] by Demod 23343 with 3081 at 1,2,2
-Id : 23345, {_}: left_division ?25090 (multiply (multiply ?25090 ?25089) (multiply ?25090 ?25089)) =>= right_division (left_division (left_inverse ?25089) ?25090) (left_inverse ?25089) [25089, 25090] by Demod 23344 with 2737 at 2,2
-Id : 23346, {_}: left_division ?25090 (multiply (multiply ?25090 ?25089) (multiply ?25090 ?25089)) =>= multiply (left_division (left_inverse ?25089) ?25090) ?25089 [25089, 25090] by Demod 23345 with 408 at 3
-Id : 23347, {_}: left_division ?25090 (multiply (multiply ?25090 ?25089) (multiply ?25090 ?25089)) =>= left_division (left_division ?25090 (left_inverse ?25089)) ?25089 [25089, 25090] by Demod 23346 with 2825 at 3
-Id : 23348, {_}: left_division ?25090 (multiply (multiply ?25090 ?25089) (multiply ?25090 ?25089)) =>= left_division (left_inverse (multiply ?25089 ?25090)) ?25089 [25089, 25090] by Demod 23347 with 2742 at 1,3
-Id : 23349, {_}: left_division ?25090 (multiply (multiply ?25090 ?25089) (multiply ?25090 ?25089)) =>= multiply (multiply ?25089 ?25090) ?25089 [25089, 25090] by Demod 23348 with 2737 at 3
-Id : 1876, {_}: left_division (right_division ?2132 ?2133) (multiply ?2132 ?2132) =>= left_division (left_inverse ?2133) ?2132 [2133, 2132] by Super 1572 with 363 at 1,2
-Id : 1882, {_}: left_division ?2150 (multiply (multiply ?2150 ?2151) (multiply ?2150 ?2151)) =>= left_division (left_inverse ?2151) (multiply ?2150 ?2151) [2151, 2150] by Super 1876 with 14 at 1,2
-Id : 24844, {_}: left_division ?2150 (multiply (multiply ?2150 ?2151) (multiply ?2150 ?2151)) =>= multiply ?2151 (multiply ?2150 ?2151) [2151, 2150] by Demod 1882 with 2737 at 3
-Id : 189960, {_}: multiply ?25089 (multiply ?25090 ?25089) =?= multiply (multiply ?25089 ?25090) ?25089 [25090, 25089] by Demod 23349 with 24844 at 2
-Id : 2985, {_}: right_division (left_division ?3370 ?3371) ?3371 =>= left_inverse ?3370 [3371, 3370] by Super 14 with 2823 at 1,2
-Id : 4879, {_}: right_division (right_division ?5359 (left_division (multiply ?5359 ?5361) ?5360)) ?5361 =>= left_inverse (left_division ?5359 (right_division ?5360 ?5359)) [5360, 5361, 5359] by Super 2985 with 4878 at 1,2
-Id : 4974, {_}: right_division (right_division ?5359 (left_division (multiply ?5359 ?5361) ?5360)) ?5361 =>= left_division (right_division ?5360 ?5359) ?5359 [5360, 5361, 5359] by Demod 4879 with 495 at 3
-Id : 41940, {_}: right_division (right_division ?5359 (left_division (multiply ?5359 ?5361) ?5360)) ?5361 =>= right_division ?5359 (left_division ?5359 ?5360) [5360, 5361, 5359] by Demod 4974 with 4963 at 3
-Id : 41979, {_}: right_division ?43925 (left_division ?43925 ?43926) =<= multiply (right_division ?43925 (left_division (multiply ?43925 (left_inverse ?43927)) ?43926)) ?43927 [43927, 43926, 43925] by Super 408 with 41940 at 2
-Id : 42108, {_}: right_division ?43925 (left_division ?43925 ?43926) =<= left_division (right_division (left_division (multiply ?43925 (left_inverse ?43927)) ?43926) ?43925) ?43927 [43927, 43926, 43925] by Demod 41979 with 3156 at 3
-Id : 42109, {_}: right_division ?43925 (left_division ?43925 ?43926) =<= left_division (right_division (left_division (right_division ?43925 ?43927) ?43926) ?43925) ?43927 [43927, 43926, 43925] by Demod 42108 with 363 at 1,1,1,3
-Id : 42000, {_}: right_division (right_division ?44019 (left_division (multiply ?44019 ?44020) ?44021)) ?44020 =>= right_division ?44019 (left_division ?44019 ?44021) [44021, 44020, 44019] by Demod 4974 with 4963 at 3
-Id : 42010, {_}: right_division (right_division (left_inverse ?44060) (left_division (left_division ?44060 ?44061) ?44062)) ?44061 =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44062, 44061, 44060] by Super 42000 with 2823 at 1,2,1,2
-Id : 42174, {_}: right_division (left_inverse (multiply (left_division (left_division ?44060 ?44061) ?44062) ?44060)) ?44061 =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44062, 44061, 44060] by Demod 42010 with 3081 at 1,2
-Id : 42175, {_}: left_inverse (multiply ?44061 (multiply (left_division (left_division ?44060 ?44061) ?44062) ?44060)) =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44062, 44060, 44061] by Demod 42174 with 3081 at 2
-Id : 42176, {_}: left_inverse (multiply ?44061 (left_division (left_division ?44062 (left_division ?44060 ?44061)) ?44060)) =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44060, 44062, 44061] by Demod 42175 with 2825 at 2,1,2
-Id : 42177, {_}: left_inverse (right_division ?44061 (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061)))) =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44062, 44060, 44061] by Demod 42176 with 514 at 1,2
-Id : 42178, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= right_division (left_inverse ?44060) (left_division (left_inverse ?44060) ?44062) [44061, 44062, 44060] by Demod 42177 with 2944 at 2
-Id : 42179, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= left_inverse (multiply (left_division (left_inverse ?44060) ?44062) ?44060) [44061, 44062, 44060] by Demod 42178 with 3081 at 3
-Id : 42180, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= left_inverse (left_division (left_division ?44062 (left_inverse ?44060)) ?44060) [44061, 44062, 44060] by Demod 42179 with 2825 at 1,3
-Id : 42181, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= left_division ?44060 (left_division ?44062 (left_inverse ?44060)) [44061, 44062, 44060] by Demod 42180 with 495 at 3
-Id : 42182, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= left_division ?44060 (left_inverse (multiply ?44060 ?44062)) [44061, 44062, 44060] by Demod 42181 with 2742 at 2,3
-Id : 42183, {_}: right_division (left_division ?44060 (left_division ?44062 (left_division ?44060 ?44061))) ?44061 =>= left_inverse (multiply (multiply ?44060 ?44062) ?44060) [44061, 44062, 44060] by Demod 42182 with 2742 at 3
-Id : 265196, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 (left_division (right_division ?249956 ?249957) ?249956))) =?= left_division (left_inverse (multiply (multiply (right_division ?249956 ?249957) ?249955) (right_division ?249956 ?249957))) ?249957 [249957, 249955, 249956] by Super 42109 with 42183 at 1,3
-Id : 265432, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= left_division (left_inverse (multiply (multiply (right_division ?249956 ?249957) ?249955) (right_division ?249956 ?249957))) ?249957 [249957, 249955, 249956] by Demod 265196 with 38 at 2,2,2,2
-Id : 265433, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= multiply (multiply (multiply (right_division ?249956 ?249957) ?249955) (right_division ?249956 ?249957)) ?249957 [249957, 249955, 249956] by Demod 265432 with 2737 at 3
-Id : 265434, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= multiply (right_division ?249956 ?249957) (multiply ?249955 (multiply (right_division ?249956 ?249957) ?249957)) [249957, 249955, 249956] by Demod 265433 with 20 at 3
-Id : 265435, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= left_division (right_division ?249957 ?249956) (multiply ?249955 (multiply (right_division ?249956 ?249957) ?249957)) [249957, 249955, 249956] by Demod 265434 with 3156 at 3
-Id : 265436, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= left_division (right_division ?249957 ?249956) (multiply ?249955 (left_division (right_division ?249957 ?249956) ?249957)) [249957, 249955, 249956] by Demod 265435 with 3156 at 2,2,3
-Id : 265437, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= left_division (right_division ?249957 ?249956) (right_division ?249955 (left_division ?249957 (right_division ?249957 ?249956))) [249957, 249955, 249956] by Demod 265436 with 514 at 2,3
-Id : 265438, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= right_division (right_division ?249956 ?249957) (right_division (left_division ?249957 (right_division ?249957 ?249956)) ?249955) [249957, 249955, 249956] by Demod 265437 with 3956 at 3
-Id : 427, {_}: left_division ?583 (right_division ?583 ?584) =>= left_inverse ?584 [584, 583] by Super 10 with 363 at 2,2
-Id : 265439, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= right_division (right_division ?249956 ?249957) (right_division (left_inverse ?249956) ?249955) [249957, 249955, 249956] by Demod 265438 with 427 at 1,2,3
-Id : 265440, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= right_division (right_division ?249956 ?249957) (left_inverse (multiply ?249955 ?249956)) [249957, 249955, 249956] by Demod 265439 with 3081 at 2,3
-Id : 265441, {_}: right_division ?249956 (left_division ?249956 (left_division ?249955 ?249957)) =<= multiply (right_division ?249956 ?249957) (multiply ?249955 ?249956) [249957, 249955, 249956] by Demod 265440 with 408 at 3
-Id : 267669, {_}: right_division ?251794 (left_division ?251794 (left_division ?251795 ?251796)) =<= left_division (right_division ?251796 ?251794) (multiply ?251795 ?251794) [251796, 251795, 251794] by Demod 265441 with 3156 at 3
-Id : 267708, {_}: right_division ?251955 (left_division ?251955 (left_division ?251956 (left_inverse ?251954))) =<= left_division (left_inverse (multiply ?251955 ?251954)) (multiply ?251956 ?251955) [251954, 251956, 251955] by Super 267669 with 3081 at 1,3
-Id : 268416, {_}: right_division ?251955 (left_division ?251955 (left_inverse (multiply ?251954 ?251956))) =<= left_division (left_inverse (multiply ?251955 ?251954)) (multiply ?251956 ?251955) [251956, 251954, 251955] by Demod 267708 with 2742 at 2,2,2
-Id : 268417, {_}: right_division ?251955 (left_inverse (multiply (multiply ?251954 ?251956) ?251955)) =<= left_division (left_inverse (multiply ?251955 ?251954)) (multiply ?251956 ?251955) [251956, 251954, 251955] by Demod 268416 with 2742 at 2,2
-Id : 268418, {_}: multiply ?251955 (multiply (multiply ?251954 ?251956) ?251955) =<= left_division (left_inverse (multiply ?251955 ?251954)) (multiply ?251956 ?251955) [251956, 251954, 251955] by Demod 268417 with 408 at 2
-Id : 268419, {_}: multiply ?251955 (multiply (multiply ?251954 ?251956) ?251955) =?= multiply (multiply ?251955 ?251954) (multiply ?251956 ?251955) [251956, 251954, 251955] by Demod 268418 with 2737 at 3
-Id : 997758, {_}: multiply (multiply a b) (multiply c a) === multiply (multiply a b) (multiply c a) [] by Super 190709 with 268419 at 2
-Id : 190709, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 2 with 189960 at 2
-Id : 2, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
-% SZS output end CNFRefutation for GRP202-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Last chance: 1246070086.51
-Last chance: all is indexed 1246072016.7
-Last chance: failed over 100 goal 1246072026.66
-FAILURE in 0 iterations
-% SZS status Timeout for GRP404-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 220.388793s
-% SZS status Unsatisfiable for GRP405-1.p
-% SZS output start CNFRefutation for GRP405-1.p
-Id : 4, {_}: multiply ?2 (inverse (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) =>= ?4 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: multiply ?6 (inverse (multiply (inverse (multiply (inverse (multiply ?6 ?7)) ?8)) (inverse (multiply ?7 (multiply (inverse ?7) ?7))))) =>= ?8 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 7, {_}: multiply ?17 (inverse (multiply (inverse ?16) (inverse (multiply ?18 (multiply (inverse ?18) ?18))))) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16)) (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) [15, 18, 16, 17] by Super 5 with 4 at 1,1,1,2,2
-Id : 40, {_}: multiply (inverse (multiply ?213 ?214)) (multiply ?213 (inverse (multiply (inverse ?215) (inverse (multiply ?214 (multiply (inverse ?214) ?214)))))) =>= ?215 [215, 214, 213] by Super 4 with 7 at 2,2
-Id : 64, {_}: multiply (inverse (multiply ?350 ?351)) (multiply ?350 (multiply ?352 (inverse (multiply (inverse ?353) (inverse (multiply ?354 (multiply (inverse ?354) ?354))))))) =>= multiply (inverse (multiply (inverse (multiply ?352 ?354)) ?351)) ?353 [354, 353, 352, 351, 350] by Super 40 with 7 at 2,2,2
-Id : 124, {_}: multiply (inverse (multiply ?685 ?686)) (multiply ?685 ?687) =?= multiply (inverse (multiply (inverse (multiply ?688 ?689)) ?686)) (multiply (inverse (multiply ?688 ?689)) ?687) [689, 688, 687, 686, 685] by Super 64 with 4 at 2,2,2
-Id : 70, {_}: multiply (inverse (multiply ?400 ?401)) (multiply ?400 ?399) =?= multiply (inverse (multiply (inverse (multiply ?402 ?403)) ?401)) (multiply (inverse (multiply ?402 ?403)) ?399) [403, 402, 399, 401, 400] by Super 64 with 4 at 2,2,2
-Id : 155, {_}: multiply (inverse (multiply ?925 ?926)) (multiply ?925 ?927) =?= multiply (inverse (multiply ?924 ?926)) (multiply ?924 ?927) [924, 927, 926, 925] by Super 124 with 70 at 3
-Id : 113, {_}: multiply ?598 (inverse (multiply (inverse (multiply (inverse (multiply ?598 ?599)) ?597)) (inverse (multiply ?599 (multiply (inverse ?599) ?599))))) =?= inverse (multiply (inverse (multiply (inverse (multiply ?595 ?596)) (multiply ?595 ?597))) (inverse (multiply ?596 (multiply (inverse ?596) ?596)))) [596, 595, 597, 599, 598] by Super 7 with 70 at 1,1,1,3
-Id : 176, {_}: ?597 =<= inverse (multiply (inverse (multiply (inverse (multiply ?595 ?596)) (multiply ?595 ?597))) (inverse (multiply ?596 (multiply (inverse ?596) ?596)))) [596, 595, 597] by Demod 113 with 4 at 2
-Id : 9637, {_}: multiply (inverse (multiply ?67788 (inverse (multiply ?67789 (multiply (inverse ?67789) ?67789))))) (multiply ?67788 ?67790) =?= multiply ?67791 (multiply (inverse (multiply (inverse (multiply ?67792 ?67789)) (multiply ?67792 ?67791))) ?67790) [67792, 67791, 67790, 67789, 67788] by Super 155 with 176 at 1,3
-Id : 10194, {_}: multiply ?72717 (multiply (inverse (multiply (inverse (multiply ?72718 ?72719)) (multiply ?72718 ?72717))) ?72720) =?= multiply ?72721 (multiply (inverse (multiply (inverse (multiply ?72722 ?72719)) (multiply ?72722 ?72721))) ?72720) [72722, 72721, 72720, 72719, 72718, 72717] by Super 9637 with 176 at 1,2
-Id : 10232, {_}: multiply ?73113 (multiply (inverse (multiply (inverse (multiply ?73114 (inverse (multiply (inverse (multiply (inverse (multiply ?73117 ?73111)) ?73112)) (inverse (multiply ?73111 (multiply (inverse ?73111) ?73111))))))) (multiply ?73114 ?73113))) ?73115) =?= multiply ?73116 (multiply (inverse (multiply (inverse ?73112) (multiply ?73117 ?73116))) ?73115) [73116, 73115, 73112, 73111, 73117, 73114, 73113] by Super 10194 with 4 at 1,1,1,1,2,3
-Id : 227, {_}: multiply (inverse (multiply ?1261 ?1262)) (multiply ?1261 ?1263) =?= multiply (inverse (multiply ?1264 ?1262)) (multiply ?1264 ?1263) [1264, 1263, 1262, 1261] by Super 124 with 70 at 3
-Id : 234, {_}: multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply (inverse (multiply ?1311 ?1307)) ?1308)) (inverse (multiply ?1307 (multiply (inverse ?1307) ?1307))))))) (multiply ?1309 ?1310) =>= multiply (inverse ?1308) (multiply ?1311 ?1310) [1310, 1308, 1307, 1311, 1309] by Super 227 with 4 at 1,1,3
-Id : 10841, {_}: multiply ?78382 (multiply (inverse (multiply (inverse ?78383) (multiply ?78384 ?78382))) ?78385) =?= multiply ?78386 (multiply (inverse (multiply (inverse ?78383) (multiply ?78384 ?78386))) ?78385) [78386, 78385, 78384, 78383, 78382] by Demod 10232 with 234 at 1,1,2,2
-Id : 10882, {_}: multiply ?78768 (multiply (inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?78766 ?78767)) (multiply ?78766 ?78765))) (inverse (multiply ?78767 (multiply (inverse ?78767) ?78767))))) (multiply ?78769 ?78768))) ?78770) =?= multiply ?78771 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78771))) ?78770) [78771, 78770, 78769, 78765, 78767, 78766, 78768] by Super 10841 with 176 at 1,1,1,2,3
-Id : 11114, {_}: multiply ?78768 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78768))) ?78770) =?= multiply ?78771 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78771))) ?78770) [78771, 78770, 78769, 78765, 78768] by Demod 10882 with 176 at 1,1,1,2,2
-Id : 11923, {_}: multiply ?86959 (inverse (multiply (inverse (multiply ?86960 (multiply (inverse (multiply ?86961 (multiply ?86962 ?86960))) ?86963))) (inverse (multiply ?86964 (multiply (inverse ?86964) ?86964))))) =>= multiply (inverse (multiply ?86961 (multiply ?86962 (inverse (multiply ?86959 ?86964))))) ?86963 [86964, 86963, 86962, 86961, 86960, 86959] by Super 4 with 11114 at 1,1,1,2,2
-Id : 31525, {_}: multiply ?228038 (multiply ?228039 (inverse (multiply (inverse (multiply (inverse (multiply ?228040 (multiply ?228041 (inverse (multiply (inverse (multiply ?228039 ?228042)) ?228043))))) ?228044)) (inverse (multiply ?228042 (multiply (inverse ?228042) ?228042)))))) =>= multiply (inverse (multiply ?228040 (multiply ?228041 (inverse (multiply ?228038 ?228043))))) ?228044 [228044, 228043, 228042, 228041, 228040, 228039, 228038] by Super 11923 with 7 at 2,2
-Id : 31856, {_}: multiply ?231713 (multiply ?231714 (inverse (multiply (inverse (multiply (inverse (multiply ?231714 ?231716)) ?231717)) (inverse (multiply ?231716 (multiply (inverse ?231716) ?231716)))))) =?= multiply (inverse (multiply (inverse (multiply ?231715 ?231712)) (multiply ?231715 (inverse (multiply ?231713 ?231717))))) (inverse (multiply ?231712 (multiply (inverse ?231712) ?231712))) [231712, 231715, 231717, 231716, 231714, 231713] by Super 31525 with 176 at 1,1,2,2,2
-Id : 32694, {_}: multiply ?234105 ?234106 =<= multiply (inverse (multiply (inverse (multiply ?234107 ?234108)) (multiply ?234107 (inverse (multiply ?234105 ?234106))))) (inverse (multiply ?234108 (multiply (inverse ?234108) ?234108))) [234108, 234107, 234106, 234105] by Demod 31856 with 4 at 2,2
-Id : 32770, {_}: multiply ?234751 (inverse (multiply (inverse (multiply (inverse (multiply ?234751 ?234749)) ?234750)) (inverse (multiply ?234749 (multiply (inverse ?234749) ?234749))))) =?= multiply (inverse (multiply (inverse (multiply ?234752 ?234753)) (multiply ?234752 (inverse ?234750)))) (inverse (multiply ?234753 (multiply (inverse ?234753) ?234753))) [234753, 234752, 234750, 234749, 234751] by Super 32694 with 4 at 1,2,2,1,1,3
-Id : 33040, {_}: ?234750 =<= multiply (inverse (multiply (inverse (multiply ?234752 ?234753)) (multiply ?234752 (inverse ?234750)))) (inverse (multiply ?234753 (multiply (inverse ?234753) ?234753))) [234753, 234752, 234750] by Demod 32770 with 4 at 2
-Id : 15, {_}: multiply (inverse (multiply ?60 ?62)) (multiply ?60 (inverse (multiply (inverse ?61) (inverse (multiply ?62 (multiply (inverse ?62) ?62)))))) =>= ?61 [61, 62, 60] by Super 4 with 7 at 2,2
-Id : 11333, {_}: multiply ?82186 (inverse (multiply (inverse (multiply ?82185 (multiply (inverse (multiply ?82182 (multiply ?82183 ?82185))) ?82184))) (inverse (multiply ?82187 (multiply (inverse ?82187) ?82187))))) =>= multiply (inverse (multiply ?82182 (multiply ?82183 (inverse (multiply ?82186 ?82187))))) ?82184 [82187, 82184, 82183, 82182, 82185, 82186] by Super 4 with 11114 at 1,1,1,2,2
-Id : 33373, {_}: multiply ?237625 (inverse (multiply (inverse (multiply (inverse ?237622) ?237622)) (inverse (multiply ?237626 (multiply (inverse ?237626) ?237626))))) =?= multiply (inverse (multiply (inverse (multiply ?237623 ?237624)) (multiply ?237623 (inverse (multiply ?237625 ?237626))))) (inverse (multiply ?237624 (multiply (inverse ?237624) ?237624))) [237624, 237623, 237626, 237622, 237625] by Super 11333 with 33040 at 2,1,1,1,2,2
-Id : 33632, {_}: multiply ?237625 (inverse (multiply (inverse (multiply (inverse ?237622) ?237622)) (inverse (multiply ?237626 (multiply (inverse ?237626) ?237626))))) =>= multiply ?237625 ?237626 [237626, 237622, 237625] by Demod 33373 with 33040 at 3
-Id : 33860, {_}: multiply (inverse (multiply ?240296 ?240298)) (multiply ?240296 ?240298) =?= multiply (inverse ?240297) ?240297 [240297, 240298, 240296] by Super 15 with 33632 at 2,2
-Id : 40668, {_}: ?278603 =<= multiply (inverse (multiply (inverse ?278604) ?278604)) (inverse (multiply (inverse ?278603) (multiply (inverse (inverse ?278603)) (inverse ?278603)))) [278604, 278603] by Super 33040 with 33860 at 1,1,3
-Id : 35324, {_}: multiply (inverse (multiply ?248214 ?248215)) (multiply ?248214 ?248215) =?= multiply (inverse ?248216) ?248216 [248216, 248215, 248214] by Super 15 with 33632 at 2,2
-Id : 35547, {_}: multiply (inverse ?249874) ?249874 =?= multiply (inverse ?249877) ?249877 [249877, 249874] by Super 35324 with 33860 at 2
-Id : 40715, {_}: ?278907 =<= multiply (inverse (multiply (inverse ?278908) ?278908)) (inverse (multiply (inverse ?278907) (multiply (inverse ?278906) ?278906))) [278906, 278908, 278907] by Super 40668 with 35547 at 2,1,2,3
-Id : 300, {_}: ?1622 =<= inverse (multiply (inverse (multiply (inverse (multiply ?1623 ?1624)) (multiply ?1623 ?1622))) (inverse (multiply ?1624 (multiply (inverse ?1624) ?1624)))) [1624, 1623, 1622] by Demod 113 with 4 at 2
-Id : 305, {_}: ?1655 =<= inverse (multiply (inverse (multiply (inverse (multiply ?1656 (multiply ?1652 ?1653))) (multiply ?1656 ?1655))) (inverse (multiply (multiply ?1652 ?1653) (multiply (inverse (multiply ?1654 ?1653)) (multiply ?1654 ?1653))))) [1654, 1653, 1652, 1656, 1655] by Super 300 with 155 at 2,1,2,1,3
-Id : 11337, {_}: multiply (inverse (multiply ?82211 (multiply ?82212 ?82210))) ?82213 =<= inverse (multiply (inverse (multiply (inverse (multiply ?82210 ?82215)) (multiply ?82214 (multiply (inverse (multiply ?82211 (multiply ?82212 ?82214))) ?82213)))) (inverse (multiply ?82215 (multiply (inverse ?82215) ?82215)))) [82214, 82215, 82213, 82210, 82212, 82211] by Super 176 with 11114 at 2,1,1,1,3
-Id : 14547, {_}: multiply ?104639 (multiply (inverse (multiply ?104634 (multiply ?104635 ?104636))) ?104637) =<= multiply (inverse (multiply ?104640 (multiply ?104641 (inverse (multiply ?104639 ?104638))))) (multiply (inverse (multiply ?104634 (multiply ?104635 (inverse (multiply ?104640 (multiply ?104641 (inverse (multiply ?104636 ?104638)))))))) ?104637) [104638, 104641, 104640, 104637, 104636, 104635, 104634, 104639] by Super 11333 with 11337 at 2,2
-Id : 368, {_}: multiply (inverse (multiply ?1959 (multiply ?1960 (inverse (multiply (inverse ?1961) (inverse (multiply ?1962 (multiply (inverse ?1962) ?1962)))))))) (multiply ?1959 ?1963) =>= multiply (inverse ?1961) (multiply (inverse (multiply ?1960 ?1962)) ?1963) [1963, 1962, 1961, 1960, 1959] by Super 124 with 15 at 1,1,3
-Id : 384, {_}: multiply (inverse (multiply ?2092 (multiply ?2093 (inverse (multiply ?2089 (inverse (multiply ?2094 (multiply (inverse ?2094) ?2094)))))))) (multiply ?2092 ?2095) =?= multiply (inverse (multiply (inverse (multiply (inverse (multiply ?2090 ?2091)) (multiply ?2090 ?2089))) (inverse (multiply ?2091 (multiply (inverse ?2091) ?2091))))) (multiply (inverse (multiply ?2093 ?2094)) ?2095) [2091, 2090, 2095, 2094, 2089, 2093, 2092] by Super 368 with 176 at 1,1,2,2,1,1,2
-Id : 409, {_}: multiply (inverse (multiply ?2092 (multiply ?2093 (inverse (multiply ?2089 (inverse (multiply ?2094 (multiply (inverse ?2094) ?2094)))))))) (multiply ?2092 ?2095) =>= multiply ?2089 (multiply (inverse (multiply ?2093 ?2094)) ?2095) [2095, 2094, 2089, 2093, 2092] by Demod 384 with 176 at 1,3
-Id : 11831, {_}: multiply (inverse (multiply ?86031 (multiply ?86037 (inverse (multiply ?86038 (inverse (multiply ?86039 (multiply (inverse ?86039) ?86039)))))))) (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply ?86031 ?86036))))) ?86035) =?= multiply ?86038 (multiply (inverse (multiply ?86037 ?86039)) (inverse (multiply (inverse (multiply ?86032 (multiply (inverse (multiply ?86033 (multiply ?86034 ?86032))) ?86035))) (inverse (multiply ?86036 (multiply (inverse ?86036) ?86036)))))) [86032, 86035, 86036, 86034, 86033, 86039, 86038, 86037, 86031] by Super 409 with 11333 at 2,2
-Id : 12202, {_}: multiply (inverse (multiply ?86031 (multiply ?86037 (inverse (multiply ?86038 (inverse (multiply ?86039 (multiply (inverse ?86039) ?86039)))))))) (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply ?86031 ?86036))))) ?86035) =>= multiply ?86038 (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply (inverse (multiply ?86037 ?86039)) ?86036))))) ?86035) [86035, 86036, 86034, 86033, 86039, 86038, 86037, 86031] by Demod 11831 with 11333 at 2,3
-Id : 18076, {_}: multiply ?132847 (multiply (inverse (multiply ?132848 (multiply ?132849 ?132850))) ?132851) =<= multiply ?132847 (multiply (inverse (multiply ?132848 (multiply ?132849 (inverse (multiply (inverse (multiply ?132853 ?132846)) (multiply ?132853 (inverse (multiply ?132850 (inverse (multiply ?132846 (multiply (inverse ?132846) ?132846))))))))))) ?132851) [132846, 132853, 132851, 132850, 132849, 132848, 132847] by Super 14547 with 12202 at 3
-Id : 21064, {_}: multiply ?157169 (inverse (multiply (inverse (multiply (inverse (multiply ?157169 ?157170)) (multiply (inverse (multiply ?157163 (multiply ?157164 ?157165))) ?157166))) (inverse (multiply ?157170 (multiply (inverse ?157170) ?157170))))) =?= multiply (inverse (multiply ?157163 (multiply ?157164 (inverse (multiply (inverse (multiply ?157167 ?157168)) (multiply ?157167 (inverse (multiply ?157165 (inverse (multiply ?157168 (multiply (inverse ?157168) ?157168))))))))))) ?157166 [157168, 157167, 157166, 157165, 157164, 157163, 157170, 157169] by Super 4 with 18076 at 1,1,1,2,2
-Id : 21742, {_}: multiply (inverse (multiply ?157163 (multiply ?157164 ?157165))) ?157166 =<= multiply (inverse (multiply ?157163 (multiply ?157164 (inverse (multiply (inverse (multiply ?157167 ?157168)) (multiply ?157167 (inverse (multiply ?157165 (inverse (multiply ?157168 (multiply (inverse ?157168) ?157168))))))))))) ?157166 [157168, 157167, 157166, 157165, 157164, 157163] by Demod 21064 with 4 at 2
-Id : 22341, {_}: inverse (multiply (inverse (multiply ?165075 ?165076)) (multiply ?165075 (inverse (multiply ?165074 (inverse (multiply ?165076 (multiply (inverse ?165076) ?165076))))))) =?= inverse (multiply (inverse (multiply (inverse (multiply ?165073 (multiply ?165077 ?165078))) (multiply ?165073 ?165074))) (inverse (multiply (multiply ?165077 ?165078) (multiply (inverse (multiply ?165079 ?165078)) (multiply ?165079 ?165078))))) [165079, 165078, 165077, 165073, 165074, 165076, 165075] by Super 305 with 21742 at 1,3
-Id : 22802, {_}: inverse (multiply (inverse (multiply ?165075 ?165076)) (multiply ?165075 (inverse (multiply ?165074 (inverse (multiply ?165076 (multiply (inverse ?165076) ?165076))))))) =>= ?165074 [165074, 165076, 165075] by Demod 22341 with 305 at 3
-Id : 38026, {_}: inverse (multiply (inverse (multiply ?263789 ?263790)) (multiply ?263789 ?263790)) =?= inverse (multiply (inverse ?263791) ?263791) [263791, 263790, 263789] by Super 22802 with 33632 at 2,1,2
-Id : 38262, {_}: inverse (multiply (inverse ?265529) ?265529) =?= inverse (multiply (inverse ?265532) ?265532) [265532, 265529] by Super 38026 with 35547 at 1,2
-Id : 38507, {_}: multiply (inverse ?265709) ?265709 =?= multiply (inverse (multiply (inverse ?265708) ?265708)) (multiply (inverse ?265707) ?265707) [265707, 265708, 265709] by Super 35547 with 38262 at 1,3
-Id : 40747, {_}: multiply (inverse ?279111) ?279111 =?= multiply (inverse (multiply (inverse ?279112) ?279112)) (inverse (multiply (inverse ?279110) ?279110)) [279110, 279112, 279111] by Super 40668 with 38507 at 1,2,3
-Id : 41831, {_}: multiply (inverse ?285057) (inverse (multiply (inverse (multiply (inverse ?285056) ?285056)) (inverse (multiply ?285057 (multiply (inverse ?285057) ?285057))))) =?= inverse (multiply (inverse ?285058) ?285058) [285058, 285056, 285057] by Super 4 with 40747 at 1,1,1,2,2
-Id : 33864, {_}: multiply ?240317 (inverse (multiply (inverse (multiply (inverse (multiply ?240317 ?240318)) ?240316)) (inverse (multiply ?240318 (multiply (inverse ?240318) ?240318))))) =?= inverse (multiply (inverse (multiply (inverse ?240315) ?240315)) (inverse (multiply ?240316 (multiply (inverse ?240316) ?240316)))) [240315, 240316, 240318, 240317] by Super 4 with 33632 at 1,1,1,2,2
-Id : 36969, {_}: ?257201 =<= inverse (multiply (inverse (multiply (inverse ?257202) ?257202)) (inverse (multiply ?257201 (multiply (inverse ?257201) ?257201)))) [257202, 257201] by Demod 33864 with 4 at 2
-Id : 37018, {_}: ?257524 =<= inverse (multiply (inverse (multiply (inverse ?257525) ?257525)) (inverse (multiply ?257524 (multiply (inverse ?257523) ?257523)))) [257523, 257525, 257524] by Super 36969 with 35547 at 2,1,2,1,3
-Id : 42424, {_}: multiply (inverse ?285057) ?285057 =?= inverse (multiply (inverse ?285058) ?285058) [285058, 285057] by Demod 41831 with 37018 at 2,2
-Id : 59456, {_}: ?377115 =<= multiply (inverse (inverse (multiply (inverse ?377116) ?377116))) (inverse (multiply (inverse ?377115) (multiply (inverse ?377117) ?377117))) [377117, 377116, 377115] by Super 40715 with 42424 at 1,1,3
-Id : 59618, {_}: multiply (inverse ?378144) ?378141 =<= multiply (inverse (inverse (multiply (inverse ?378143) ?378143))) (inverse (multiply (inverse (multiply ?378142 ?378141)) (multiply ?378142 ?378144))) [378142, 378143, 378141, 378144] by Super 59456 with 155 at 1,2,3
-Id : 293, {_}: multiply ?1577 ?1574 =<= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?1577 ?1576)) ?1578)) (multiply (inverse (multiply ?1575 ?1576)) (multiply ?1575 ?1574)))) (inverse (multiply ?1578 (multiply (inverse ?1578) ?1578)))) [1575, 1578, 1576, 1574, 1577] by Super 7 with 176 at 2,2
-Id : 49313, {_}: ?325983 =<= multiply (multiply (inverse ?325984) ?325984) (inverse (multiply (inverse ?325983) (multiply (inverse ?325985) ?325985))) [325985, 325984, 325983] by Super 40715 with 42424 at 1,3
-Id : 70497, {_}: multiply (inverse ?433725) ?433726 =<= multiply (multiply (inverse ?433727) ?433727) (inverse (multiply (inverse (multiply ?433728 ?433726)) (multiply ?433728 ?433725))) [433728, 433727, 433726, 433725] by Super 49313 with 155 at 1,2,3
-Id : 104522, {_}: multiply (inverse ?611346) ?611347 =<= multiply (multiply (inverse ?611348) ?611348) (inverse (multiply (multiply (inverse ?611349) ?611349) (multiply (inverse ?611347) ?611346))) [611349, 611348, 611347, 611346] by Super 70497 with 42424 at 1,1,2,3
-Id : 104531, {_}: multiply (inverse ?611424) (multiply (inverse ?611422) ?611422) =?= multiply (multiply (inverse ?611425) ?611425) (inverse (multiply (multiply (inverse ?611426) ?611426) (multiply (inverse (multiply (inverse ?611423) ?611423)) ?611424))) [611423, 611426, 611425, 611422, 611424] by Super 104522 with 38262 at 1,2,1,2,3
-Id : 70690, {_}: multiply (inverse ?435205) ?435206 =<= multiply (multiply (inverse ?435207) ?435207) (inverse (multiply (multiply (inverse ?435204) ?435204) (multiply (inverse ?435206) ?435205))) [435204, 435207, 435206, 435205] by Super 70497 with 42424 at 1,1,2,3
-Id : 105085, {_}: multiply (inverse ?611424) (multiply (inverse ?611422) ?611422) =?= multiply (inverse ?611424) (multiply (inverse ?611423) ?611423) [611423, 611422, 611424] by Demod 104531 with 70690 at 3
-Id : 105821, {_}: multiply ?618521 (multiply (inverse ?618519) ?618519) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?618521 ?618522)) ?618523)) (multiply (inverse (multiply (inverse ?618518) ?618522)) (multiply (inverse ?618518) (multiply (inverse ?618520) ?618520))))) (inverse (multiply ?618523 (multiply (inverse ?618523) ?618523)))) [618520, 618518, 618523, 618522, 618519, 618521] by Super 293 with 105085 at 2,2,1,1,1,3
-Id : 108557, {_}: multiply ?634262 (multiply (inverse ?634263) ?634263) =?= multiply ?634262 (multiply (inverse ?634264) ?634264) [634264, 634263, 634262] by Demod 105821 with 293 at 3
-Id : 108677, {_}: multiply ?635011 (multiply (inverse ?635012) ?635012) =?= multiply ?635011 (inverse (multiply (inverse ?635010) ?635010)) [635010, 635012, 635011] by Super 108557 with 42424 at 2,3
-Id : 41162, {_}: ?281232 =<= multiply (inverse (multiply (inverse ?281233) ?281233)) (inverse (multiply (inverse ?281232) (multiply (inverse ?281234) ?281234))) [281234, 281233, 281232] by Super 40668 with 35547 at 2,1,2,3
-Id : 41252, {_}: multiply (inverse ?281896) ?281893 =<= multiply (inverse (multiply (inverse ?281895) ?281895)) (inverse (multiply (inverse (multiply ?281894 ?281893)) (multiply ?281894 ?281896))) [281894, 281895, 281893, 281896] by Super 41162 with 155 at 1,2,3
-Id : 104693, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?612594 ?612592)) (multiply ?612594 ?612591)))) (multiply (inverse ?612593) ?612593) =?= multiply (multiply (inverse ?612595) ?612595) (inverse (multiply (multiply (inverse ?612596) ?612596) (multiply (inverse ?612591) ?612592))) [612596, 612595, 612593, 612591, 612592, 612594] by Super 104522 with 41252 at 2,1,2,3
-Id : 105218, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?612594 ?612592)) (multiply ?612594 ?612591)))) (multiply (inverse ?612593) ?612593) =>= multiply (inverse ?612592) ?612591 [612593, 612591, 612592, 612594] by Demod 104693 with 70690 at 3
-Id : 118665, {_}: multiply (inverse ?687026) ?687027 =<= multiply (inverse (inverse (multiply (inverse (multiply ?687025 ?687026)) (multiply ?687025 ?687027)))) (inverse (multiply (inverse ?687029) ?687029)) [687029, 687025, 687027, 687026] by Super 108677 with 105218 at 2
-Id : 118666, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?687031 ?687032)) (multiply ?687031 ?687033)))) (multiply (inverse ?687034) ?687034) =>= multiply (inverse ?687032) ?687033 [687034, 687033, 687032, 687031] by Demod 104693 with 70690 at 3
-Id : 202978, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1106072) ?1106072) (multiply (inverse ?1106073) ?1106074)))) (multiply (inverse ?1106075) ?1106075) =>= multiply (inverse ?1106073) ?1106074 [1106075, 1106074, 1106073, 1106072] by Super 118666 with 42424 at 1,1,1,1,2
-Id : 203337, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1108543) ?1108543) ?1108542))) (multiply (inverse ?1108545) ?1108545) =?= multiply (inverse ?1108544) (inverse (multiply (inverse (multiply (inverse (multiply (inverse ?1108544) ?1108541)) ?1108542)) (inverse (multiply ?1108541 (multiply (inverse ?1108541) ?1108541))))) [1108541, 1108544, 1108545, 1108542, 1108543] by Super 202978 with 4 at 2,1,1,1,2
-Id : 203960, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1108543) ?1108543) ?1108542))) (multiply (inverse ?1108545) ?1108545) =>= ?1108542 [1108545, 1108542, 1108543] by Demod 203337 with 4 at 3
-Id : 204499, {_}: ?1113563 =<= multiply (inverse (inverse (multiply (multiply (inverse ?1113562) ?1113562) ?1113563))) (inverse (multiply (inverse ?1113565) ?1113565)) [1113565, 1113562, 1113563] by Super 108677 with 203960 at 2
-Id : 42548, {_}: ?289376 =<= multiply (multiply (inverse ?289374) ?289374) (inverse (multiply (inverse ?289376) (multiply (inverse ?289377) ?289377))) [289377, 289374, 289376] by Super 40715 with 42424 at 1,3
-Id : 204490, {_}: inverse (multiply (multiply (inverse ?1113513) ?1113513) ?1113514) =?= multiply (multiply (inverse ?1113516) ?1113516) (inverse ?1113514) [1113516, 1113514, 1113513] by Super 42548 with 203960 at 1,2,3
-Id : 209225, {_}: ?1138104 =<= multiply (inverse (multiply (multiply (inverse ?1138103) ?1138103) (inverse ?1138104))) (inverse (multiply (inverse ?1138106) ?1138106)) [1138106, 1138103, 1138104] by Super 204499 with 204490 at 1,1,3
-Id : 232, {_}: multiply (inverse (multiply ?1297 ?1298)) (multiply ?1297 (multiply ?1293 ?1295)) =?= multiply (inverse (multiply (inverse (multiply ?1293 ?1294)) ?1298)) (multiply (inverse (multiply ?1296 ?1294)) (multiply ?1296 ?1295)) [1296, 1294, 1295, 1293, 1298, 1297] by Super 227 with 155 at 2,3
-Id : 210415, {_}: multiply (inverse (multiply (multiply (inverse ?1144394) ?1144394) (inverse ?1144395))) (multiply (inverse ?1144396) ?1144396) =>= ?1144395 [1144396, 1144395, 1144394] by Super 203960 with 204490 at 1,1,2
-Id : 210932, {_}: multiply (inverse (multiply (inverse (multiply (inverse ?1147471) ?1147471)) (inverse ?1147473))) (multiply (inverse ?1147474) ?1147474) =>= ?1147473 [1147474, 1147473, 1147471] by Super 210415 with 42424 at 1,1,1,2
-Id : 224465, {_}: multiply (inverse (multiply ?1210775 (inverse ?1210776))) (multiply ?1210775 (multiply (inverse ?1210777) ?1210777)) =>= ?1210776 [1210777, 1210776, 1210775] by Super 232 with 210932 at 3
-Id : 224626, {_}: multiply (inverse (multiply ?1211759 (inverse ?1211760))) (multiply ?1211759 (inverse (multiply (inverse ?1211758) ?1211758))) =>= ?1211760 [1211758, 1211760, 1211759] by Super 224465 with 42424 at 2,2,2
-Id : 227024, {_}: ?1221988 =<= inverse (multiply (inverse ?1221988) (multiply (inverse (inverse ?1221988)) (inverse ?1221988))) [1221988] by Super 15 with 224626 at 2
-Id : 228909, {_}: ?1228455 =<= multiply (multiply (inverse ?1228456) ?1228456) ?1228455 [1228456, 1228455] by Super 42548 with 227024 at 2,3
-Id : 230161, {_}: ?1138104 =<= multiply (inverse (inverse ?1138104)) (inverse (multiply (inverse ?1138106) ?1138106)) [1138106, 1138104] by Demod 209225 with 228909 at 1,1,3
-Id : 230162, {_}: multiply (inverse ?687026) ?687027 =<= multiply (inverse (multiply ?687025 ?687026)) (multiply ?687025 ?687027) [687025, 687027, 687026] by Demod 118665 with 230161 at 3
-Id : 230229, {_}: multiply (inverse ?378144) ?378141 =<= multiply (inverse (inverse (multiply (inverse ?378143) ?378143))) (inverse (multiply (inverse ?378141) ?378144)) [378143, 378141, 378144] by Demod 59618 with 230162 at 1,2,3
-Id : 70571, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =?= multiply (multiply (inverse ?434318) ?434318) (inverse (multiply (inverse (multiply (inverse (multiply (inverse ?434315) ?434315)) ?434317)) (multiply (inverse ?434314) ?434314))) [434314, 434315, 434318, 434317, 434316] by Super 70497 with 40747 at 2,1,2,3
-Id : 70940, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =?= multiply (inverse (multiply (inverse ?434315) ?434315)) ?434317 [434315, 434317, 434316] by Demod 70571 with 42548 at 3
-Id : 204504, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1113587) ?1113587) ?1113588))) (multiply (inverse ?1113589) ?1113589) =>= ?1113588 [1113589, 1113588, 1113587] by Demod 203337 with 4 at 3
-Id : 204894, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?1115926) ?1115926)) ?1115928))) (multiply (inverse ?1115929) ?1115929) =>= ?1115928 [1115929, 1115928, 1115926] by Super 204504 with 42424 at 1,1,1,1,2
-Id : 222906, {_}: multiply (inverse (multiply ?1203249 (inverse ?1203248))) (multiply ?1203249 (multiply (inverse ?1203247) ?1203247)) =>= ?1203248 [1203247, 1203248, 1203249] by Super 232 with 210932 at 3
-Id : 230230, {_}: multiply (inverse (inverse ?1203248)) (multiply (inverse ?1203247) ?1203247) =>= ?1203248 [1203247, 1203248] by Demod 222906 with 230162 at 2
-Id : 230233, {_}: multiply (inverse (multiply (inverse ?1115926) ?1115926)) ?1115928 =>= ?1115928 [1115928, 1115926] by Demod 204894 with 230230 at 2
-Id : 230259, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =>= ?434317 [434317, 434316] by Demod 70940 with 230233 at 3
-Id : 230302, {_}: multiply (inverse ?378144) ?378141 =<= inverse (multiply (inverse ?378141) ?378144) [378141, 378144] by Demod 230229 with 230259 at 3
-Id : 230467, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16)) (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) [15, 16, 18, 17] by Demod 7 with 230302 at 2,2
-Id : 230468, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16) [15, 16, 18, 17] by Demod 230467 with 230302 at 3
-Id : 230469, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230468 with 230302 at 1,2,3
-Id : 43162, {_}: ?293590 =<= inverse (multiply (inverse (inverse (multiply (inverse ?293589) ?293589))) (inverse (multiply ?293590 (multiply (inverse ?293591) ?293591)))) [293591, 293589, 293590] by Super 37018 with 42424 at 1,1,1,3
-Id : 230270, {_}: ?293590 =<= inverse (inverse (multiply ?293590 (multiply (inverse ?293591) ?293591))) [293591, 293590] by Demod 43162 with 230259 at 1,3
-Id : 230643, {_}: multiply ?17 (multiply ?18 ?16) =<= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230469 with 230270 at 1,2,2
-Id : 230644, {_}: multiply ?17 (multiply ?18 ?16) =<= multiply ?15 (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230643 with 230270 at 1,3
-Id : 298, {_}: multiply (inverse (multiply ?1613 (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612))))) (multiply ?1613 ?1614) =?= multiply ?1610 (multiply (inverse (multiply (inverse (multiply ?1611 ?1612)) (multiply ?1611 ?1610))) ?1614) [1611, 1610, 1614, 1612, 1613] by Super 155 with 176 at 1,3
-Id : 230219, {_}: multiply (inverse (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612)))) ?1614 =?= multiply ?1610 (multiply (inverse (multiply (inverse (multiply ?1611 ?1612)) (multiply ?1611 ?1610))) ?1614) [1611, 1610, 1614, 1612] by Demod 298 with 230162 at 2
-Id : 230220, {_}: multiply (inverse (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612)))) ?1614 =?= multiply ?1610 (multiply (inverse (multiply (inverse ?1612) ?1610)) ?1614) [1610, 1614, 1612] by Demod 230219 with 230162 at 1,1,2,3
-Id : 230678, {_}: multiply ?1612 ?1614 =<= multiply ?1610 (multiply (inverse (multiply (inverse ?1612) ?1610)) ?1614) [1610, 1614, 1612] by Demod 230220 with 230270 at 1,2
-Id : 230679, {_}: multiply ?1612 ?1614 =<= multiply ?1610 (multiply (multiply (inverse ?1610) ?1612) ?1614) [1610, 1614, 1612] by Demod 230678 with 230302 at 1,2,3
-Id : 230680, {_}: multiply ?17 (multiply ?18 ?16) =?= multiply (multiply ?17 ?18) ?16 [16, 18, 17] by Demod 230644 with 230679 at 3
-Id : 231308, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 230680 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP405-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 13.442565s
-% SZS status Unsatisfiable for GRP422-1.p
-% SZS output start CNFRefutation for GRP422-1.p
-Id : 5, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (multiply (inverse ?8) (inverse (multiply (inverse ?8) ?8))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 4, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (multiply (inverse ?4) (inverse (multiply (inverse ?4) ?4))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 20, {_}: inverse (multiply (inverse (multiply ?72 ?73)) (multiply ?72 ?74)) =?= multiply (inverse ?74) (inverse (multiply (inverse ?73) (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse ?74) ?74))))))) [74, 73, 72] by Super 5 with 4 at 2,1,1,1,2
-Id : 9, {_}: inverse (multiply (inverse (multiply ?29 ?28)) (multiply ?29 ?30)) =?= multiply (inverse ?30) (inverse (multiply (inverse ?28) (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse ?30) ?30))))))) [30, 28, 29] by Super 5 with 4 at 2,1,1,1,2
-Id : 35, {_}: inverse (multiply (inverse (multiply ?156 ?157)) (multiply ?156 ?158)) =?= inverse (multiply (inverse (multiply ?155 ?157)) (multiply ?155 ?158)) [155, 158, 157, 156] by Super 20 with 9 at 3
-Id : 59, {_}: inverse (multiply (inverse (multiply ?228 (inverse (multiply (inverse (multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226))) (multiply (inverse ?229) (inverse (multiply (inverse ?229) ?229))))))) (multiply ?228 ?229)) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 229, 226, 225, 227, 228] by Super 4 with 35 at 1,1,2,1,1,1,2
-Id : 156, {_}: multiply (inverse (multiply ?725 ?726)) (multiply ?725 ?727) =?= multiply (inverse (multiply ?728 ?726)) (multiply ?728 ?727) [728, 727, 726, 725] by Demod 59 with 4 at 2
-Id : 163, {_}: multiply (inverse (multiply ?773 (multiply ?770 ?772))) (multiply ?773 ?774) =?= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770, 773] by Super 156 with 4 at 1,3
-Id : 55, {_}: inverse (multiply (inverse (multiply ?201 (inverse (multiply (inverse ?202) (multiply (inverse (multiply ?198 ?199)) (inverse (multiply (inverse (multiply ?200 ?199)) (multiply ?200 ?199)))))))) (multiply ?201 (multiply ?198 ?199))) =>= ?202 [200, 199, 198, 202, 201] by Super 4 with 35 at 2,2,1,2,1,1,1,2
-Id : 3142, {_}: inverse (multiply (inverse (multiply ?22079 (inverse (multiply (inverse (multiply ?22076 (multiply ?22077 ?22078))) (multiply ?22076 (inverse (multiply (inverse (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))))))))) (multiply ?22079 (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078)))))))) =>= ?22080 [22080, 22081, 22078, 22077, 22076, 22079] by Super 55 with 163 at 1,2,1,1,1,2
-Id : 290, {_}: inverse (multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply ?1310 ?1311)) (multiply ?1310 (inverse (multiply (inverse ?1312) ?1312))))))) (multiply ?1309 ?1312)) =>= multiply (inverse ?1312) ?1311 [1312, 1311, 1310, 1309] by Super 4 with 35 at 2,1,1,1,2
-Id : 110, {_}: multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 226, 225, 227] by Demod 59 with 4 at 2
-Id : 300, {_}: inverse (multiply (inverse (multiply ?1382 (inverse (multiply (inverse (multiply ?1383 ?1384)) (multiply ?1383 (inverse (multiply (inverse (multiply ?1381 ?1380)) (multiply ?1381 ?1380)))))))) (multiply ?1382 (multiply ?1379 ?1380))) =>= multiply (inverse (multiply ?1379 ?1380)) ?1384 [1379, 1380, 1381, 1384, 1383, 1382] by Super 290 with 110 at 1,2,2,1,2,1,1,1,2
-Id : 3323, {_}: multiply (inverse (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22077 ?22078) =>= ?22080 [22078, 22080, 22077] by Demod 3142 with 300 at 2
-Id : 3887, {_}: multiply (inverse (multiply ?27309 (multiply ?27310 ?27311))) (multiply ?27309 (multiply ?27310 ?27311)) =?= multiply (inverse ?27312) ?27312 [27312, 27311, 27310, 27309] by Super 163 with 3323 at 2,3
-Id : 3460, {_}: multiply (inverse (multiply ?24443 (multiply ?24440 ?24442))) (multiply ?24443 (multiply ?24440 ?24442)) =?= multiply (inverse ?24441) ?24441 [24441, 24442, 24440, 24443] by Super 163 with 3323 at 2,3
-Id : 3992, {_}: multiply (inverse ?28111) ?28111 =?= multiply (inverse ?28115) ?28115 [28115, 28111] by Super 3887 with 3460 at 2
-Id : 157, {_}: multiply (inverse (multiply ?734 ?735)) (multiply ?734 (multiply ?730 ?732)) =?= multiply (inverse (multiply (inverse (multiply ?730 ?731)) ?735)) (multiply (inverse (multiply ?733 ?731)) (multiply ?733 ?732)) [733, 731, 732, 730, 735, 734] by Super 156 with 110 at 2,3
-Id : 160, {_}: multiply (inverse (multiply ?754 (multiply ?750 ?752))) (multiply ?754 ?755) =?= multiply (inverse (multiply (inverse (multiply ?753 ?751)) (multiply ?753 ?752))) (multiply (inverse (multiply ?750 ?751)) ?755) [751, 753, 755, 752, 750, 754] by Super 156 with 110 at 1,1,3
-Id : 587, {_}: multiply (inverse (multiply ?3234 (multiply ?3232 ?3231))) (multiply ?3234 (multiply ?3232 ?3235)) =?= multiply (inverse (multiply ?3229 (multiply ?3230 ?3231))) (multiply ?3229 (multiply ?3230 ?3235)) [3230, 3229, 3235, 3231, 3232, 3234] by Super 157 with 160 at 3
-Id : 61, {_}: inverse (multiply (inverse (multiply ?240 (inverse (multiply (inverse (multiply ?239 ?238)) (multiply ?239 (inverse (multiply (inverse ?241) ?241))))))) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 239, 240] by Super 4 with 35 at 2,1,1,1,2
-Id : 4188, {_}: multiply (inverse (multiply ?29120 ?29121)) (multiply ?29120 ?29118) =?= multiply (inverse (multiply (inverse ?29118) ?29121)) (multiply (inverse ?29119) ?29119) [29119, 29118, 29121, 29120] by Super 110 with 3992 at 2,3
-Id : 10540, {_}: inverse (multiply (inverse (multiply ?66148 (inverse (multiply (inverse (multiply (inverse (multiply ?66144 ?66145)) (multiply ?66144 ?66146))) (multiply (inverse (multiply (inverse ?66146) ?66145)) (inverse (multiply (inverse ?66149) ?66149))))))) (multiply ?66148 ?66149)) =?= multiply (inverse ?66149) (multiply (inverse ?66147) ?66147) [66147, 66149, 66146, 66145, 66144, 66148] by Super 61 with 4188 at 1,1,1,2,1,1,1,2
-Id : 306, {_}: inverse (multiply (inverse (multiply ?1422 (inverse (multiply (inverse (multiply (inverse (multiply ?1421 ?1419)) (multiply ?1421 ?1420))) (multiply (inverse (multiply ?1418 ?1419)) (inverse (multiply (inverse ?1423) ?1423))))))) (multiply ?1422 ?1423)) =>= multiply (inverse ?1423) (multiply ?1418 ?1420) [1423, 1418, 1420, 1419, 1421, 1422] by Super 290 with 110 at 1,1,1,2,1,1,1,2
-Id : 10986, {_}: multiply (inverse ?66149) (multiply (inverse ?66146) ?66146) =?= multiply (inverse ?66149) (multiply (inverse ?66147) ?66147) [66147, 66146, 66149] by Demod 10540 with 306 at 2
-Id : 18, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?64 ?65)) (multiply ?64 ?66)))) (multiply (inverse ?66) (inverse (multiply (inverse ?66) ?66)))) =>= ?65 [66, 65, 64] by Super 4 with 9 at 1,1,1,2
-Id : 20513, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?122739 ?122740)) (multiply ?122739 ?122741)))) (multiply (inverse ?122741) (inverse (multiply (inverse ?122742) ?122742)))) =>= ?122740 [122742, 122741, 122740, 122739] by Super 18 with 3992 at 1,2,2,1,2
-Id : 23232, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?138627 ?138628)) (multiply ?138627 (inverse (multiply (inverse ?138629) ?138629)))))) (multiply (inverse ?138630) ?138630)) =>= ?138628 [138630, 138629, 138628, 138627] by Super 20513 with 3992 at 2,1,2
-Id : 20104, {_}: multiply (inverse (multiply ?120500 (inverse (multiply (inverse (inverse ?120501)) (multiply (inverse ?120502) (inverse (multiply (inverse ?120503) ?120503))))))) (multiply ?120500 ?120502) =>= ?120501 [120503, 120502, 120501, 120500] by Super 3323 with 3992 at 1,2,2,1,2,1,1,2
-Id : 20225, {_}: multiply (inverse (multiply ?121420 (inverse (multiply (inverse (inverse ?121421)) (multiply (inverse ?121419) ?121419))))) (multiply ?121420 (inverse (multiply (inverse ?121422) ?121422))) =>= ?121421 [121422, 121419, 121421, 121420] by Super 20104 with 3992 at 2,1,2,1,1,2
-Id : 23426, {_}: inverse (multiply (inverse (inverse ?140049)) (multiply (inverse ?140053) ?140053)) =?= inverse (multiply (inverse (inverse ?140049)) (multiply (inverse ?140050) ?140050)) [140050, 140053, 140049] by Super 23232 with 20225 at 1,1,1,1,2
-Id : 4770, {_}: inverse (multiply (inverse (multiply ?32594 ?32595)) (multiply ?32594 ?32595)) =?= inverse (multiply (inverse ?32596) ?32596) [32596, 32595, 32594] by Super 35 with 3992 at 1,3
-Id : 4818, {_}: inverse (multiply (inverse (multiply (inverse ?32938) ?32938)) (multiply (inverse ?32937) ?32937)) =?= inverse (multiply (inverse ?32939) ?32939) [32939, 32937, 32938] by Super 4770 with 3992 at 2,1,2
-Id : 21029, {_}: inverse (multiply (inverse (multiply ?125759 (inverse (multiply (inverse ?125760) (multiply (inverse ?125761) (inverse (multiply (inverse ?125762) ?125762))))))) (multiply ?125759 ?125761)) =>= ?125760 [125762, 125761, 125760, 125759] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 21146, {_}: inverse (multiply (inverse (multiply ?126647 (inverse (multiply (inverse ?126648) (multiply (inverse ?126646) ?126646))))) (multiply ?126647 (inverse (multiply (inverse ?126649) ?126649)))) =>= ?126648 [126649, 126646, 126648, 126647] by Super 21029 with 3992 at 2,1,2,1,1,1,2
-Id : 26499, {_}: multiply (inverse ?155764) ?155764 =?= inverse (multiply (inverse ?155765) ?155765) [155765, 155764] by Super 4818 with 21146 at 2
-Id : 4144, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?28920 ?28921)) (multiply ?28920 ?28918)))) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28918, 28921, 28920] by Super 18 with 3992 at 1,2,2,1,2
-Id : 27501, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?161353) ?161353))) (multiply (inverse (inverse (multiply (inverse ?161354) (multiply (inverse ?161355) ?161355)))) (inverse (multiply (inverse ?161356) ?161356)))) =>= ?161354 [161356, 161355, 161354, 161353] by Super 21146 with 26499 at 1,1,1,2
-Id : 5969, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?38946) ?38946))) (multiply (inverse ?38947) (inverse (multiply (inverse ?38947) ?38947)))) =>= ?38947 [38947, 38946] by Super 18 with 3992 at 1,1,1,1,2
-Id : 5995, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?39112) ?39112))) (multiply (inverse ?39113) (inverse (multiply (inverse ?39111) ?39111)))) =>= ?39113 [39111, 39113, 39112] by Super 5969 with 3992 at 1,2,2,1,2
-Id : 27636, {_}: inverse (multiply (inverse ?161354) (multiply (inverse ?161355) ?161355)) =>= ?161354 [161355, 161354] by Demod 27501 with 5995 at 2
-Id : 28099, {_}: inverse (multiply (inverse (multiply ?126647 ?126648)) (multiply ?126647 (inverse (multiply (inverse ?126649) ?126649)))) =>= ?126648 [126649, 126648, 126647] by Demod 21146 with 27636 at 2,1,1,1,2
-Id : 28101, {_}: inverse (multiply (inverse (multiply ?240 ?238)) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 240] by Demod 61 with 28099 at 2,1,1,1,2
-Id : 28103, {_}: inverse (multiply (inverse (multiply (inverse ?28918) ?28921)) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28921, 28918] by Demod 4144 with 28101 at 1,1,1,2
-Id : 28104, {_}: multiply (inverse (inverse (multiply (inverse ?28919) ?28919))) ?28921 =>= ?28921 [28921, 28919] by Demod 28103 with 28101 at 2
-Id : 28383, {_}: a2 === a2 [] by Demod 27989 with 28104 at 2
-Id : 27989, {_}: multiply (inverse (inverse (multiply (inverse ?163408) ?163408))) a2 =>= a2 [163408] by Super 27714 with 26499 at 1,1,2
-Id : 27714, {_}: multiply (inverse (multiply (inverse ?162124) ?162124)) a2 =>= a2 [162124] by Super 24198 with 26499 at 1,2
-Id : 24198, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?143636)) (multiply (inverse ?143638) ?143638))) (multiply (inverse (inverse ?143636)) (multiply (inverse ?143639) ?143639))) a2 =>= a2 [143639, 143638, 143636] by Super 11949 with 23426 at 1,1,2
-Id : 11949, {_}: multiply (multiply (inverse (multiply (inverse ?73741) (multiply (inverse ?73744) ?73744))) (multiply (inverse ?73741) (multiply (inverse ?73743) ?73743))) a2 =>= a2 [73743, 73744, 73741] by Super 5806 with 10986 at 2,1,2
-Id : 5806, {_}: multiply (multiply (inverse (multiply ?38037 (multiply (inverse ?38038) ?38038))) (multiply ?38037 (multiply (inverse ?38036) ?38036))) a2 =>= a2 [38036, 38038, 38037] by Super 4426 with 3992 at 2,2,1,2
-Id : 4426, {_}: multiply (multiply (inverse (multiply ?30432 (multiply ?30433 ?30431))) (multiply ?30432 (multiply ?30433 ?30431))) a2 =>= a2 [30431, 30433, 30432] by Super 4403 with 587 at 1,2
-Id : 4403, {_}: multiply (multiply (inverse ?30303) ?30303) a2 =>= a2 [30303] by Super 2 with 3992 at 1,2
-Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP422-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 11.146148s
-% SZS status Unsatisfiable for GRP423-1.p
-% SZS output start CNFRefutation for GRP423-1.p
-Id : 5, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (multiply (inverse ?8) (inverse (multiply (inverse ?8) ?8))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 4, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (multiply (inverse ?4) (inverse (multiply (inverse ?4) ?4))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 20, {_}: inverse (multiply (inverse (multiply ?72 ?73)) (multiply ?72 ?74)) =?= multiply (inverse ?74) (inverse (multiply (inverse ?73) (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse ?74) ?74))))))) [74, 73, 72] by Super 5 with 4 at 2,1,1,1,2
-Id : 9, {_}: inverse (multiply (inverse (multiply ?29 ?28)) (multiply ?29 ?30)) =?= multiply (inverse ?30) (inverse (multiply (inverse ?28) (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse ?30) ?30))))))) [30, 28, 29] by Super 5 with 4 at 2,1,1,1,2
-Id : 35, {_}: inverse (multiply (inverse (multiply ?156 ?157)) (multiply ?156 ?158)) =?= inverse (multiply (inverse (multiply ?155 ?157)) (multiply ?155 ?158)) [155, 158, 157, 156] by Super 20 with 9 at 3
-Id : 59, {_}: inverse (multiply (inverse (multiply ?228 (inverse (multiply (inverse (multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226))) (multiply (inverse ?229) (inverse (multiply (inverse ?229) ?229))))))) (multiply ?228 ?229)) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 229, 226, 225, 227, 228] by Super 4 with 35 at 1,1,2,1,1,1,2
-Id : 156, {_}: multiply (inverse (multiply ?725 ?726)) (multiply ?725 ?727) =?= multiply (inverse (multiply ?728 ?726)) (multiply ?728 ?727) [728, 727, 726, 725] by Demod 59 with 4 at 2
-Id : 163, {_}: multiply (inverse (multiply ?773 (multiply ?770 ?772))) (multiply ?773 ?774) =?= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770, 773] by Super 156 with 4 at 1,3
-Id : 110, {_}: multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 226, 225, 227] by Demod 59 with 4 at 2
-Id : 55, {_}: inverse (multiply (inverse (multiply ?201 (inverse (multiply (inverse ?202) (multiply (inverse (multiply ?198 ?199)) (inverse (multiply (inverse (multiply ?200 ?199)) (multiply ?200 ?199)))))))) (multiply ?201 (multiply ?198 ?199))) =>= ?202 [200, 199, 198, 202, 201] by Super 4 with 35 at 2,2,1,2,1,1,1,2
-Id : 3142, {_}: inverse (multiply (inverse (multiply ?22079 (inverse (multiply (inverse (multiply ?22076 (multiply ?22077 ?22078))) (multiply ?22076 (inverse (multiply (inverse (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))))))))) (multiply ?22079 (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078)))))))) =>= ?22080 [22080, 22081, 22078, 22077, 22076, 22079] by Super 55 with 163 at 1,2,1,1,1,2
-Id : 290, {_}: inverse (multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply ?1310 ?1311)) (multiply ?1310 (inverse (multiply (inverse ?1312) ?1312))))))) (multiply ?1309 ?1312)) =>= multiply (inverse ?1312) ?1311 [1312, 1311, 1310, 1309] by Super 4 with 35 at 2,1,1,1,2
-Id : 300, {_}: inverse (multiply (inverse (multiply ?1382 (inverse (multiply (inverse (multiply ?1383 ?1384)) (multiply ?1383 (inverse (multiply (inverse (multiply ?1381 ?1380)) (multiply ?1381 ?1380)))))))) (multiply ?1382 (multiply ?1379 ?1380))) =>= multiply (inverse (multiply ?1379 ?1380)) ?1384 [1379, 1380, 1381, 1384, 1383, 1382] by Super 290 with 110 at 1,2,2,1,2,1,1,1,2
-Id : 3323, {_}: multiply (inverse (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22077 ?22078) =>= ?22080 [22078, 22080, 22077] by Demod 3142 with 300 at 2
-Id : 3887, {_}: multiply (inverse (multiply ?27309 (multiply ?27310 ?27311))) (multiply ?27309 (multiply ?27310 ?27311)) =?= multiply (inverse ?27312) ?27312 [27312, 27311, 27310, 27309] by Super 163 with 3323 at 2,3
-Id : 3460, {_}: multiply (inverse (multiply ?24443 (multiply ?24440 ?24442))) (multiply ?24443 (multiply ?24440 ?24442)) =?= multiply (inverse ?24441) ?24441 [24441, 24442, 24440, 24443] by Super 163 with 3323 at 2,3
-Id : 3992, {_}: multiply (inverse ?28111) ?28111 =?= multiply (inverse ?28115) ?28115 [28115, 28111] by Super 3887 with 3460 at 2
-Id : 4190, {_}: multiply (inverse (multiply ?29130 ?29128)) (multiply ?29130 ?29131) =?= multiply (inverse (multiply (inverse ?29129) ?29129)) (multiply (inverse ?29128) ?29131) [29129, 29131, 29128, 29130] by Super 110 with 3992 at 1,1,3
-Id : 18, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?64 ?65)) (multiply ?64 ?66)))) (multiply (inverse ?66) (inverse (multiply (inverse ?66) ?66)))) =>= ?65 [66, 65, 64] by Super 4 with 9 at 1,1,1,2
-Id : 4144, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?28920 ?28921)) (multiply ?28920 ?28918)))) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28918, 28921, 28920] by Super 18 with 3992 at 1,2,2,1,2
-Id : 61, {_}: inverse (multiply (inverse (multiply ?240 (inverse (multiply (inverse (multiply ?239 ?238)) (multiply ?239 (inverse (multiply (inverse ?241) ?241))))))) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 239, 240] by Super 4 with 35 at 2,1,1,1,2
-Id : 14797, {_}: inverse (multiply (inverse (multiply ?88631 (inverse (multiply (inverse ?88632) (multiply (inverse ?88633) (inverse (multiply (inverse ?88634) ?88634))))))) (multiply ?88631 ?88633)) =>= ?88632 [88634, 88633, 88632, 88631] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 14914, {_}: inverse (multiply (inverse (multiply ?89519 (inverse (multiply (inverse ?89520) (multiply (inverse ?89518) ?89518))))) (multiply ?89519 (inverse (multiply (inverse ?89521) ?89521)))) =>= ?89520 [89521, 89518, 89520, 89519] by Super 14797 with 3992 at 2,1,2,1,1,1,2
-Id : 4605, {_}: inverse (multiply (inverse (multiply ?31655 ?31656)) (multiply ?31655 ?31656)) =?= inverse (multiply (inverse ?31657) ?31657) [31657, 31656, 31655] by Super 35 with 3992 at 1,3
-Id : 4653, {_}: inverse (multiply (inverse (multiply (inverse ?31999) ?31999)) (multiply (inverse ?31998) ?31998)) =?= inverse (multiply (inverse ?32000) ?32000) [32000, 31998, 31999] by Super 4605 with 3992 at 2,1,2
-Id : 18958, {_}: multiply (inverse ?111309) ?111309 =?= inverse (multiply (inverse ?111310) ?111310) [111310, 111309] by Super 4653 with 14914 at 2
-Id : 19832, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?116164) ?116164))) (multiply (inverse (inverse (multiply (inverse ?116165) (multiply (inverse ?116166) ?116166)))) (inverse (multiply (inverse ?116167) ?116167)))) =>= ?116165 [116167, 116166, 116165, 116164] by Super 14914 with 18958 at 1,1,1,2
-Id : 5672, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?37316) ?37316))) (multiply (inverse ?37317) (inverse (multiply (inverse ?37317) ?37317)))) =>= ?37317 [37317, 37316] by Super 18 with 3992 at 1,1,1,1,2
-Id : 5698, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?37482) ?37482))) (multiply (inverse ?37483) (inverse (multiply (inverse ?37481) ?37481)))) =>= ?37483 [37481, 37483, 37482] by Super 5672 with 3992 at 1,2,2,1,2
-Id : 19967, {_}: inverse (multiply (inverse ?116165) (multiply (inverse ?116166) ?116166)) =>= ?116165 [116166, 116165] by Demod 19832 with 5698 at 2
-Id : 20043, {_}: inverse (multiply (inverse (multiply ?89519 ?89520)) (multiply ?89519 (inverse (multiply (inverse ?89521) ?89521)))) =>= ?89520 [89521, 89520, 89519] by Demod 14914 with 19967 at 2,1,1,1,2
-Id : 20045, {_}: inverse (multiply (inverse (multiply ?240 ?238)) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 240] by Demod 61 with 20043 at 2,1,1,1,2
-Id : 20047, {_}: inverse (multiply (inverse (multiply (inverse ?28918) ?28921)) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28921, 28918] by Demod 4144 with 20045 at 1,1,1,2
-Id : 20048, {_}: multiply (inverse (inverse (multiply (inverse ?28919) ?28919))) ?28921 =>= ?28921 [28921, 28919] by Demod 20047 with 20045 at 2
-Id : 20166, {_}: multiply (inverse (multiply (inverse ?117322) ?117322)) ?117323 =>= ?117323 [117323, 117322] by Super 20048 with 19967 at 1,1,2
-Id : 20329, {_}: multiply (inverse (multiply ?29130 ?29128)) (multiply ?29130 ?29131) =>= multiply (inverse ?29128) ?29131 [29131, 29128, 29130] by Demod 4190 with 20166 at 3
-Id : 20341, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770] by Demod 163 with 20329 at 2
-Id : 20330, {_}: inverse (multiply (inverse ?238) ?241) =>= multiply (inverse ?241) ?238 [241, 238] by Demod 20045 with 20329 at 1,2
-Id : 20355, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (inverse (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772)))) ?771))) ?774) [771, 774, 772, 770] by Demod 20341 with 20330 at 2,1,1,2,3
-Id : 20356, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (inverse (inverse (multiply (inverse ?772) ?772))) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20355 with 20330 at 1,2,1,1,2,3
-Id : 20357, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (inverse (multiply (inverse ?772) ?772)) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20356 with 20330 at 1,1,1,2,1,1,2,3
-Id : 20358, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (multiply (inverse ?772) ?772) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20357 with 20330 at 1,1,2,1,1,2,3
-Id : 20377, {_}: multiply (multiply (inverse ?117322) ?117322) ?117323 =>= ?117323 [117323, 117322] by Demod 20166 with 20330 at 1,2
-Id : 20385, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply ?772 ?771))) ?774) [771, 774, 772, 770] by Demod 20358 with 20377 at 1,2,1,1,2,3
-Id : 20405, {_}: multiply (inverse (multiply (multiply (inverse ?117787) ?117787) ?117788)) ?117789 =?= multiply ?117790 (multiply (inverse (multiply ?117788 ?117790)) ?117789) [117790, 117789, 117788, 117787] by Super 20385 with 20377 at 1,1,2,3
-Id : 20523, {_}: multiply (inverse ?118011) ?118012 =<= multiply ?118013 (multiply (inverse (multiply ?118011 ?118013)) ?118012) [118013, 118012, 118011] by Demod 20405 with 20377 at 1,1,2
-Id : 20527, {_}: multiply (inverse (inverse (multiply ?118030 ?118031))) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (inverse (multiply (inverse ?118031) ?118032)) ?118033) [118032, 118033, 118031, 118030] by Super 20523 with 20329 at 1,1,2,3
-Id : 20587, {_}: multiply (inverse (inverse (multiply ?118030 ?118031))) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (multiply (inverse ?118032) ?118031) ?118033) [118032, 118033, 118031, 118030] by Demod 20527 with 20330 at 1,2,3
-Id : 3464, {_}: multiply (inverse (multiply ?24465 (inverse (multiply (inverse (inverse ?24466)) (multiply (inverse ?24467) (inverse (multiply (inverse ?24467) ?24467))))))) (multiply ?24465 ?24467) =>= ?24466 [24467, 24466, 24465] by Demod 3142 with 300 at 2
-Id : 12890, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?78617 (inverse ?78618))) (multiply ?78617 ?78619)))) (multiply (inverse ?78619) (inverse (multiply (inverse ?78619) ?78619))) =>= ?78618 [78619, 78618, 78617] by Super 3464 with 9 at 1,1,2
-Id : 13250, {_}: multiply (inverse (inverse (multiply (inverse ?80376) ?80376))) (multiply (inverse (inverse ?80377)) (inverse (multiply (inverse (inverse ?80377)) (inverse ?80377)))) =>= ?80377 [80377, 80376] by Super 12890 with 3992 at 1,1,1,2
-Id : 13299, {_}: multiply (inverse (inverse (multiply (inverse ?80682) ?80682))) (multiply (inverse (inverse ?80683)) (inverse (multiply (inverse ?80681) ?80681))) =>= ?80683 [80681, 80683, 80682] by Super 13250 with 3992 at 1,2,2,2
-Id : 209, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?973 ?974)) (multiply ?973 ?975)))) (multiply (inverse ?975) (inverse (multiply (inverse ?975) ?975)))) =>= ?974 [975, 974, 973] by Super 4 with 9 at 1,1,1,2
-Id : 228, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse (multiply ?1090 ?1088)) (multiply ?1090 ?1089))) (multiply (inverse (multiply ?1087 ?1088)) ?1091)))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1091, 1087, 1089, 1088, 1090] by Super 209 with 110 at 1,1,1,1,1,1,2
-Id : 20052, {_}: inverse (multiply (inverse (inverse (multiply (multiply (inverse ?1089) ?1088) (multiply (inverse (multiply ?1087 ?1088)) ?1091)))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1091, 1087, 1088, 1089] by Demod 228 with 20045 at 1,1,1,1,1,2
-Id : 87, {_}: inverse (multiply (inverse (multiply ?396 ?397)) (multiply ?396 ?398)) =?= inverse (multiply (inverse (multiply ?399 ?397)) (multiply ?399 ?398)) [399, 398, 397, 396] by Super 20 with 9 at 3
-Id : 92, {_}: inverse (multiply (inverse (multiply ?429 (multiply ?425 ?427))) (multiply ?429 ?430)) =?= inverse (multiply (inverse (multiply (inverse (multiply ?428 ?426)) (multiply ?428 ?427))) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 428, 430, 427, 425, 429] by Super 87 with 35 at 1,1,3
-Id : 20057, {_}: multiply (inverse ?430) (multiply ?425 ?427) =<= inverse (multiply (inverse (multiply (inverse (multiply ?428 ?426)) (multiply ?428 ?427))) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 428, 427, 425, 430] by Demod 92 with 20045 at 2
-Id : 20058, {_}: multiply (inverse ?430) (multiply ?425 ?427) =<= inverse (multiply (multiply (inverse ?427) ?426) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 427, 425, 430] by Demod 20057 with 20045 at 1,1,3
-Id : 20064, {_}: inverse (multiply (inverse (multiply (inverse ?1091) (multiply ?1087 ?1089))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1089, 1087, 1091] by Demod 20052 with 20058 at 1,1,1,2
-Id : 20065, {_}: multiply (inverse (inverse (multiply (inverse ?1091) ?1091))) (multiply ?1087 ?1089) =>= multiply ?1087 ?1089 [1089, 1087, 1091] by Demod 20064 with 20045 at 2
-Id : 20068, {_}: multiply (inverse (inverse ?80683)) (inverse (multiply (inverse ?80681) ?80681)) =>= ?80683 [80681, 80683] by Demod 13299 with 20065 at 2
-Id : 20372, {_}: multiply (inverse (inverse ?80683)) (multiply (inverse ?80681) ?80681) =>= ?80683 [80681, 80683] by Demod 20068 with 20330 at 2,2
-Id : 20427, {_}: multiply (inverse ?117788) ?117789 =<= multiply ?117790 (multiply (inverse (multiply ?117788 ?117790)) ?117789) [117790, 117789, 117788] by Demod 20405 with 20377 at 1,1,2
-Id : 20499, {_}: multiply (inverse ?117898) (multiply ?117898 (inverse (inverse ?117899))) =>= ?117899 [117899, 117898] by Super 20372 with 20427 at 2
-Id : 4166, {_}: inverse (multiply (inverse (multiply ?29022 (inverse (multiply (inverse ?29023) (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021))))))) (multiply ?29022 ?29020)) =>= ?29023 [29021, 29020, 29023, 29022] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 20061, {_}: multiply (inverse ?29020) (inverse (multiply (inverse ?29023) (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021))))) =>= ?29023 [29021, 29023, 29020] by Demod 4166 with 20045 at 2
-Id : 20368, {_}: multiply (inverse ?29020) (multiply (inverse (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021)))) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20061 with 20330 at 2,2
-Id : 20369, {_}: multiply (inverse ?29020) (multiply (multiply (inverse (inverse (multiply (inverse ?29021) ?29021))) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20368 with 20330 at 1,2,2
-Id : 20370, {_}: multiply (inverse ?29020) (multiply (multiply (inverse (multiply (inverse ?29021) ?29021)) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20369 with 20330 at 1,1,1,2,2
-Id : 20371, {_}: multiply (inverse ?29020) (multiply (multiply (multiply (inverse ?29021) ?29021) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20370 with 20330 at 1,1,2,2
-Id : 20379, {_}: multiply (inverse ?29020) (multiply ?29020 ?29023) =>= ?29023 [29023, 29020] by Demod 20371 with 20377 at 1,2,2
-Id : 20582, {_}: inverse (inverse ?117899) =>= ?117899 [117899] by Demod 20499 with 20379 at 2
-Id : 32543, {_}: multiply (multiply ?118030 ?118031) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (multiply (inverse ?118032) ?118031) ?118033) [118032, 118033, 118031, 118030] by Demod 20587 with 20582 at 1,2
-Id : 20530, {_}: multiply (inverse (multiply (inverse ?118044) ?118044)) ?118045 =?= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045, 118044] by Super 20523 with 20377 at 1,1,2,3
-Id : 20593, {_}: multiply (multiply (inverse ?118044) ?118044) ?118045 =?= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045, 118044] by Demod 20530 with 20330 at 1,2
-Id : 20594, {_}: ?118045 =<= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045] by Demod 20593 with 20377 at 2
-Id : 20765, {_}: multiply (inverse ?118471) (multiply ?118472 ?118473) =<= multiply (inverse (multiply (inverse ?118472) ?118471)) ?118473 [118473, 118472, 118471] by Super 20329 with 20594 at 1,1,2
-Id : 20804, {_}: multiply (inverse ?118471) (multiply ?118472 ?118473) =<= multiply (multiply (inverse ?118471) ?118472) ?118473 [118473, 118472, 118471] by Demod 20765 with 20330 at 1,3
-Id : 32544, {_}: multiply (multiply ?118030 ?118031) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (inverse ?118032) (multiply ?118031 ?118033)) [118032, 118033, 118031, 118030] by Demod 32543 with 20804 at 2,3
-Id : 20531, {_}: multiply (inverse (inverse ?118048)) ?118050 =<= multiply (multiply ?118048 ?118049) (multiply (inverse ?118049) ?118050) [118049, 118050, 118048] by Super 20523 with 20379 at 1,1,2,3
-Id : 22088, {_}: multiply ?118048 ?118050 =<= multiply (multiply ?118048 ?118049) (multiply (inverse ?118049) ?118050) [118049, 118050, 118048] by Demod 20531 with 20582 at 1,2
-Id : 32545, {_}: multiply (multiply ?118030 ?118031) ?118033 =?= multiply ?118030 (multiply ?118031 ?118033) [118033, 118031, 118030] by Demod 32544 with 22088 at 3
-Id : 33073, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 32545 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP423-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 19.895017s
-% SZS status Unsatisfiable for GRP444-1.p
-% SZS output start CNFRefutation for GRP444-1.p
-Id : 5, {_}: inverse (multiply ?7 (multiply ?8 (multiply (multiply ?9 (inverse ?9)) (inverse (multiply ?10 (multiply ?7 ?8)))))) =>= ?10 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (multiply ?2 (multiply ?3 (multiply (multiply ?4 (inverse ?4)) (inverse (multiply ?5 (multiply ?2 ?3)))))) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 6, {_}: inverse (multiply ?14 (multiply (multiply (multiply ?12 (inverse ?12)) (inverse (multiply ?13 (multiply ?16 ?14)))) (multiply (multiply ?15 (inverse ?15)) ?13))) =>= ?16 [15, 16, 13, 12, 14] by Super 5 with 4 at 2,2,2,1,2
-Id : 9, {_}: inverse (multiply (multiply (multiply ?32 (inverse ?32)) (inverse (multiply ?33 (multiply ?34 ?31)))) (multiply (multiply (multiply ?35 (inverse ?35)) ?33) (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 35, 31, 34, 33, 32] by Super 4 with 6 at 2,2,2,1,2
-Id : 11, {_}: inverse (multiply ?47 (multiply (multiply (multiply ?48 (inverse ?48)) (inverse (multiply ?49 (multiply ?50 ?47)))) (multiply (multiply ?51 (inverse ?51)) ?49))) =>= ?50 [51, 50, 49, 48, 47] by Super 5 with 4 at 2,2,2,1,2
-Id : 15, {_}: inverse (multiply (multiply (multiply ?82 (inverse ?82)) ?80) (multiply (multiply (multiply ?83 (inverse ?83)) ?81) (multiply (multiply ?85 (inverse ?85)) ?84))) =?= multiply (multiply ?79 (inverse ?79)) (inverse (multiply ?80 (multiply ?81 ?84))) [79, 84, 85, 81, 83, 80, 82] by Super 11 with 6 at 2,1,2,1,2
-Id : 70, {_}: multiply (multiply ?656 (inverse ?656)) (inverse (multiply (inverse (multiply ?653 (multiply ?655 ?657))) (multiply ?653 ?655))) =>= ?657 [657, 655, 653, 656] by Super 9 with 15 at 2
-Id : 7, {_}: inverse (multiply ?22 (multiply ?23 (multiply (multiply (multiply ?18 (multiply ?19 (multiply (multiply ?20 (inverse ?20)) (inverse (multiply ?21 (multiply ?18 ?19)))))) ?21) (inverse (multiply ?24 (multiply ?22 ?23)))))) =>= ?24 [24, 21, 20, 19, 18, 23, 22] by Super 5 with 4 at 2,1,2,2,1,2
-Id : 141, {_}: multiply (multiply ?1411 (inverse ?1411)) (inverse (multiply (inverse (multiply ?1412 (multiply ?1413 ?1414))) (multiply ?1412 ?1413))) =>= ?1414 [1414, 1413, 1412, 1411] by Super 9 with 15 at 2
-Id : 147, {_}: multiply (multiply ?1460 (inverse ?1460)) (inverse (multiply ?1458 (multiply ?1461 (multiply (multiply ?1456 (inverse ?1456)) (inverse (multiply ?1457 (multiply ?1458 ?1461))))))) =?= multiply (multiply ?1459 (inverse ?1459)) ?1457 [1459, 1457, 1456, 1461, 1458, 1460] by Super 141 with 6 at 1,1,2,2
-Id : 163, {_}: multiply (multiply ?1460 (inverse ?1460)) ?1457 =?= multiply (multiply ?1459 (inverse ?1459)) ?1457 [1459, 1457, 1460] by Demod 147 with 4 at 2,2
-Id : 237, {_}: inverse (multiply ?2095 (multiply ?2096 (multiply (multiply (multiply ?2097 (multiply ?2098 (multiply (multiply ?2099 (inverse ?2099)) (inverse (multiply ?2100 (multiply ?2097 ?2098)))))) ?2100) (inverse (multiply (multiply ?2094 (inverse ?2094)) (multiply ?2095 ?2096)))))) =?= multiply ?2093 (inverse ?2093) [2093, 2094, 2100, 2099, 2098, 2097, 2096, 2095] by Super 7 with 163 at 1,2,2,2,1,2
-Id : 290, {_}: multiply ?2094 (inverse ?2094) =?= multiply ?2093 (inverse ?2093) [2093, 2094] by Demod 237 with 7 at 2
-Id : 326, {_}: multiply (multiply ?2479 (inverse ?2479)) (inverse (multiply (inverse (multiply ?2477 (multiply (inverse ?2477) ?2480))) (multiply ?2478 (inverse ?2478)))) =>= ?2480 [2478, 2480, 2477, 2479] by Super 70 with 290 at 2,1,2,2
-Id : 328, {_}: multiply (multiply ?2489 (inverse ?2489)) (inverse (multiply (inverse (multiply ?2490 (multiply ?2488 (inverse ?2488)))) (multiply ?2490 ?2487))) =>= inverse ?2487 [2487, 2488, 2490, 2489] by Super 70 with 290 at 2,1,1,1,2,2
-Id : 604, {_}: inverse (multiply ?3845 (multiply ?3847 (inverse ?3847))) =?= inverse (multiply ?3845 (multiply ?3846 (inverse ?3846))) [3846, 3847, 3845] by Super 4 with 328 at 2,2,1,2
-Id : 792, {_}: inverse (multiply ?4988 (multiply (inverse ?4988) ?4987)) =?= inverse (multiply ?4986 (multiply (inverse ?4986) ?4987)) [4986, 4987, 4988] by Super 4 with 326 at 2,2,1,2
-Id : 870, {_}: inverse (multiply ?5461 (multiply ?5463 (inverse ?5463))) =?= inverse (multiply ?5462 (multiply (inverse ?5462) (inverse (inverse ?5461)))) [5462, 5463, 5461] by Super 604 with 792 at 3
-Id : 2786, {_}: inverse (multiply (inverse ?15453) (multiply ?15454 (multiply (multiply ?15455 (inverse ?15455)) (inverse (multiply ?15456 (multiply (inverse ?15456) ?15454)))))) =>= ?15453 [15456, 15455, 15454, 15453] by Super 6 with 326 at 1,2,1,2
-Id : 2859, {_}: inverse (multiply (inverse ?15956) (multiply (inverse (inverse (inverse (multiply ?15954 (multiply (inverse ?15954) ?15955))))) ?15955)) =>= ?15956 [15955, 15954, 15956] by Super 2786 with 326 at 2,2,1,2
-Id : 3662, {_}: inverse (multiply (inverse (inverse (inverse (multiply ?19641 (multiply (inverse ?19641) ?19642))))) (multiply ?19642 (multiply (multiply ?19643 (inverse ?19643)) ?19640))) =>= inverse ?19640 [19640, 19643, 19642, 19641] by Super 4 with 2859 at 2,2,2,1,2
-Id : 13794, {_}: inverse (inverse (multiply ?72764 (multiply (inverse (inverse (inverse (multiply ?72761 (multiply (inverse ?72761) ?72762))))) ?72762))) =>= ?72764 [72762, 72761, 72764] by Super 4 with 3662 at 2
-Id : 3676, {_}: multiply (multiply ?19736 (inverse ?19736)) (multiply (inverse (inverse (inverse (multiply ?19734 (multiply (inverse ?19734) ?19735))))) (multiply ?19737 (inverse ?19737))) =>= inverse ?19735 [19737, 19735, 19734, 19736] by Super 328 with 2859 at 2,2
-Id : 16741, {_}: inverse (inverse (inverse (multiply ?88187 (inverse ?88187)))) =?= multiply ?88186 (inverse ?88186) [88186, 88187] by Super 13794 with 3676 at 1,1,2
-Id : 17199, {_}: inverse (multiply ?90662 (multiply ?90661 (inverse ?90661))) =?= inverse (multiply ?90662 (inverse (inverse (inverse (multiply ?90660 (inverse ?90660)))))) [90660, 90661, 90662] by Super 870 with 16741 at 2,1,3
-Id : 3671, {_}: multiply (multiply ?19707 (inverse ?19707)) (multiply (inverse (inverse (inverse (multiply ?19705 (multiply (inverse ?19705) ?19706))))) (multiply ?19706 ?19708)) =>= ?19708 [19708, 19706, 19705, 19707] by Super 70 with 2859 at 2,2
-Id : 2874, {_}: inverse (multiply (inverse (multiply ?16071 (multiply (inverse ?16071) (inverse (inverse ?16069))))) (multiply ?16072 (multiply (multiply ?16073 (inverse ?16073)) (inverse (multiply ?16074 (multiply (inverse ?16074) ?16072)))))) =?= multiply ?16069 (multiply ?16070 (inverse ?16070)) [16070, 16074, 16073, 16072, 16069, 16071] by Super 2786 with 870 at 1,1,2
-Id : 790, {_}: inverse (multiply (inverse ?4975) (multiply ?4974 (multiply (multiply ?4976 (inverse ?4976)) (inverse (multiply ?4973 (multiply (inverse ?4973) ?4974)))))) =>= ?4975 [4973, 4976, 4974, 4975] by Super 6 with 326 at 1,2,1,2
-Id : 2903, {_}: multiply ?16071 (multiply (inverse ?16071) (inverse (inverse ?16069))) =?= multiply ?16069 (multiply ?16070 (inverse ?16070)) [16070, 16069, 16071] by Demod 2874 with 790 at 2
-Id : 17213, {_}: multiply ?90740 (inverse ?90740) =?= multiply (inverse (inverse (multiply ?90738 (inverse ?90738)))) (multiply ?90739 (inverse ?90739)) [90739, 90738, 90740] by Super 290 with 16741 at 2,3
-Id : 20625, {_}: multiply ?106744 (multiply (inverse ?106744) (inverse (inverse (inverse (inverse (multiply ?106742 (inverse ?106742))))))) =?= multiply ?106741 (inverse ?106741) [106741, 106742, 106744] by Super 2903 with 17213 at 3
-Id : 31961, {_}: multiply (multiply ?163343 (inverse ?163343)) (multiply (inverse (inverse (inverse (multiply ?163344 (multiply (inverse ?163344) ?163340))))) (multiply ?163342 (inverse ?163342))) =?= multiply (inverse ?163340) (inverse (inverse (inverse (inverse (multiply ?163341 (inverse ?163341)))))) [163341, 163342, 163340, 163344, 163343] by Super 3671 with 20625 at 2,2,2
-Id : 32420, {_}: inverse ?163340 =<= multiply (inverse ?163340) (inverse (inverse (inverse (inverse (multiply ?163341 (inverse ?163341)))))) [163341, 163340] by Demod 31961 with 3676 at 2
-Id : 32623, {_}: inverse (multiply (inverse ?166463) (multiply (inverse (inverse (inverse (multiply ?166461 (inverse ?166461))))) (inverse (inverse (inverse (inverse (multiply ?166462 (inverse ?166462)))))))) =>= ?166463 [166462, 166461, 166463] by Super 2859 with 32420 at 2,1,1,1,1,2,1,2
-Id : 32947, {_}: inverse (multiply (inverse ?166463) (inverse (inverse (inverse (multiply ?166461 (inverse ?166461)))))) =>= ?166463 [166461, 166463] by Demod 32623 with 32420 at 2,1,2
-Id : 34867, {_}: inverse (multiply (inverse ?172645) (multiply ?172647 (inverse ?172647))) =>= ?172645 [172647, 172645] by Super 17199 with 32947 at 3
-Id : 35297, {_}: multiply (multiply ?2479 (inverse ?2479)) (multiply ?2477 (multiply (inverse ?2477) ?2480)) =>= ?2480 [2480, 2477, 2479] by Demod 326 with 34867 at 2,2
-Id : 35489, {_}: inverse (multiply (inverse ?174505) (multiply ?174506 (inverse ?174506))) =>= ?174505 [174506, 174505] by Super 17199 with 32947 at 3
-Id : 616, {_}: multiply (multiply ?3943 (inverse ?3943)) (inverse (multiply (inverse (multiply ?3944 (multiply ?3945 (inverse ?3945)))) (multiply ?3944 ?3946))) =>= inverse ?3946 [3946, 3945, 3944, 3943] by Super 70 with 290 at 2,1,1,1,2,2
-Id : 619, {_}: multiply (multiply ?3962 (inverse ?3962)) (inverse (multiply (inverse (multiply ?3963 (multiply ?3964 (inverse ?3964)))) (multiply ?3961 (inverse ?3961)))) =>= inverse (inverse ?3963) [3961, 3964, 3963, 3962] by Super 616 with 290 at 2,1,2,2
-Id : 35296, {_}: multiply (multiply ?3962 (inverse ?3962)) (multiply ?3963 (multiply ?3964 (inverse ?3964))) =>= inverse (inverse ?3963) [3964, 3963, 3962] by Demod 619 with 34867 at 2,2
-Id : 35298, {_}: inverse (inverse (inverse (inverse (inverse (multiply ?19734 (multiply (inverse ?19734) ?19735)))))) =>= inverse ?19735 [19735, 19734] by Demod 3676 with 35296 at 2
-Id : 35615, {_}: inverse (multiply (inverse ?175100) (multiply ?175101 (inverse ?175101))) =?= inverse (inverse (inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))))) [175099, 175101, 175100] by Super 35489 with 35298 at 1,1,2
-Id : 35759, {_}: ?175100 =<= inverse (inverse (inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))))) [175099, 175100] by Demod 35615 with 34867 at 2
-Id : 14284, {_}: inverse (inverse (multiply ?75692 (multiply (inverse (inverse (inverse (multiply ?75693 (multiply (inverse ?75693) ?75694))))) ?75694))) =>= ?75692 [75694, 75693, 75692] by Super 4 with 3662 at 2
-Id : 14330, {_}: inverse (inverse (multiply ?75974 (multiply (inverse (inverse (inverse (multiply ?75975 (multiply ?75973 (inverse ?75973)))))) (inverse (inverse ?75975))))) =>= ?75974 [75973, 75975, 75974] by Super 14284 with 290 at 2,1,1,1,1,2,1,1,2
-Id : 36610, {_}: inverse (inverse (multiply ?177975 (multiply (inverse (inverse (inverse (multiply (inverse (inverse (inverse (multiply ?177974 (multiply (inverse ?177974) ?177973))))) (multiply ?177976 (inverse ?177976)))))) (inverse ?177973)))) =>= ?177975 [177976, 177973, 177974, 177975] by Super 14330 with 35759 at 1,2,2,1,1,2
-Id : 36795, {_}: inverse (inverse (multiply ?177975 (multiply (inverse (inverse (inverse (inverse (multiply ?177974 (multiply (inverse ?177974) ?177973)))))) (inverse ?177973)))) =>= ?177975 [177973, 177974, 177975] by Demod 36610 with 34867 at 1,1,1,2,1,1,2
-Id : 37525, {_}: inverse (inverse (multiply ?181200 (multiply ?181201 (inverse ?181201)))) =>= ?181200 [181201, 181200] by Demod 36795 with 35759 at 1,2,1,1,2
-Id : 37547, {_}: inverse (inverse (multiply ?181321 (multiply (inverse (inverse (multiply ?181319 (inverse ?181319)))) (multiply ?181320 (inverse ?181320))))) =>= ?181321 [181320, 181319, 181321] by Super 37525 with 16741 at 2,2,1,1,2
-Id : 36638, {_}: ?178102 =<= inverse (inverse (inverse (inverse (multiply ?178103 (multiply (inverse ?178103) ?178102))))) [178103, 178102] by Demod 35615 with 34867 at 2
-Id : 36754, {_}: multiply (inverse (inverse (multiply ?178614 (inverse ?178614)))) ?178615 =>= inverse (inverse (inverse (inverse ?178615))) [178615, 178614] by Super 36638 with 35297 at 1,1,1,1,3
-Id : 37663, {_}: inverse (inverse (multiply ?181321 (inverse (inverse (inverse (inverse (multiply ?181320 (inverse ?181320)))))))) =>= ?181321 [181320, 181321] by Demod 37547 with 36754 at 2,1,1,2
-Id : 32690, {_}: inverse ?166743 =<= multiply (inverse ?166743) (inverse (inverse (inverse (inverse (multiply ?166744 (inverse ?166744)))))) [166744, 166743] by Demod 31961 with 3676 at 2
-Id : 32829, {_}: inverse (multiply ?167379 (multiply ?167380 (multiply (multiply ?167381 (inverse ?167381)) (inverse (multiply ?167382 (multiply ?167379 ?167380)))))) =?= multiply ?167382 (inverse (inverse (inverse (inverse (multiply ?167383 (inverse ?167383)))))) [167383, 167382, 167381, 167380, 167379] by Super 32690 with 4 at 1,3
-Id : 33031, {_}: ?167382 =<= multiply ?167382 (inverse (inverse (inverse (inverse (multiply ?167383 (inverse ?167383)))))) [167383, 167382] by Demod 32829 with 4 at 2
-Id : 37664, {_}: inverse (inverse ?181321) =>= ?181321 [181321] by Demod 37663 with 33031 at 1,1,2
-Id : 37819, {_}: ?175100 =<= inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))) [175099, 175100] by Demod 35759 with 37664 at 3
-Id : 37820, {_}: ?175100 =<= multiply ?175099 (multiply (inverse ?175099) ?175100) [175099, 175100] by Demod 37819 with 37664 at 3
-Id : 37837, {_}: multiply (multiply ?2479 (inverse ?2479)) ?2480 =>= ?2480 [2480, 2479] by Demod 35297 with 37820 at 2,2
-Id : 37843, {_}: inverse (multiply ?2 (multiply ?3 (inverse (multiply ?5 (multiply ?2 ?3))))) =>= ?5 [5, 3, 2] by Demod 4 with 37837 at 2,2,1,2
-Id : 37841, {_}: inverse (multiply ?14 (multiply (inverse (multiply ?13 (multiply ?16 ?14))) (multiply (multiply ?15 (inverse ?15)) ?13))) =>= ?16 [15, 16, 13, 14] by Demod 6 with 37837 at 1,2,1,2
-Id : 37842, {_}: inverse (multiply ?14 (multiply (inverse (multiply ?13 (multiply ?16 ?14))) ?13)) =>= ?16 [16, 13, 14] by Demod 37841 with 37837 at 2,2,1,2
-Id : 13762, {_}: inverse (multiply (inverse ?72514) (multiply ?72515 (multiply (multiply ?72516 (inverse ?72516)) (inverse (multiply ?72517 (multiply (inverse ?72517) ?72515)))))) =?= multiply (inverse (inverse (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72517, 72516, 72515, 72514] by Super 790 with 3662 at 1,1,2
-Id : 14092, {_}: ?72514 =<= multiply (inverse (inverse (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72514] by Demod 13762 with 790 at 2
-Id : 37791, {_}: ?72514 =<= multiply (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72514] by Demod 14092 with 37664 at 1,3
-Id : 37888, {_}: ?72514 =<= multiply (inverse ?72512) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72514] by Demod 37791 with 37820 at 1,1,3
-Id : 37889, {_}: ?72514 =<= multiply (inverse ?72512) (multiply ?72512 ?72514) [72512, 72514] by Demod 37888 with 37837 at 2,2,3
-Id : 37945, {_}: multiply (multiply (inverse ?181731) ?181731) ?181732 =>= ?181732 [181732, 181731] by Super 37837 with 37664 at 2,1,2
-Id : 37993, {_}: inverse (multiply (multiply (inverse ?181852) ?181852) (multiply ?181853 (inverse (multiply ?181854 ?181853)))) =>= ?181854 [181854, 181853, 181852] by Super 37843 with 37945 at 2,1,2,2,1,2
-Id : 38039, {_}: inverse (multiply ?181853 (inverse (multiply ?181854 ?181853))) =>= ?181854 [181854, 181853] by Demod 37993 with 37945 at 1,2
-Id : 38275, {_}: inverse ?182456 =<= multiply ?182455 (inverse (multiply ?182456 ?182455)) [182455, 182456] by Super 37664 with 38039 at 1,2
-Id : 38457, {_}: inverse (multiply ?182870 ?182871) =<= multiply (inverse ?182871) (inverse ?182870) [182871, 182870] by Super 37889 with 38275 at 2,3
-Id : 38459, {_}: inverse (multiply (inverse ?182877) ?182878) =>= multiply (inverse ?182878) ?182877 [182878, 182877] by Super 38457 with 37664 at 2,3
-Id : 38608, {_}: multiply (inverse (multiply (inverse (multiply ?183123 (multiply ?183124 (inverse ?183122)))) ?183123)) ?183122 =>= ?183124 [183122, 183124, 183123] by Super 37842 with 38459 at 2
-Id : 38646, {_}: multiply (multiply (inverse ?183123) (multiply ?183123 (multiply ?183124 (inverse ?183122)))) ?183122 =>= ?183124 [183122, 183124, 183123] by Demod 38608 with 38459 at 1,2
-Id : 38647, {_}: multiply (multiply ?183124 (inverse ?183122)) ?183122 =>= ?183124 [183122, 183124] by Demod 38646 with 37889 at 1,2
-Id : 39562, {_}: inverse (multiply ?184856 (multiply ?184857 (inverse ?184858))) =>= multiply ?184858 (inverse (multiply ?184856 ?184857)) [184858, 184857, 184856] by Super 37843 with 38647 at 1,2,2,1,2
-Id : 39573, {_}: inverse (multiply ?184910 (inverse ?184909)) =<= multiply (multiply ?184909 ?184911) (inverse (multiply ?184910 ?184911)) [184911, 184909, 184910] by Super 39562 with 38275 at 2,1,2
-Id : 38360, {_}: inverse (multiply ?182630 (inverse ?182631)) =>= multiply ?182631 (inverse ?182630) [182631, 182630] by Super 37820 with 38275 at 2,3
-Id : 40719, {_}: multiply ?186598 (inverse ?186599) =<= multiply (multiply ?186598 ?186600) (inverse (multiply ?186599 ?186600)) [186600, 186599, 186598] by Demod 39573 with 38360 at 2
-Id : 37844, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply (multiply (multiply ?35 (inverse ?35)) ?33) (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 35, 31, 34, 33] by Demod 9 with 37837 at 1,1,2
-Id : 37845, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply ?33 (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 31, 34, 33] by Demod 37844 with 37837 at 1,2,1,2
-Id : 37846, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply ?33 ?34)) =>= ?31 [31, 34, 33] by Demod 37845 with 37837 at 2,2,1,2
-Id : 38597, {_}: multiply (inverse (multiply ?33 ?34)) (multiply ?33 (multiply ?34 ?31)) =>= ?31 [31, 34, 33] by Demod 37846 with 38459 at 2
-Id : 40727, {_}: multiply ?186633 (inverse (inverse (multiply ?186630 ?186631))) =<= multiply (multiply ?186633 (multiply ?186630 (multiply ?186631 ?186632))) (inverse ?186632) [186632, 186631, 186630, 186633] by Super 40719 with 38597 at 1,2,3
-Id : 40827, {_}: multiply ?186633 (multiply ?186630 ?186631) =<= multiply (multiply ?186633 (multiply ?186630 (multiply ?186631 ?186632))) (inverse ?186632) [186632, 186631, 186630, 186633] by Demod 40727 with 37664 at 2,2
-Id : 38369, {_}: inverse ?182667 =<= multiply ?182668 (inverse (multiply ?182667 ?182668)) [182668, 182667] by Super 37664 with 38039 at 1,2
-Id : 38383, {_}: inverse ?182710 =<= multiply (inverse (multiply ?182709 ?182710)) (inverse (inverse ?182709)) [182709, 182710] by Super 38369 with 38275 at 1,2,3
-Id : 38416, {_}: inverse ?182710 =<= multiply (inverse (multiply ?182709 ?182710)) ?182709 [182709, 182710] by Demod 38383 with 37664 at 2,3
-Id : 38850, {_}: inverse (multiply ?183591 (multiply ?183592 (inverse ?183590))) =>= multiply ?183590 (inverse (multiply ?183591 ?183592)) [183590, 183592, 183591] by Super 37843 with 38647 at 1,2,2,1,2
-Id : 39557, {_}: inverse (multiply ?184829 (inverse ?184830)) =<= multiply (multiply ?184830 (inverse (multiply ?184828 ?184829))) ?184828 [184828, 184830, 184829] by Super 38416 with 38850 at 1,3
-Id : 40495, {_}: multiply ?186270 (inverse ?186271) =<= multiply (multiply ?186270 (inverse (multiply ?186272 ?186271))) ?186272 [186272, 186271, 186270] by Demod 39557 with 38360 at 2
-Id : 38758, {_}: inverse ?183471 =<= multiply (inverse (multiply ?183472 ?183471)) ?183472 [183472, 183471] by Demod 38383 with 37664 at 2,3
-Id : 38773, {_}: inverse (multiply ?183521 (inverse (multiply ?183522 (multiply ?183523 ?183521)))) =>= multiply ?183522 ?183523 [183523, 183522, 183521] by Super 38758 with 37843 at 1,3
-Id : 38833, {_}: multiply (multiply ?183522 (multiply ?183523 ?183521)) (inverse ?183521) =>= multiply ?183522 ?183523 [183521, 183523, 183522] by Demod 38773 with 38360 at 2
-Id : 40530, {_}: multiply (multiply ?186419 (multiply ?186420 (multiply ?186422 ?186421))) (inverse ?186421) =>= multiply (multiply ?186419 ?186420) ?186422 [186421, 186422, 186420, 186419] by Super 40495 with 38833 at 1,3
-Id : 56629, {_}: multiply ?186633 (multiply ?186630 ?186631) =?= multiply (multiply ?186633 ?186630) ?186631 [186631, 186630, 186633] by Demod 40827 with 40530 at 3
-Id : 57301, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 56629 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP444-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- divide is 93
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 0.103879s
-% SZS status Unsatisfiable for GRP452-1.p
-% SZS output start CNFRefutation for GRP452-1.p
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
-Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 265, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 269, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 265 with 33 at 2,1,1,3
-Id : 285, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 269 with 33 at 2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 270, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 265 with 40 at 2,1,1,3
-Id : 286, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 270 with 8 at 1,1,2
-Id : 306, {_}: divide (divide (inverse (inverse ?778)) ?779) (inverse ?779) =>= ?778 [779, 778] by Super 63 with 286 at 1,2
-Id : 319, {_}: multiply (divide (inverse (inverse ?778)) ?779) ?779 =>= ?778 [779, 778] by Demod 306 with 33 at 2
-Id : 743, {_}: ?1513 =<= inverse (inverse (inverse (inverse ?1513))) [1513] by Super 36 with 319 at 2
-Id : 138, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 1751, {_}: multiply ?3407 (divide (inverse ?3408) ?3409) =<= inverse (inverse (divide (inverse (divide ?3408 ?3407)) ?3409)) [3409, 3408, 3407] by Super 743 with 138 at 1,1,3
-Id : 1830, {_}: multiply ?3532 (divide (inverse ?3532) ?3533) =>= inverse (inverse (inverse ?3533)) [3533, 3532] by Super 1751 with 40 at 1,1,3
-Id : 682, {_}: ?1380 =<= inverse (inverse (inverse (inverse ?1380))) [1380] by Super 36 with 319 at 2
-Id : 735, {_}: multiply ?1490 (inverse (inverse (inverse ?1489))) =>= divide ?1490 ?1489 [1489, 1490] by Super 33 with 682 at 2,3
-Id : 742, {_}: multiply (divide ?1510 ?1511) ?1511 =>= inverse (inverse ?1510) [1511, 1510] by Super 319 with 682 at 1,1,2
-Id : 868, {_}: inverse (inverse ?1672) =<= divide (divide ?1672 (inverse (inverse (inverse ?1673)))) ?1673 [1673, 1672] by Super 735 with 742 at 2
-Id : 1203, {_}: inverse (inverse ?2233) =<= divide (multiply ?2233 (inverse (inverse ?2234))) ?2234 [2234, 2233] by Demod 868 with 33 at 1,3
-Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
-Id : 1217, {_}: inverse (inverse (inverse (inverse (divide ?2285 ?2285)))) =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Super 1203 with 55 at 1,3
-Id : 1250, {_}: divide ?2285 ?2285 =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Demod 1217 with 682 at 2
-Id : 1251, {_}: divide ?2285 ?2285 =?= divide ?2286 ?2286 [2286, 2285] by Demod 1250 with 682 at 1,3
-Id : 1840, {_}: multiply ?3573 (divide ?3572 ?3572) =?= inverse (inverse (inverse (inverse ?3573))) [3572, 3573] by Super 1830 with 1251 at 2,2
-Id : 1879, {_}: multiply ?3573 (divide ?3572 ?3572) =>= ?3573 [3572, 3573] by Demod 1840 with 682 at 3
-Id : 1919, {_}: multiply (inverse (divide ?3678 ?3679)) (divide ?3677 ?3677) =>= inverse (inverse (multiply ?3679 (inverse ?3678))) [3677, 3679, 3678] by Super 285 with 1879 at 2,1,1,3
-Id : 1946, {_}: inverse (divide ?3678 ?3679) =<= inverse (inverse (multiply ?3679 (inverse ?3678))) [3679, 3678] by Demod 1919 with 1879 at 2
-Id : 1947, {_}: inverse (divide ?3678 ?3679) =<= divide (inverse (inverse ?3679)) ?3678 [3679, 3678] by Demod 1946 with 286 at 3
-Id : 1966, {_}: inverse (divide ?126 (multiply ?128 ?126)) =>= ?128 [128, 126] by Demod 63 with 1947 at 2
-Id : 748, {_}: multiply ?1528 (inverse ?1529) =<= inverse (inverse (divide (inverse (inverse ?1528)) ?1529)) [1529, 1528] by Super 743 with 286 at 1,1,3
-Id : 1970, {_}: multiply ?1528 (inverse ?1529) =<= inverse (inverse (inverse (divide ?1529 ?1528))) [1529, 1528] by Demod 748 with 1947 at 1,1,3
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 1967, {_}: inverse ?121 =<= inverse (divide ?121 (divide ?120 ?120)) [120, 121] by Demod 50 with 1947 at 3
-Id : 1903, {_}: divide ?3630 (divide ?3629 ?3629) =>= inverse (inverse ?3630) [3629, 3630] by Super 742 with 1879 at 2
-Id : 2257, {_}: inverse ?121 =<= inverse (inverse (inverse ?121)) [121] by Demod 1967 with 1903 at 1,3
-Id : 2261, {_}: multiply ?1528 (inverse ?1529) =<= inverse (divide ?1529 ?1528) [1529, 1528] by Demod 1970 with 2257 at 3
-Id : 2271, {_}: multiply (multiply ?128 ?126) (inverse ?126) =>= ?128 [126, 128] by Demod 1966 with 2261 at 2
-Id : 869, {_}: multiply (divide ?1675 ?1676) ?1676 =>= inverse (inverse ?1675) [1676, 1675] by Super 319 with 682 at 1,1,2
-Id : 873, {_}: multiply (multiply ?1689 ?1688) (inverse ?1688) =>= inverse (inverse ?1689) [1688, 1689] by Super 869 with 33 at 1,2
-Id : 2276, {_}: inverse (inverse ?128) =>= ?128 [128] by Demod 2271 with 873 at 2
-Id : 2434, {_}: a2 === a2 [] by Demod 85 with 2276 at 2
-Id : 85, {_}: inverse (inverse a2) =>= a2 [] by Demod 2 with 47 at 2
-Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP452-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 91
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 0.111823s
-% SZS status Unsatisfiable for GRP453-1.p
-% SZS output start CNFRefutation for GRP453-1.p
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 264, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 268, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 264 with 33 at 2,1,1,3
-Id : 284, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 268 with 33 at 2
-Id : 269, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 264 with 40 at 2,1,1,3
-Id : 285, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 269 with 8 at 1,1,2
-Id : 307, {_}: divide (inverse (inverse ?786)) ?787 =<= inverse (inverse (multiply ?786 (inverse ?787))) [787, 786] by Demod 269 with 8 at 1,1,2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 310, {_}: divide (inverse (inverse (divide ?798 ?798))) ?799 =>= inverse (inverse (inverse (inverse (inverse ?799)))) [799, 798] by Super 307 with 36 at 1,1,3
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 325, {_}: inverse ?799 =<= inverse (inverse (inverse (inverse (inverse ?799)))) [799] by Demod 310 with 50 at 2
-Id : 332, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= divide ?837 (inverse ?836) [836, 837] by Super 33 with 325 at 2,3
-Id : 354, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= multiply ?837 ?836 [836, 837] by Demod 332 with 33 at 3
-Id : 364, {_}: divide (inverse (inverse ?880)) (inverse (inverse (inverse ?881))) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Super 285 with 354 at 1,1,3
-Id : 423, {_}: multiply (inverse (inverse ?880)) (inverse (inverse ?881)) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Demod 364 with 33 at 2
-Id : 448, {_}: divide (inverse (inverse (inverse (inverse ?1012)))) (inverse ?1013) =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Super 285 with 423 at 1,1,3
-Id : 470, {_}: multiply (inverse (inverse (inverse (inverse ?1012)))) ?1013 =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Demod 448 with 33 at 2
-Id : 499, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1108 ?1109))))))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Super 63 with 470 at 1,1,1,2
-Id : 519, {_}: divide (inverse (inverse (multiply ?1108 ?1109))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Demod 499 with 325 at 1,2
-Id : 571, {_}: ?1204 =<= inverse (inverse (inverse (inverse ?1204))) [1204] by Demod 519 with 63 at 2
-Id : 137, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 1535, {_}: multiply ?2972 (divide (inverse ?2973) ?2974) =<= inverse (inverse (divide (inverse (divide ?2973 ?2972)) ?2974)) [2974, 2973, 2972] by Super 571 with 137 at 1,1,3
-Id : 1610, {_}: multiply ?3089 (divide (inverse ?3089) ?3090) =>= inverse (inverse (inverse ?3090)) [3090, 3089] by Super 1535 with 40 at 1,1,3
-Id : 520, {_}: ?1108 =<= inverse (inverse (inverse (inverse ?1108))) [1108] by Demod 519 with 63 at 2
-Id : 565, {_}: multiply ?1187 (inverse (inverse (inverse ?1186))) =>= divide ?1187 ?1186 [1186, 1187] by Super 33 with 520 at 2,3
-Id : 590, {_}: divide (inverse (inverse ?1228)) (inverse (inverse ?1229)) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Super 285 with 565 at 1,1,3
-Id : 652, {_}: multiply (inverse (inverse ?1228)) (inverse ?1229) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Demod 590 with 33 at 2
-Id : 676, {_}: divide (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) (inverse ?1337) =>= inverse (inverse ?1336) [1337, 1336] by Super 63 with 652 at 1,1,1,2
-Id : 716, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 676 with 33 at 2
-Id : 717, {_}: multiply (divide ?1336 ?1337) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 716 with 520 at 1,2
-Id : 729, {_}: inverse (inverse ?1423) =<= divide (divide ?1423 (inverse (inverse (inverse ?1424)))) ?1424 [1424, 1423] by Super 565 with 717 at 2
-Id : 1120, {_}: inverse (inverse ?2062) =<= divide (multiply ?2062 (inverse (inverse ?2063))) ?2063 [2063, 2062] by Demod 729 with 33 at 1,3
-Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
-Id : 1134, {_}: inverse (inverse (inverse (inverse (divide ?2114 ?2114)))) =?= divide (inverse (inverse (inverse (inverse ?2115)))) ?2115 [2115, 2114] by Super 1120 with 55 at 1,3
-Id : 1167, {_}: divide ?2114 ?2114 =?= divide (inverse (inverse (inverse (inverse ?2115)))) ?2115 [2115, 2114] by Demod 1134 with 520 at 2
-Id : 1168, {_}: divide ?2114 ?2114 =?= divide ?2115 ?2115 [2115, 2114] by Demod 1167 with 520 at 1,3
-Id : 1620, {_}: multiply ?3130 (divide ?3129 ?3129) =>= inverse (inverse (inverse (inverse ?3130))) [3129, 3130] by Super 1610 with 1168 at 2,2
-Id : 1658, {_}: multiply ?3130 (divide ?3129 ?3129) =>= ?3130 [3129, 3130] by Demod 1620 with 520 at 3
-Id : 1679, {_}: multiply (inverse (divide ?3178 ?3179)) (divide ?3177 ?3177) =>= inverse (inverse (multiply ?3179 (inverse ?3178))) [3177, 3179, 3178] by Super 284 with 1658 at 2,1,1,3
-Id : 1729, {_}: inverse (divide ?3178 ?3179) =<= inverse (inverse (multiply ?3179 (inverse ?3178))) [3179, 3178] by Demod 1679 with 1658 at 2
-Id : 1730, {_}: inverse (divide ?3178 ?3179) =<= divide (inverse (inverse ?3179)) ?3178 [3179, 3178] by Demod 1729 with 285 at 3
-Id : 1760, {_}: multiply (inverse (inverse ?3336)) ?3337 =>= inverse (divide (inverse ?3337) ?3336) [3337, 3336] by Super 33 with 1730 at 3
-Id : 1861, {_}: multiply (inverse (divide (inverse ?3480) ?3482)) ?3481 =<= inverse (inverse (multiply ?3482 (inverse (divide (inverse ?3481) ?3480)))) [3481, 3482, 3480] by Super 284 with 1760 at 2,1,1,3
-Id : 1743, {_}: inverse (divide ?689 ?688) =<= inverse (inverse (multiply ?688 (inverse ?689))) [688, 689] by Demod 285 with 1730 at 2
-Id : 1928, {_}: multiply (inverse (divide (inverse ?3480) ?3482)) ?3481 =>= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3482, 3480] by Demod 1861 with 1743 at 3
-Id : 1740, {_}: inverse (divide ?126 (multiply ?128 ?126)) =>= ?128 [128, 126] by Demod 63 with 1730 at 2
-Id : 1855, {_}: inverse (divide ?3461 (inverse (divide (inverse ?3461) ?3460))) =>= inverse (inverse ?3460) [3460, 3461] by Super 1740 with 1760 at 2,1,2
-Id : 1942, {_}: inverse (multiply ?3461 (divide (inverse ?3461) ?3460)) =>= inverse (inverse ?3460) [3460, 3461] by Demod 1855 with 33 at 1,2
-Id : 1552, {_}: multiply ?3041 (divide (inverse ?3041) ?3042) =>= inverse (inverse (inverse ?3042)) [3042, 3041] by Super 1535 with 40 at 1,1,3
-Id : 1943, {_}: inverse (inverse (inverse (inverse ?3460))) =>= inverse (inverse ?3460) [3460] by Demod 1942 with 1552 at 1,2
-Id : 1944, {_}: ?3460 =<= inverse (inverse ?3460) [3460] by Demod 1943 with 520 at 2
-Id : 1988, {_}: multiply ?1187 (inverse ?1186) =>= divide ?1187 ?1186 [1186, 1187] by Demod 565 with 1944 at 2,2
-Id : 1992, {_}: inverse (divide ?689 ?688) =<= multiply ?688 (inverse ?689) [688, 689] by Demod 1743 with 1944 at 3
-Id : 1998, {_}: inverse (divide ?1186 ?1187) =>= divide ?1187 ?1186 [1187, 1186] by Demod 1988 with 1992 at 2
-Id : 2689, {_}: multiply (divide ?3482 (inverse ?3480)) ?3481 =<= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3480, 3482] by Demod 1928 with 1998 at 1,2
-Id : 2690, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3480, 3482] by Demod 2689 with 33 at 1,2
-Id : 2691, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= divide ?3482 (divide (inverse ?3481) ?3480) [3481, 3480, 3482] by Demod 2690 with 1998 at 3
-Id : 2002, {_}: divide (multiply ?128 ?126) ?126 =>= ?128 [126, 128] by Demod 1740 with 1998 at 2
-Id : 1619, {_}: multiply (inverse (multiply ?3126 ?3127)) ?3126 =>= inverse (inverse (inverse ?3127)) [3127, 3126] by Super 1610 with 63 at 2,2
-Id : 2085, {_}: multiply (inverse (multiply ?3126 ?3127)) ?3126 =>= inverse ?3127 [3127, 3126] by Demod 1619 with 1944 at 3
-Id : 2092, {_}: divide (inverse ?3663) ?3662 =>= inverse (multiply ?3662 ?3663) [3662, 3663] by Super 2002 with 2085 at 1,2
-Id : 2692, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= divide ?3482 (inverse (multiply ?3480 ?3481)) [3481, 3480, 3482] by Demod 2691 with 2092 at 2,3
-Id : 2693, {_}: multiply (multiply ?3482 ?3480) ?3481 =?= multiply ?3482 (multiply ?3480 ?3481) [3481, 3480, 3482] by Demod 2692 with 33 at 3
-Id : 2797, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 2693 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP453-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 127.901553s
-% SZS status Unsatisfiable for GRP471-1.p
-% SZS output start CNFRefutation for GRP471-1.p
-Id : 7, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 4, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 466, {_}: divide (inverse (divide (inverse ?2074) (divide ?2075 (divide ?2076 ?2077)))) (multiply (divide ?2077 ?2076) ?2074) =>= ?2075 [2077, 2076, 2075, 2074] by Super 4 with 6 at 2,2
-Id : 2222, {_}: divide (inverse ?10322) (multiply (divide ?10323 ?10324) (divide (divide ?10324 ?10323) (divide ?10322 (divide ?10325 ?10326)))) =>= divide ?10326 ?10325 [10326, 10325, 10324, 10323, 10322] by Super 466 with 4 at 1,1,2
-Id : 498, {_}: divide (inverse ?2307) (multiply (divide ?2311 ?2310) (divide (divide ?2310 ?2311) (divide ?2307 (divide ?2308 ?2309)))) =>= divide ?2309 ?2308 [2309, 2308, 2310, 2311, 2307] by Super 466 with 4 at 1,1,2
-Id : 2240, {_}: divide (inverse ?10483) (multiply (divide ?10484 ?10485) (divide (divide ?10485 ?10484) (divide ?10483 (divide ?10482 ?10481)))) =?= divide (multiply (divide ?10479 ?10480) (divide (divide ?10480 ?10479) (divide ?10478 (divide ?10481 ?10482)))) (inverse ?10478) [10478, 10480, 10479, 10481, 10482, 10485, 10484, 10483] by Super 2222 with 498 at 2,2,2,2,2
-Id : 2367, {_}: divide ?10481 ?10482 =<= divide (multiply (divide ?10479 ?10480) (divide (divide ?10480 ?10479) (divide ?10478 (divide ?10481 ?10482)))) (inverse ?10478) [10478, 10480, 10479, 10482, 10481] by Demod 2240 with 498 at 2
-Id : 2430, {_}: divide ?11142 ?11143 =<= multiply (multiply (divide ?11144 ?11145) (divide (divide ?11145 ?11144) (divide ?11146 (divide ?11142 ?11143)))) ?11146 [11146, 11145, 11144, 11143, 11142] by Demod 2367 with 6 at 3
-Id : 2431, {_}: divide (inverse (divide ?11148 (divide ?11149 (divide ?11150 ?11151)))) (divide (divide ?11151 ?11150) ?11148) =?= multiply (multiply (divide ?11152 ?11153) (divide (divide ?11153 ?11152) (divide ?11154 ?11149))) ?11154 [11154, 11153, 11152, 11151, 11150, 11149, 11148] by Super 2430 with 4 at 2,2,2,1,3
-Id : 2616, {_}: ?11858 =<= multiply (multiply (divide ?11859 ?11860) (divide (divide ?11860 ?11859) (divide ?11861 ?11858))) ?11861 [11861, 11860, 11859, 11858] by Demod 2431 with 4 at 2
-Id : 2673, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (divide (divide (inverse ?12296) ?12298) (divide ?12299 ?12297))) ?12299 [12299, 12296, 12298, 12297] by Super 2616 with 6 at 1,1,3
-Id : 398, {_}: divide (inverse (divide ?1784 (divide ?1785 (divide (inverse ?1786) ?1787)))) (divide (multiply ?1787 ?1786) ?1784) =>= ?1785 [1787, 1786, 1785, 1784] by Super 4 with 6 at 1,2,2
-Id : 1221, {_}: divide (inverse (divide ?5281 (divide ?5282 (multiply (inverse ?5283) ?5284)))) (divide (multiply (inverse ?5284) ?5283) ?5281) =>= ?5282 [5284, 5283, 5282, 5281] by Super 398 with 6 at 2,2,1,1,2
-Id : 15, {_}: divide (inverse (divide ?58 (divide ?59 (multiply ?56 ?57)))) (divide (divide (inverse ?57) ?56) ?58) =>= ?59 [57, 56, 59, 58] by Super 4 with 6 at 2,2,1,1,2
-Id : 1238, {_}: divide (inverse ?5406) (divide (multiply (inverse ?5410) ?5409) (inverse (divide (multiply (inverse ?5409) ?5410) (divide ?5406 (multiply ?5407 ?5408))))) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5409, 5410, 5406] by Super 1221 with 15 at 1,1,2
-Id : 1282, {_}: divide (inverse ?5406) (multiply (multiply (inverse ?5410) ?5409) (divide (multiply (inverse ?5409) ?5410) (divide ?5406 (multiply ?5407 ?5408)))) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5409, 5410, 5406] by Demod 1238 with 6 at 2,2
-Id : 2872, {_}: ?12927 =<= multiply (multiply (divide (inverse ?12928) ?12929) (divide (multiply ?12929 ?12928) (divide ?12930 ?12927))) ?12930 [12930, 12929, 12928, 12927] by Super 2616 with 6 at 1,2,1,3
-Id : 3248, {_}: ?15081 =<= multiply (multiply (multiply (inverse ?15082) ?15083) (divide (multiply (inverse ?15083) ?15082) (divide ?15084 ?15081))) ?15084 [15084, 15083, 15082, 15081] by Super 2872 with 6 at 1,1,3
-Id : 10, {_}: divide (inverse (divide ?32 ?29)) (divide (divide ?33 (divide ?31 ?30)) ?32) =>= inverse (divide ?33 (divide ?29 (divide ?30 ?31))) [30, 31, 33, 29, 32] by Super 7 with 4 at 2,1,1,2
-Id : 22, {_}: inverse (divide ?98 (divide (divide ?101 (divide (divide ?99 ?100) ?98)) (divide ?100 ?99))) =>= ?101 [100, 99, 101, 98] by Super 4 with 10 at 2
-Id : 313, {_}: multiply ?1410 (divide ?1406 (divide (divide ?1407 (divide (divide ?1408 ?1409) ?1406)) (divide ?1409 ?1408))) =>= divide ?1410 ?1407 [1409, 1408, 1407, 1406, 1410] by Super 6 with 22 at 2,3
-Id : 13731, {_}: divide ?59402 ?59403 =<= multiply (divide (multiply (inverse ?59404) ?59405) ?59406) (divide ?59406 (divide (divide ?59403 ?59402) (multiply (inverse ?59405) ?59404))) [59406, 59405, 59404, 59403, 59402] by Super 3248 with 313 at 1,3
-Id : 13819, {_}: divide ?60191 ?60192 =<= multiply (multiply (multiply (inverse ?60193) ?60194) ?60190) (divide (inverse ?60190) (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193))) [60190, 60194, 60193, 60192, 60191] by Super 13731 with 6 at 1,3
-Id : 318, {_}: inverse (divide ?1446 (divide (divide ?1447 (divide (divide ?1448 ?1449) ?1446)) (divide ?1449 ?1448))) =>= ?1447 [1449, 1448, 1447, 1446] by Super 4 with 10 at 2
-Id : 1006, {_}: inverse (inverse (divide ?4256 (divide ?4257 (divide (inverse (divide (divide ?4258 ?4259) ?4257)) (divide ?4259 ?4258))))) =>= ?4256 [4259, 4258, 4257, 4256] by Super 318 with 10 at 1,2
-Id : 10788, {_}: inverse (inverse (inverse (divide ?46213 (divide ?46214 (divide ?46215 ?46216))))) =<= inverse (divide (divide (inverse (divide (divide ?46217 ?46218) (divide ?46213 (divide ?46216 ?46215)))) (divide ?46218 ?46217)) ?46214) [46218, 46217, 46216, 46215, 46214, 46213] by Super 1006 with 10 at 1,1,2
-Id : 31179, {_}: inverse (inverse (inverse (divide (divide ?147814 (divide (divide ?147815 ?147816) (divide ?147817 ?147818))) (divide ?147819 (divide ?147815 ?147816))))) =>= inverse (divide (divide ?147814 (divide ?147818 ?147817)) ?147819) [147819, 147818, 147817, 147816, 147815, 147814] by Super 10788 with 22 at 1,1,1,3
-Id : 23, {_}: divide (inverse (divide ?103 ?104)) (divide (divide ?105 (divide ?106 ?107)) ?103) =>= inverse (divide ?105 (divide ?104 (divide ?107 ?106))) [107, 106, 105, 104, 103] by Super 7 with 4 at 2,1,1,2
-Id : 32, {_}: divide (inverse (multiply ?171 ?170)) (divide (divide ?172 (divide ?173 ?174)) ?171) =>= inverse (divide ?172 (divide (inverse ?170) (divide ?174 ?173))) [174, 173, 172, 170, 171] by Super 23 with 6 at 1,1,2
-Id : 346, {_}: inverse (inverse (divide ?1643 (divide (inverse ?1642) (divide (inverse (multiply (divide ?1645 ?1644) ?1642)) (divide ?1644 ?1645))))) =>= ?1643 [1644, 1645, 1642, 1643] by Super 318 with 32 at 1,2
-Id : 31311, {_}: inverse (divide ?149137 (divide (divide (inverse (multiply (divide ?149135 ?149136) ?149134)) (divide ?149136 ?149135)) (divide ?149138 ?149139))) =>= inverse (divide (divide ?149137 (divide ?149139 ?149138)) (inverse ?149134)) [149139, 149138, 149134, 149136, 149135, 149137] by Super 31179 with 346 at 1,2
-Id : 57522, {_}: inverse (divide ?312686 (divide (divide (inverse (multiply (divide ?312687 ?312688) ?312689)) (divide ?312688 ?312687)) (divide ?312690 ?312691))) =>= inverse (multiply (divide ?312686 (divide ?312691 ?312690)) ?312689) [312691, 312690, 312689, 312688, 312687, 312686] by Demod 31311 with 6 at 1,3
-Id : 3434, {_}: divide ?16101 ?16102 =<= multiply (divide (divide ?16103 ?16104) ?16105) (divide ?16105 (divide (divide ?16102 ?16101) (divide ?16104 ?16103))) [16105, 16104, 16103, 16102, 16101] by Super 2430 with 313 at 1,3
-Id : 3646, {_}: divide (inverse ?16919) ?16920 =<= multiply (divide (divide ?16921 ?16922) ?16923) (divide ?16923 (divide (multiply ?16920 ?16919) (divide ?16922 ?16921))) [16923, 16922, 16921, 16920, 16919] by Super 3434 with 6 at 1,2,2,3
-Id : 3697, {_}: divide (inverse ?17353) ?17354 =<= multiply (divide (multiply ?17355 ?17352) ?17356) (divide ?17356 (divide (multiply ?17354 ?17353) (divide (inverse ?17352) ?17355))) [17356, 17352, 17355, 17354, 17353] by Super 3646 with 6 at 1,1,3
-Id : 154000, {_}: inverse (divide ?867821 (divide (divide (inverse (divide (inverse ?867822) ?867823)) (divide ?867824 (multiply ?867825 ?867826))) (divide ?867827 ?867828))) =>= inverse (multiply (divide ?867821 (divide ?867828 ?867827)) (divide ?867824 (divide (multiply ?867823 ?867822) (divide (inverse ?867826) ?867825)))) [867828, 867827, 867826, 867825, 867824, 867823, 867822, 867821] by Super 57522 with 3697 at 1,1,1,2,1,2
-Id : 412, {_}: divide (inverse ?1885) (divide (multiply ?1889 ?1888) (inverse (divide (divide (inverse ?1888) ?1889) (divide ?1885 (divide ?1886 ?1887))))) =>= divide ?1887 ?1886 [1887, 1886, 1888, 1889, 1885] by Super 398 with 4 at 1,1,2
-Id : 440, {_}: divide (inverse ?1885) (multiply (multiply ?1889 ?1888) (divide (divide (inverse ?1888) ?1889) (divide ?1885 (divide ?1886 ?1887)))) =>= divide ?1887 ?1886 [1887, 1886, 1888, 1889, 1885] by Demod 412 with 6 at 2,2
-Id : 154130, {_}: inverse (divide ?869515 (divide (divide (inverse (divide (inverse ?869516) ?869517)) (divide ?869514 ?869513)) (divide ?869518 ?869519))) =<= inverse (multiply (divide ?869515 (divide ?869519 ?869518)) (divide (inverse ?869510) (divide (multiply ?869517 ?869516) (divide (inverse (divide (divide (inverse ?869512) ?869511) (divide ?869510 (divide ?869513 ?869514)))) (multiply ?869511 ?869512))))) [869511, 869512, 869510, 869519, 869518, 869513, 869514, 869517, 869516, 869515] by Super 154000 with 440 at 2,1,2,1,2
-Id : 31180, {_}: inverse (inverse (inverse (divide (divide ?147825 (divide (divide (inverse (divide ?147821 (divide ?147822 (divide ?147823 ?147824)))) (divide (divide ?147824 ?147823) ?147821)) (divide ?147826 ?147827))) (divide ?147828 ?147822)))) =>= inverse (divide (divide ?147825 (divide ?147827 ?147826)) ?147828) [147828, 147827, 147826, 147824, 147823, 147822, 147821, 147825] by Super 31179 with 4 at 2,2,1,1,1,2
-Id : 31662, {_}: inverse (inverse (inverse (divide (divide ?150376 (divide ?150377 (divide ?150378 ?150379))) (divide ?150380 ?150377)))) =>= inverse (divide (divide ?150376 (divide ?150379 ?150378)) ?150380) [150380, 150379, 150378, 150377, 150376] by Demod 31180 with 4 at 1,2,1,1,1,1,2
-Id : 399, {_}: divide (inverse (divide (inverse ?1789) (divide ?1790 (divide (inverse ?1791) ?1792)))) (multiply (multiply ?1792 ?1791) ?1789) =>= ?1790 [1792, 1791, 1790, 1789] by Super 398 with 6 at 2,2
-Id : 31677, {_}: inverse (inverse (inverse (divide (divide ?150512 (divide (multiply (multiply ?150511 ?150510) ?150508) (divide ?150513 ?150514))) ?150509))) =<= inverse (divide (divide ?150512 (divide ?150514 ?150513)) (inverse (divide (inverse ?150508) (divide ?150509 (divide (inverse ?150510) ?150511))))) [150509, 150514, 150513, 150508, 150510, 150511, 150512] by Super 31662 with 399 at 2,1,1,1,2
-Id : 31809, {_}: inverse (inverse (inverse (divide (divide ?150512 (divide (multiply (multiply ?150511 ?150510) ?150508) (divide ?150513 ?150514))) ?150509))) =<= inverse (multiply (divide ?150512 (divide ?150514 ?150513)) (divide (inverse ?150508) (divide ?150509 (divide (inverse ?150510) ?150511)))) [150509, 150514, 150513, 150508, 150510, 150511, 150512] by Demod 31677 with 6 at 1,3
-Id : 154818, {_}: inverse (divide ?869515 (divide (divide (inverse (divide (inverse ?869516) ?869517)) (divide ?869514 ?869513)) (divide ?869518 ?869519))) =<= inverse (inverse (inverse (divide (divide ?869515 (divide (multiply (multiply (multiply ?869511 ?869512) (divide (divide (inverse ?869512) ?869511) (divide ?869510 (divide ?869513 ?869514)))) ?869510) (divide ?869518 ?869519))) (multiply ?869517 ?869516)))) [869510, 869512, 869511, 869519, 869518, 869513, 869514, 869517, 869516, 869515] by Demod 154130 with 31809 at 3
-Id : 155388, {_}: inverse (divide ?877204 (divide (divide (inverse (divide (inverse ?877205) ?877206)) (divide ?877207 ?877208)) (divide ?877209 ?877210))) =>= inverse (inverse (inverse (divide (divide ?877204 (divide (divide ?877208 ?877207) (divide ?877209 ?877210))) (multiply ?877206 ?877205)))) [877210, 877209, 877208, 877207, 877206, 877205, 877204] by Demod 154818 with 2673 at 1,2,1,1,1,1,3
-Id : 155389, {_}: inverse (divide ?877216 (divide (divide (inverse (divide (inverse ?877217) ?877218)) (divide ?877219 ?877220)) ?877213)) =<= inverse (inverse (inverse (divide (divide ?877216 (divide (divide ?877220 ?877219) (divide (inverse (divide ?877212 (divide ?877213 (divide ?877214 ?877215)))) (divide (divide ?877215 ?877214) ?877212)))) (multiply ?877218 ?877217)))) [877215, 877214, 877212, 877213, 877220, 877219, 877218, 877217, 877216] by Super 155388 with 4 at 2,2,1,2
-Id : 156615, {_}: inverse (divide ?885441 (divide (divide (inverse (divide (inverse ?885442) ?885443)) (divide ?885444 ?885445)) ?885446)) =>= inverse (inverse (inverse (divide (divide ?885441 (divide (divide ?885445 ?885444) ?885446)) (multiply ?885443 ?885442)))) [885446, 885445, 885444, 885443, 885442, 885441] by Demod 155389 with 4 at 2,2,1,1,1,1,3
-Id : 156655, {_}: inverse (divide ?885869 (divide (divide (inverse (divide ?885866 ?885870)) (divide ?885871 ?885872)) ?885873)) =<= inverse (inverse (inverse (divide (divide ?885869 (divide (divide ?885872 ?885871) ?885873)) (multiply ?885870 (divide ?885865 (divide (divide ?885866 (divide (divide ?885867 ?885868) ?885865)) (divide ?885868 ?885867))))))) [885868, 885867, 885865, 885873, 885872, 885871, 885870, 885866, 885869] by Super 156615 with 22 at 1,1,1,1,2,1,2
-Id : 157579, {_}: inverse (divide ?891923 (divide (divide (inverse (divide ?891924 ?891925)) (divide ?891926 ?891927)) ?891928)) =<= inverse (inverse (inverse (divide (divide ?891923 (divide (divide ?891927 ?891926) ?891928)) (divide ?891925 ?891924)))) [891928, 891927, 891926, 891925, 891924, 891923] by Demod 156655 with 313 at 2,1,1,1,3
-Id : 157660, {_}: inverse (divide (inverse (divide ?892784 ?892778)) (divide (divide (inverse (divide ?892781 ?892782)) (divide (divide ?892779 ?892780) ?892783)) ?892784)) =>= inverse (inverse (inverse (divide (inverse (divide ?892783 (divide ?892778 (divide ?892780 ?892779)))) (divide ?892782 ?892781)))) [892783, 892780, 892779, 892782, 892781, 892778, 892784] by Super 157579 with 10 at 1,1,1,1,3
-Id : 164761, {_}: inverse (inverse (divide (inverse (divide ?938345 ?938346)) (divide ?938347 (divide ?938348 (divide ?938349 ?938350))))) =<= inverse (inverse (inverse (divide (inverse (divide ?938348 (divide ?938347 (divide ?938350 ?938349)))) (divide ?938346 ?938345)))) [938350, 938349, 938348, 938347, 938346, 938345] by Demod 157660 with 10 at 1,2
-Id : 345, {_}: inverse (inverse (divide ?1638 (divide ?1637 (divide (inverse (divide (divide ?1640 ?1639) ?1637)) (divide ?1639 ?1640))))) =>= ?1638 [1639, 1640, 1637, 1638] by Super 318 with 10 at 1,2
-Id : 31310, {_}: inverse (divide ?149129 (divide (divide (inverse (divide (divide ?149127 ?149128) ?149132)) (divide ?149128 ?149127)) (divide ?149130 ?149131))) =>= inverse (divide (divide ?149129 (divide ?149131 ?149130)) ?149132) [149131, 149130, 149132, 149128, 149127, 149129] by Super 31179 with 345 at 1,2
-Id : 164877, {_}: inverse (inverse (divide (inverse (divide ?939554 ?939555)) (divide (divide (inverse (divide (divide ?939551 ?939552) ?939553)) (divide ?939552 ?939551)) (divide ?939556 (divide ?939557 ?939558))))) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?939556 (divide ?939557 ?939558)) ?939553)) (divide ?939555 ?939554)))) [939558, 939557, 939556, 939553, 939552, 939551, 939555, 939554] by Super 164761 with 31310 at 1,1,1,1,3
-Id : 177719, {_}: inverse (inverse (divide (divide (inverse (divide ?1018267 ?1018268)) (divide (divide ?1018269 ?1018270) ?1018271)) ?1018272)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1018271 (divide ?1018269 ?1018270)) ?1018272)) (divide ?1018268 ?1018267)))) [1018272, 1018271, 1018270, 1018269, 1018268, 1018267] by Demod 164877 with 31310 at 1,2
-Id : 177759, {_}: inverse (inverse (divide (divide (inverse (divide ?1018695 ?1018696)) (divide (divide (inverse (divide ?1018691 (divide ?1018692 (divide ?1018693 ?1018694)))) (divide (divide ?1018694 ?1018693) ?1018691)) ?1018697)) ?1018698)) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?1018697 ?1018692) ?1018698)) (divide ?1018696 ?1018695)))) [1018698, 1018697, 1018694, 1018693, 1018692, 1018691, 1018696, 1018695] by Super 177719 with 4 at 2,1,1,1,1,1,1,3
-Id : 178625, {_}: inverse (inverse (divide (divide (inverse (divide ?1023630 ?1023631)) (divide ?1023632 ?1023633)) ?1023634)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1023633 ?1023632) ?1023634)) (divide ?1023631 ?1023630)))) [1023634, 1023633, 1023632, 1023631, 1023630] by Demod 177759 with 4 at 1,2,1,1,1,2
-Id : 180647, {_}: inverse (inverse (divide (divide (inverse (divide ?1035759 ?1035760)) (divide (inverse ?1035761) ?1035762)) ?1035763)) =>= inverse (inverse (inverse (divide (inverse (divide (multiply ?1035762 ?1035761) ?1035763)) (divide ?1035760 ?1035759)))) [1035763, 1035762, 1035761, 1035760, 1035759] by Super 178625 with 6 at 1,1,1,1,1,1,3
-Id : 180814, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =<= inverse (inverse (inverse (divide (inverse (divide (multiply (inverse ?1037588) ?1037591) ?1037592)) (divide ?1037590 ?1037589)))) [1037592, 1037588, 1037591, 1037590, 1037589] by Super 180647 with 6 at 2,1,1,1,2
-Id : 187329, {_}: multiply ?1072739 (inverse (inverse (divide (inverse (divide (multiply (inverse ?1072737) ?1072736) ?1072738)) (divide ?1072735 ?1072734)))) =>= divide ?1072739 (inverse (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738))) [1072734, 1072735, 1072738, 1072736, 1072737, 1072739] by Super 6 with 180814 at 2,3
-Id : 187880, {_}: multiply ?1072739 (inverse (inverse (divide (inverse (divide (multiply (inverse ?1072737) ?1072736) ?1072738)) (divide ?1072735 ?1072734)))) =>= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072734, 1072735, 1072738, 1072736, 1072737, 1072739] by Demod 187329 with 6 at 3
-Id : 276296, {_}: inverse (inverse (divide (inverse (divide ?1501612 (divide ?1501613 ?1501614))) (divide ?1501615 (divide ?1501612 (divide ?1501613 ?1501614))))) =>= inverse (inverse (inverse ?1501615)) [1501615, 1501614, 1501613, 1501612] by Super 164761 with 4 at 1,1,1,3
-Id : 276336, {_}: inverse (inverse (divide (inverse (divide (inverse (divide ?1501959 (divide ?1501956 (divide ?1501957 ?1501958)))) (divide (divide ?1501958 ?1501957) ?1501959))) (divide ?1501960 ?1501956))) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501958, 1501957, 1501956, 1501959] by Super 276296 with 4 at 2,2,1,1,2
-Id : 277437, {_}: inverse (inverse (divide (inverse ?1506460) (divide ?1506461 ?1506460))) =>= inverse (inverse (inverse ?1506461)) [1506461, 1506460] by Demod 276336 with 4 at 1,1,1,1,2
-Id : 411, {_}: divide (inverse (divide ?1881 (divide ?1882 (multiply (inverse ?1883) ?1880)))) (divide (multiply (inverse ?1880) ?1883) ?1881) =>= ?1882 [1880, 1883, 1882, 1881] by Super 398 with 6 at 2,2,1,1,2
-Id : 277453, {_}: inverse (inverse (divide (inverse (divide (multiply (inverse ?1506555) ?1506554) ?1506552)) ?1506553)) =<= inverse (inverse (inverse (inverse (divide ?1506552 (divide ?1506553 (multiply (inverse ?1506554) ?1506555)))))) [1506553, 1506552, 1506554, 1506555] by Super 277437 with 411 at 2,1,1,2
-Id : 339, {_}: inverse (divide (inverse ?1603) (divide (divide ?1604 (multiply (divide ?1605 ?1606) ?1603)) (divide ?1606 ?1605))) =>= ?1604 [1606, 1605, 1604, 1603] by Super 318 with 6 at 2,1,2,1,2
-Id : 298734, {_}: inverse ?1602430 =<= inverse (inverse (inverse (divide ?1602430 (multiply (divide ?1602431 ?1602432) (divide ?1602432 ?1602431))))) [1602432, 1602431, 1602430] by Super 277437 with 339 at 1,2
-Id : 277476, {_}: inverse (inverse (divide (inverse (inverse ?1506721)) (multiply ?1506722 ?1506721))) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Super 277437 with 6 at 2,1,1,2
-Id : 298855, {_}: inverse (inverse (inverse (divide ?1603311 ?1603310))) =<= inverse (inverse (inverse (inverse (divide ?1603310 ?1603311)))) [1603310, 1603311] by Super 298734 with 277476 at 1,3
-Id : 299275, {_}: inverse (inverse (divide (inverse (divide (multiply (inverse ?1506555) ?1506554) ?1506552)) ?1506553)) =>= inverse (inverse (inverse (divide (divide ?1506553 (multiply (inverse ?1506554) ?1506555)) ?1506552))) [1506553, 1506552, 1506554, 1506555] by Demod 277453 with 298855 at 3
-Id : 299281, {_}: multiply ?1072739 (inverse (inverse (inverse (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738)))) =>= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072738, 1072737, 1072736, 1072734, 1072735, 1072739] by Demod 187880 with 299275 at 2,2
-Id : 299680, {_}: inverse (inverse (inverse (divide ?1606480 ?1606481))) =<= inverse (inverse (inverse (inverse (divide ?1606481 ?1606480)))) [1606481, 1606480] by Super 298734 with 277476 at 1,3
-Id : 299719, {_}: inverse (inverse (inverse (divide (inverse ?1606741) ?1606742))) =>= inverse (inverse (inverse (inverse (multiply ?1606742 ?1606741)))) [1606742, 1606741] by Super 299680 with 6 at 1,1,1,1,3
-Id : 300712, {_}: inverse (inverse (inverse (divide ?1610501 (inverse ?1610500)))) =<= inverse (inverse (inverse (inverse (inverse (multiply ?1610501 ?1610500))))) [1610500, 1610501] by Super 298855 with 299719 at 1,3
-Id : 303239, {_}: inverse (inverse (inverse (multiply ?1620581 ?1620582))) =<= inverse (inverse (inverse (inverse (inverse (multiply ?1620581 ?1620582))))) [1620582, 1620581] by Demod 300712 with 6 at 1,1,1,2
-Id : 2523, {_}: ?11149 =<= multiply (multiply (divide ?11152 ?11153) (divide (divide ?11153 ?11152) (divide ?11154 ?11149))) ?11154 [11154, 11153, 11152, 11149] by Demod 2431 with 4 at 2
-Id : 303314, {_}: inverse (inverse (inverse (multiply (multiply (divide ?1621150 ?1621151) (divide (divide ?1621151 ?1621150) (divide ?1621152 ?1621149))) ?1621152))) =>= inverse (inverse (inverse (inverse (inverse ?1621149)))) [1621149, 1621152, 1621151, 1621150] by Super 303239 with 2523 at 1,1,1,1,1,3
-Id : 304462, {_}: inverse (inverse (inverse ?1624383)) =<= inverse (inverse (inverse (inverse (inverse ?1624383)))) [1624383] by Demod 303314 with 2523 at 1,1,1,2
-Id : 304463, {_}: inverse (inverse (inverse (divide ?1624385 (divide (divide ?1624386 (divide (divide ?1624387 ?1624388) ?1624385)) (divide ?1624388 ?1624387))))) =>= inverse (inverse (inverse (inverse ?1624386))) [1624388, 1624387, 1624386, 1624385] by Super 304462 with 22 at 1,1,1,1,3
-Id : 305044, {_}: inverse (inverse ?1624386) =<= inverse (inverse (inverse (inverse ?1624386))) [1624386] by Demod 304463 with 22 at 1,1,2
-Id : 309508, {_}: inverse (inverse (inverse (divide ?1603311 ?1603310))) =>= inverse (inverse (divide ?1603310 ?1603311)) [1603310, 1603311] by Demod 298855 with 305044 at 3
-Id : 309601, {_}: multiply ?1072739 (inverse (inverse (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))))) =<= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 299281 with 309508 at 2,2
-Id : 310013, {_}: inverse (inverse ?1628964) =<= inverse (inverse (inverse (inverse ?1628964))) [1628964] by Demod 304463 with 22 at 1,1,2
-Id : 310154, {_}: inverse (inverse (divide ?1629909 (divide ?1629910 (divide (inverse (divide (divide ?1629911 ?1629912) ?1629910)) (divide ?1629912 ?1629911))))) =>= inverse (inverse ?1629909) [1629912, 1629911, 1629910, 1629909] by Super 310013 with 345 at 1,1,3
-Id : 310837, {_}: ?1629909 =<= inverse (inverse ?1629909) [1629909] by Demod 310154 with 345 at 2
-Id : 311136, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =<= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 309601 with 310837 at 2,2
-Id : 299278, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =<= inverse (inverse (inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)))) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 180814 with 299275 at 1,3
-Id : 299285, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =>= inverse (inverse (inverse (divide ?1037592 (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588))))) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 299278 with 298855 at 3
-Id : 309533, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =>= inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 299285 with 309508 at 3
-Id : 311173, {_}: divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592 =<= inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 309533 with 310837 at 2
-Id : 311174, {_}: divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592 =>= divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592 [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 311173 with 310837 at 3
-Id : 311184, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =<= multiply ?1072739 (inverse (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 311136 with 311174 at 1,2,3
-Id : 328, {_}: inverse (divide ?1523 (divide (divide ?1524 (divide (divide (inverse ?1522) ?1525) ?1523)) (multiply ?1525 ?1522))) =>= ?1524 [1525, 1522, 1524, 1523] by Super 318 with 6 at 2,2,1,2
-Id : 5095, {_}: multiply ?23662 (divide ?23663 (divide (divide ?23664 (divide (divide (inverse ?23665) ?23666) ?23663)) (multiply ?23666 ?23665))) =>= divide ?23662 ?23664 [23666, 23665, 23664, 23663, 23662] by Super 6 with 328 at 2,3
-Id : 5148, {_}: multiply ?24110 (inverse (divide ?24111 (divide ?24109 (divide (inverse (divide (multiply ?24113 ?24112) ?24109)) (divide (inverse ?24112) ?24113))))) =>= divide ?24110 ?24111 [24112, 24113, 24109, 24111, 24110] by Super 5095 with 10 at 2,2
-Id : 722, {_}: inverse (divide ?3136 (divide (divide ?3137 (divide (divide (inverse ?3138) ?3139) ?3136)) (multiply ?3139 ?3138))) =>= ?3137 [3139, 3138, 3137, 3136] by Super 318 with 6 at 2,2,1,2
-Id : 746, {_}: inverse (inverse (divide ?3302 (divide ?3301 (divide (inverse (divide (multiply ?3304 ?3303) ?3301)) (divide (inverse ?3303) ?3304))))) =>= ?3302 [3303, 3304, 3301, 3302] by Super 722 with 10 at 1,2
-Id : 311071, {_}: divide ?3302 (divide ?3301 (divide (inverse (divide (multiply ?3304 ?3303) ?3301)) (divide (inverse ?3303) ?3304))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 746 with 310837 at 2
-Id : 311292, {_}: multiply ?24110 (inverse ?24111) =>= divide ?24110 ?24111 [24111, 24110] by Demod 5148 with 311071 at 1,2,2
-Id : 311301, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =>= divide ?1072739 (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 311184 with 311292 at 3
-Id : 311313, {_}: divide ?60191 ?60192 =<= divide (multiply (multiply (inverse ?60193) ?60194) ?60190) (divide (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193)) (inverse ?60190)) [60190, 60194, 60193, 60192, 60191] by Demod 13819 with 311301 at 3
-Id : 311314, {_}: divide ?60191 ?60192 =<= divide (multiply (multiply (inverse ?60193) ?60194) ?60190) (multiply (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193)) ?60190) [60190, 60194, 60193, 60192, 60191] by Demod 311313 with 6 at 2,3
-Id : 54, {_}: divide (inverse (divide ?250 ?251)) (divide (divide ?252 (multiply ?253 ?254)) ?250) =>= inverse (divide ?252 (divide ?251 (divide (inverse ?254) ?253))) [254, 253, 252, 251, 250] by Super 23 with 6 at 2,1,2,2
-Id : 55, {_}: divide (inverse (divide (inverse ?256) ?257)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= inverse (divide ?258 (divide ?257 (divide (inverse ?260) ?259))) [260, 259, 258, 257, 256] by Super 54 with 6 at 2,2
-Id : 311016, {_}: inverse (divide ?1603311 ?1603310) =<= inverse (inverse (divide ?1603310 ?1603311)) [1603310, 1603311] by Demod 309508 with 310837 at 2
-Id : 311017, {_}: inverse (divide ?1603311 ?1603310) =>= divide ?1603310 ?1603311 [1603310, 1603311] by Demod 311016 with 310837 at 3
-Id : 311424, {_}: divide (divide ?257 (inverse ?256)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= inverse (divide ?258 (divide ?257 (divide (inverse ?260) ?259))) [260, 259, 258, 256, 257] by Demod 55 with 311017 at 1,2
-Id : 311425, {_}: divide (divide ?257 (inverse ?256)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (divide (inverse ?260) ?259)) ?258 [260, 259, 258, 256, 257] by Demod 311424 with 311017 at 3
-Id : 311594, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (divide (inverse ?260) ?259)) ?258 [260, 259, 258, 256, 257] by Demod 311425 with 6 at 1,2
-Id : 311596, {_}: divide ?60191 ?60192 =<= divide (divide (multiply (inverse ?60193) ?60194) (divide (inverse ?60193) (inverse ?60194))) (divide ?60192 ?60191) [60194, 60193, 60192, 60191] by Demod 311314 with 311594 at 3
-Id : 179540, {_}: inverse (inverse (divide (divide (inverse (divide (inverse ?1029056) ?1029057)) (divide ?1029058 ?1029059)) ?1029060)) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?1029059 ?1029058) ?1029060)) (multiply ?1029057 ?1029056)))) [1029060, 1029059, 1029058, 1029057, 1029056] by Super 178625 with 6 at 2,1,1,1,3
-Id : 186333, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1068110) ?1068111)) (divide ?1068112 ?1068113)) ?1068114)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1068113 ?1068112) ?1068114)) (multiply (inverse ?1068111) ?1068110)))) [1068114, 1068113, 1068112, 1068111, 1068110] by Super 179540 with 6 at 1,1,1,1,1,2
-Id : 186556, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1070554) ?1070555)) (divide (inverse ?1070553) ?1070556)) ?1070557)) =>= inverse (inverse (inverse (divide (inverse (divide (multiply ?1070556 ?1070553) ?1070557)) (multiply (inverse ?1070555) ?1070554)))) [1070557, 1070556, 1070553, 1070555, 1070554] by Super 186333 with 6 at 1,1,1,1,1,1,3
-Id : 179745, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1031256 ?1031255) ?1031257)) (multiply (inverse ?1031253) ?1031254)))) [1031257, 1031256, 1031255, 1031253, 1031254] by Super 179540 with 6 at 1,1,1,1,1,2
-Id : 277438, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =<= inverse (inverse (inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))))) [1506464, 1506463, 1506465, 1506466] by Super 277437 with 4 at 2,1,1,2
-Id : 299272, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =>= inverse (inverse (inverse (divide (divide ?1506464 (divide ?1506465 ?1506466)) ?1506463))) [1506464, 1506463, 1506465, 1506466] by Demod 277438 with 298855 at 3
-Id : 299290, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =<= inverse (inverse (inverse (inverse (divide (divide (multiply (inverse ?1031253) ?1031254) (divide ?1031255 ?1031256)) ?1031257)))) [1031257, 1031256, 1031255, 1031253, 1031254] by Demod 179745 with 299272 at 1,3
-Id : 299299, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =>= inverse (inverse (inverse (divide ?1031257 (divide (multiply (inverse ?1031253) ?1031254) (divide ?1031255 ?1031256))))) [1031257, 1031256, 1031255, 1031253, 1031254] by Demod 299290 with 298855 at 3
-Id : 299300, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =?= inverse (inverse (inverse (divide (inverse (divide (multiply ?1070556 ?1070553) ?1070557)) (multiply (inverse ?1070555) ?1070554)))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 186556 with 299299 at 2
-Id : 300336, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =>= inverse (inverse (inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 299300 with 299719 at 3
-Id : 309498, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =>= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 300336 with 305044 at 3
-Id : 309684, {_}: inverse (inverse (divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557)) =>= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 309498 with 309508 at 2
-Id : 311181, {_}: divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557 =<= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 309684 with 310837 at 2
-Id : 311182, {_}: divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557 =>= multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 311181 with 310837 at 3
-Id : 311600, {_}: divide ?60191 ?60192 =<= multiply (multiply (inverse ?60193) ?60194) (divide (multiply (inverse ?60194) ?60193) (divide ?60192 ?60191)) [60194, 60193, 60192, 60191] by Demod 311596 with 311182 at 3
-Id : 311603, {_}: divide (inverse ?5406) (divide (multiply ?5407 ?5408) ?5406) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5406] by Demod 1282 with 311600 at 2,2
-Id : 276834, {_}: inverse (inverse (divide (inverse ?1501956) (divide ?1501960 ?1501956))) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501956] by Demod 276336 with 4 at 1,1,1,1,2
-Id : 311035, {_}: divide (inverse ?1501956) (divide ?1501960 ?1501956) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501956] by Demod 276834 with 310837 at 2
-Id : 311036, {_}: divide (inverse ?1501956) (divide ?1501960 ?1501956) =>= inverse ?1501960 [1501960, 1501956] by Demod 311035 with 310837 at 3
-Id : 311604, {_}: inverse (multiply ?5407 ?5408) =<= divide (inverse ?5408) ?5407 [5408, 5407] by Demod 311603 with 311036 at 2
-Id : 311708, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (divide (inverse (multiply ?12298 ?12296)) (divide ?12299 ?12297))) ?12299 [12299, 12296, 12298, 12297] by Demod 2673 with 311604 at 1,2,1,3
-Id : 311709, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (inverse (multiply (divide ?12299 ?12297) (multiply ?12298 ?12296)))) ?12299 [12299, 12296, 12298, 12297] by Demod 311708 with 311604 at 2,1,3
-Id : 311866, {_}: ?12297 =<= multiply (divide (multiply ?12298 ?12296) (multiply (divide ?12299 ?12297) (multiply ?12298 ?12296))) ?12299 [12299, 12296, 12298, 12297] by Demod 311709 with 311292 at 1,3
-Id : 311110, {_}: divide (inverse (inverse ?1506721)) (multiply ?1506722 ?1506721) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Demod 277476 with 310837 at 2
-Id : 311111, {_}: divide ?1506721 (multiply ?1506722 ?1506721) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Demod 311110 with 310837 at 1,2
-Id : 311112, {_}: divide ?1506721 (multiply ?1506722 ?1506721) =>= inverse ?1506722 [1506722, 1506721] by Demod 311111 with 310837 at 3
-Id : 311867, {_}: ?12297 =<= multiply (inverse (divide ?12299 ?12297)) ?12299 [12299, 12297] by Demod 311866 with 311112 at 1,3
-Id : 311868, {_}: ?12297 =<= multiply (divide ?12297 ?12299) ?12299 [12299, 12297] by Demod 311867 with 311017 at 1,3
-Id : 31329, {_}: inverse (inverse (inverse (divide (divide ?147825 (divide ?147822 (divide ?147826 ?147827))) (divide ?147828 ?147822)))) =>= inverse (divide (divide ?147825 (divide ?147827 ?147826)) ?147828) [147828, 147827, 147826, 147822, 147825] by Demod 31180 with 4 at 1,2,1,1,1,1,2
-Id : 31603, {_}: multiply ?149797 (inverse (inverse (divide (divide ?149792 (divide ?149793 (divide ?149794 ?149795))) (divide ?149796 ?149793)))) =>= divide ?149797 (inverse (divide (divide ?149792 (divide ?149795 ?149794)) ?149796)) [149796, 149795, 149794, 149793, 149792, 149797] by Super 6 with 31329 at 2,3
-Id : 33302, {_}: multiply ?159935 (inverse (inverse (divide (divide ?159936 (divide ?159937 (divide ?159938 ?159939))) (divide ?159940 ?159937)))) =>= multiply ?159935 (divide (divide ?159936 (divide ?159939 ?159938)) ?159940) [159940, 159939, 159938, 159937, 159936, 159935] by Demod 31603 with 6 at 3
-Id : 33303, {_}: multiply ?159946 (inverse (inverse (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943))) =>= multiply ?159946 (divide (divide ?159947 (divide ?159949 ?159948)) (inverse (divide ?159942 (divide ?159943 (divide ?159944 ?159945))))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Super 33302 with 4 at 2,1,1,2,2
-Id : 33719, {_}: multiply ?159946 (inverse (inverse (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943))) =>= multiply ?159946 (multiply (divide ?159947 (divide ?159949 ?159948)) (divide ?159942 (divide ?159943 (divide ?159944 ?159945)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 33303 with 6 at 2,3
-Id : 311080, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =<= multiply ?159946 (multiply (divide ?159947 (divide ?159949 ?159948)) (divide ?159942 (divide ?159943 (divide ?159944 ?159945)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 33719 with 310837 at 2,2
-Id : 158025, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =<= inverse (inverse (inverse (divide (inverse (divide ?892783 (divide ?892778 (divide ?892780 ?892779)))) (divide ?892782 ?892781)))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 157660 with 10 at 1,2
-Id : 300347, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =<= inverse (inverse (inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 158025 with 299719 at 3
-Id : 309517, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =>= inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 300347 with 305044 at 3
-Id : 311023, {_}: divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =<= inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 309517 with 310837 at 2
-Id : 311024, {_}: divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =>= multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 311023 with 310837 at 3
-Id : 311478, {_}: divide (divide ?892782 ?892781) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =<= multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))) [892780, 892779, 892783, 892778, 892781, 892782] by Demod 311024 with 311017 at 1,2
-Id : 311484, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =?= multiply ?159946 (divide (divide ?159947 (divide ?159949 ?159948)) (divide ?159943 (divide ?159942 (divide ?159945 ?159944)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 311080 with 311478 at 2,3
-Id : 31729, {_}: inverse (inverse (inverse (divide (divide ?150997 ?150994) (divide ?150999 (inverse (divide ?150998 (divide ?150994 (divide ?150995 ?150996)))))))) =>= inverse (divide (divide ?150997 (divide ?150998 (divide ?150996 ?150995))) ?150999) [150996, 150995, 150998, 150999, 150994, 150997] by Super 31662 with 4 at 2,1,1,1,1,2
-Id : 36383, {_}: inverse (inverse (inverse (divide (divide ?176720 ?176721) (multiply ?176722 (divide ?176723 (divide ?176721 (divide ?176724 ?176725))))))) =>= inverse (divide (divide ?176720 (divide ?176723 (divide ?176725 ?176724))) ?176722) [176725, 176724, 176723, 176722, 176721, 176720] by Demod 31729 with 6 at 2,1,1,1,2
-Id : 36463, {_}: inverse (inverse (inverse (divide ?177473 (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479))))))) =>= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177479, 177478, 177472, 177474, 177475, 177477, 177476, 177473] by Super 36383 with 4 at 1,1,1,1,2
-Id : 309587, {_}: inverse (inverse (divide (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)))) ?177473)) =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177479, 177478, 177472, 177474, 177475, 177477, 177476] by Demod 36463 with 309508 at 2
-Id : 311007, {_}: divide (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)))) ?177473 =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177479, 177478, 177472, 177474, 177475, 177477, 177476] by Demod 309587 with 310837 at 2
-Id : 178159, {_}: inverse (inverse (divide (divide (inverse (divide ?1018695 ?1018696)) (divide ?1018692 ?1018697)) ?1018698)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1018697 ?1018692) ?1018698)) (divide ?1018696 ?1018695)))) [1018698, 1018697, 1018692, 1018696, 1018695] by Demod 177759 with 4 at 1,2,1,1,1,2
-Id : 178479, {_}: multiply ?1021991 (inverse (inverse (divide (inverse (divide (divide ?1021989 ?1021988) ?1021990)) (divide ?1021987 ?1021986)))) =>= divide ?1021991 (inverse (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990))) [1021986, 1021987, 1021990, 1021988, 1021989, 1021991] by Super 6 with 178159 at 2,3
-Id : 178887, {_}: multiply ?1021991 (inverse (inverse (divide (inverse (divide (divide ?1021989 ?1021988) ?1021990)) (divide ?1021987 ?1021986)))) =>= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021986, 1021987, 1021990, 1021988, 1021989, 1021991] by Demod 178479 with 6 at 3
-Id : 299293, {_}: multiply ?1021991 (inverse (inverse (inverse (divide (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989)) ?1021990)))) =>= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021990, 1021989, 1021988, 1021986, 1021987, 1021991] by Demod 178887 with 299272 at 2,2
-Id : 309531, {_}: multiply ?1021991 (inverse (inverse (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))))) =<= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 299293 with 309508 at 2,2
-Id : 311175, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =<= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 309531 with 310837 at 2,2
-Id : 311300, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =<= divide ?1021991 (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 311175 with 311292 at 3
-Id : 311471, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =>= divide ?1021991 (divide (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989)) ?1021990) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 311300 with 311017 at 1,1,2,3
-Id : 312117, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 311007 with 311471 at 1,2
-Id : 312118, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= divide ?177476 (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312117 with 311017 at 3
-Id : 312119, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= divide ?177476 (inverse (multiply (divide ?177477 (divide ?177479 ?177478)) (divide ?177472 (divide ?177473 (divide ?177474 ?177475))))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312118 with 311604 at 2,3
-Id : 312120, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= multiply ?177476 (multiply (divide ?177477 (divide ?177479 ?177478)) (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312119 with 6 at 3
-Id : 312121, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= multiply ?177476 (divide (divide ?177477 (divide ?177479 ?177478)) (divide ?177473 (divide ?177472 (divide ?177475 ?177474)))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312120 with 311478 at 2,3
-Id : 312122, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =>= divide (divide ?159946 (divide (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949)) ?159947)) ?159943 [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 311484 with 312121 at 3
-Id : 26, {_}: divide (inverse (divide ?127 ?128)) (divide (divide ?129 (multiply ?130 ?126)) ?127) =>= inverse (divide ?129 (divide ?128 (divide (inverse ?126) ?130))) [126, 130, 129, 128, 127] by Super 23 with 6 at 2,1,2,2
-Id : 673, {_}: inverse (divide ?2882 (divide (divide ?2883 (divide (multiply ?2884 ?2885) ?2882)) (divide (inverse ?2885) ?2884))) =>= ?2883 [2885, 2884, 2883, 2882] by Super 4 with 26 at 2
-Id : 1528, {_}: inverse (divide ?6677 (divide (divide ?6678 (divide (multiply (inverse ?6679) ?6680) ?6677)) (multiply (inverse ?6680) ?6679))) =>= ?6678 [6680, 6679, 6678, 6677] by Super 673 with 6 at 2,2,1,2
-Id : 1549, {_}: inverse (inverse (divide ?6831 (divide (inverse ?6830) (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833))))) =>= ?6831 [6832, 6833, 6830, 6831] by Super 1528 with 32 at 1,2
-Id : 311073, {_}: divide ?6831 (divide (inverse ?6830) (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833))) =>= ?6831 [6832, 6833, 6830, 6831] by Demod 1549 with 310837 at 2
-Id : 311743, {_}: divide ?6831 (inverse (multiply (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833)) ?6830)) =>= ?6831 [6830, 6832, 6833, 6831] by Demod 311073 with 311604 at 2,2
-Id : 311744, {_}: divide ?6831 (inverse (multiply (inverse (multiply (multiply (inverse ?6832) ?6833) (multiply (multiply (inverse ?6833) ?6832) ?6830))) ?6830)) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311743 with 311604 at 1,1,2,2
-Id : 311850, {_}: multiply ?6831 (multiply (inverse (multiply (multiply (inverse ?6832) ?6833) (multiply (multiply (inverse ?6833) ?6832) ?6830))) ?6830) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311744 with 6 at 2
-Id : 179801, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1031802) ?1031803)) (divide ?1031804 ?1031805)) ?1031801)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1031805 ?1031804) (inverse ?1031801))) (multiply ?1031803 ?1031802)))) [1031801, 1031805, 1031804, 1031803, 1031802] by Super 179540 with 6 at 1,1,2
-Id : 182767, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1047817) ?1047818)) (divide ?1047819 ?1047820)) ?1047821)) =>= inverse (inverse (inverse (divide (inverse (multiply (divide ?1047820 ?1047819) ?1047821)) (multiply ?1047818 ?1047817)))) [1047821, 1047820, 1047819, 1047818, 1047817] by Demod 179801 with 6 at 1,1,1,1,1,3
-Id : 190010, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1087858) ?1087859)) (multiply ?1087860 ?1087861)) ?1087862)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide (inverse ?1087861) ?1087860) ?1087862)) (multiply ?1087859 ?1087858)))) [1087862, 1087861, 1087860, 1087859, 1087858] by Super 182767 with 6 at 2,1,1,1,2
-Id : 190267, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1090617) ?1090618)) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =>= inverse (inverse (inverse (divide (inverse (multiply (multiply (inverse ?1090619) ?1090616) ?1090620)) (multiply ?1090618 ?1090617)))) [1090620, 1090619, 1090616, 1090618, 1090617] by Super 190010 with 6 at 1,1,1,1,1,1,3
-Id : 182806, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1048196) ?1048197)) (multiply ?1048198 ?1048195)) ?1048199)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide (inverse ?1048195) ?1048198) ?1048199)) (multiply ?1048197 ?1048196)))) [1048199, 1048195, 1048198, 1048197, 1048196] by Super 182767 with 6 at 2,1,1,1,2
-Id : 490, {_}: divide (inverse (divide (inverse ?2255) (divide ?2256 (multiply ?2257 ?2254)))) (multiply (divide (inverse ?2254) ?2257) ?2255) =>= ?2256 [2254, 2257, 2256, 2255] by Super 466 with 6 at 2,2,1,1,2
-Id : 277455, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =<= inverse (inverse (inverse (inverse (divide (inverse ?1506563) (divide ?1506564 (multiply ?1506565 ?1506566)))))) [1506564, 1506563, 1506565, 1506566] by Super 277437 with 490 at 2,1,1,2
-Id : 299269, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =>= inverse (inverse (inverse (divide (divide ?1506564 (multiply ?1506565 ?1506566)) (inverse ?1506563)))) [1506564, 1506563, 1506565, 1506566] by Demod 277455 with 298855 at 3
-Id : 299304, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =>= inverse (inverse (inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563))) [1506564, 1506563, 1506565, 1506566] by Demod 299269 with 6 at 1,1,1,3
-Id : 299306, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1048196) ?1048197)) (multiply ?1048198 ?1048195)) ?1048199)) =>= inverse (inverse (inverse (inverse (multiply (divide (multiply ?1048197 ?1048196) (multiply ?1048198 ?1048195)) ?1048199)))) [1048199, 1048195, 1048198, 1048197, 1048196] by Demod 182806 with 299304 at 1,3
-Id : 299307, {_}: inverse (inverse (inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)))) =<= inverse (inverse (inverse (divide (inverse (multiply (multiply (inverse ?1090619) ?1090616) ?1090620)) (multiply ?1090618 ?1090617)))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 190267 with 299306 at 2
-Id : 300335, {_}: inverse (inverse (inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)))) =<= inverse (inverse (inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 299307 with 299719 at 3
-Id : 309523, {_}: inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =<= inverse (inverse (inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 300335 with 305044 at 2
-Id : 309524, {_}: inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =<= inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 309523 with 305044 at 3
-Id : 311029, {_}: multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620 =<= inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 309524 with 310837 at 2
-Id : 311030, {_}: multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620 =<= multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 311029 with 310837 at 3
-Id : 311851, {_}: multiply ?6831 (multiply (inverse (multiply (divide (multiply (inverse ?6832) ?6833) (multiply (inverse ?6832) ?6833)) ?6830)) ?6830) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311850 with 311030 at 1,1,2,2
-Id : 692, {_}: inverse (inverse (divide ?3016 (divide (inverse ?3015) (divide (inverse (multiply (divide (inverse ?3018) ?3017) ?3015)) (multiply ?3017 ?3018))))) =>= ?3016 [3017, 3018, 3015, 3016] by Super 673 with 32 at 1,2
-Id : 277278, {_}: inverse (inverse (inverse (inverse ?1505137))) =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Super 692 with 276834 at 2
-Id : 309511, {_}: inverse (inverse ?1505137) =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Demod 277278 with 305044 at 2
-Id : 311129, {_}: ?1505137 =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Demod 309511 with 310837 at 2
-Id : 311117, {_}: divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564 =<= inverse (inverse (inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563))) [1506564, 1506563, 1506565, 1506566] by Demod 299304 with 310837 at 2
-Id : 311118, {_}: divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564 =>= inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563) [1506564, 1506563, 1506565, 1506566] by Demod 311117 with 310837 at 3
-Id : 311205, {_}: ?1505137 =<= inverse (inverse (multiply (divide (multiply ?1505139 ?1505138) (multiply ?1505139 ?1505138)) ?1505137)) [1505138, 1505139, 1505137] by Demod 311129 with 311118 at 1,3
-Id : 311206, {_}: ?1505137 =<= multiply (divide (multiply ?1505139 ?1505138) (multiply ?1505139 ?1505138)) ?1505137 [1505138, 1505139, 1505137] by Demod 311205 with 310837 at 3
-Id : 311852, {_}: multiply ?6831 (multiply (inverse ?6830) ?6830) =>= ?6831 [6830, 6831] by Demod 311851 with 311206 at 1,1,2,2
-Id : 312318, {_}: multiply ?1630838 (multiply ?1630837 (inverse ?1630837)) =>= ?1630838 [1630837, 1630838] by Super 311852 with 310837 at 1,2,2
-Id : 312456, {_}: multiply ?1630838 (divide ?1630837 ?1630837) =>= ?1630838 [1630837, 1630838] by Demod 312318 with 311292 at 2,2
-Id : 312737, {_}: divide (divide ?1631485 (divide (divide (divide (divide ?1631486 ?1631487) ?1631488) (divide (divide ?1631486 ?1631487) ?1631488)) ?1631489)) ?1631489 =>= ?1631485 [1631489, 1631488, 1631487, 1631486, 1631485] by Super 312121 with 312456 at 3
-Id : 164905, {_}: inverse (inverse (divide (inverse (divide ?939850 (divide ?939851 ?939852))) (divide ?939849 (divide ?939850 (divide ?939851 ?939852))))) =>= inverse (inverse (inverse ?939849)) [939849, 939852, 939851, 939850] by Super 164761 with 4 at 1,1,1,3
-Id : 276099, {_}: inverse (inverse (inverse ?1499672)) =<= inverse (divide (inverse (divide (divide ?1499671 ?1499670) ?1499672)) (divide ?1499670 ?1499671)) [1499670, 1499671, 1499672] by Super 345 with 164905 at 2
-Id : 311033, {_}: inverse ?1499672 =<= inverse (divide (inverse (divide (divide ?1499671 ?1499670) ?1499672)) (divide ?1499670 ?1499671)) [1499670, 1499671, 1499672] by Demod 276099 with 310837 at 2
-Id : 309603, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =>= inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))) [1506464, 1506463, 1506465, 1506466] by Demod 299272 with 309508 at 3
-Id : 311134, {_}: divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464 =<= inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))) [1506464, 1506463, 1506465, 1506466] by Demod 309603 with 310837 at 2
-Id : 311135, {_}: divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464 =>= divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)) [1506464, 1506463, 1506465, 1506466] by Demod 311134 with 310837 at 3
-Id : 311365, {_}: inverse ?1499672 =<= inverse (divide ?1499672 (divide (divide ?1499670 ?1499671) (divide ?1499670 ?1499671))) [1499671, 1499670, 1499672] by Demod 311033 with 311135 at 1,3
-Id : 311372, {_}: inverse ?1499672 =<= divide (divide (divide ?1499670 ?1499671) (divide ?1499670 ?1499671)) ?1499672 [1499671, 1499670, 1499672] by Demod 311365 with 311017 at 3
-Id : 313817, {_}: divide (divide ?1631485 (inverse ?1631489)) ?1631489 =>= ?1631485 [1631489, 1631485] by Demod 312737 with 311372 at 2,1,2
-Id : 313818, {_}: divide (multiply ?1631485 ?1631489) ?1631489 =>= ?1631485 [1631489, 1631485] by Demod 313817 with 6 at 1,2
-Id : 317392, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =<= divide (divide ?1642981 (divide (divide (divide (divide ?1642982 ?1642983) ?1642984) (divide ?1642985 ?1642986)) (multiply ?1642980 (divide (divide (divide ?1642982 ?1642983) ?1642984) (divide ?1642985 ?1642986))))) ?1642987 [1642986, 1642985, 1642984, 1642983, 1642982, 1642987, 1642980, 1642981] by Super 312122 with 313818 at 1,2,2
-Id : 318522, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =<= divide (divide ?1642981 (inverse ?1642980)) ?1642987 [1642987, 1642980, 1642981] by Demod 317392 with 311112 at 2,1,3
-Id : 318523, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =>= divide (multiply ?1642981 ?1642980) ?1642987 [1642987, 1642980, 1642981] by Demod 318522 with 6 at 1,3
-Id : 311394, {_}: divide (divide ?1506463 (divide ?1506466 ?1506465)) ?1506464 =?= divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)) [1506464, 1506465, 1506466, 1506463] by Demod 311135 with 311017 at 1,2
-Id : 277640, {_}: inverse ?1508034 =<= inverse (inverse (inverse (divide ?1508034 (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035))))) [1508036, 1508035, 1508034] by Super 277437 with 339 at 1,2
-Id : 309536, {_}: inverse ?1508034 =<= inverse (inverse (divide (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035)) ?1508034)) [1508036, 1508035, 1508034] by Demod 277640 with 309508 at 3
-Id : 310975, {_}: inverse ?1508034 =<= divide (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035)) ?1508034 [1508036, 1508035, 1508034] by Demod 309536 with 310837 at 3
-Id : 312719, {_}: inverse ?1631352 =<= divide (divide ?1631351 ?1631351) ?1631352 [1631351, 1631352] by Super 310975 with 312456 at 1,3
-Id : 314397, {_}: divide (divide ?1637990 (divide ?1637991 ?1637992)) (divide ?1637989 ?1637989) =>= divide ?1637990 (inverse (divide ?1637992 ?1637991)) [1637989, 1637992, 1637991, 1637990] by Super 311394 with 312719 at 2,3
-Id : 311378, {_}: divide ?3302 (divide ?3301 (divide (divide ?3301 (multiply ?3304 ?3303)) (divide (inverse ?3303) ?3304))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 311071 with 311017 at 1,2,2,2
-Id : 312063, {_}: divide ?3302 (divide ?3301 (divide (divide ?3301 (multiply ?3304 ?3303)) (inverse (multiply ?3304 ?3303)))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 311378 with 311604 at 2,2,2,2
-Id : 312064, {_}: divide ?3302 (divide ?3301 (multiply (divide ?3301 (multiply ?3304 ?3303)) (multiply ?3304 ?3303))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 312063 with 6 at 2,2,2
-Id : 312065, {_}: divide ?3302 (divide ?3301 ?3301) =>= ?3302 [3301, 3302] by Demod 312064 with 311868 at 2,2,2
-Id : 314879, {_}: divide ?1637990 (divide ?1637991 ?1637992) =<= divide ?1637990 (inverse (divide ?1637992 ?1637991)) [1637992, 1637991, 1637990] by Demod 314397 with 312065 at 2
-Id : 314880, {_}: divide ?1637990 (divide ?1637991 ?1637992) =<= multiply ?1637990 (divide ?1637992 ?1637991) [1637992, 1637991, 1637990] by Demod 314879 with 6 at 3
-Id : 320415, {_}: divide ?1642981 (divide ?1642987 ?1642980) =?= divide (multiply ?1642981 ?1642980) ?1642987 [1642980, 1642987, 1642981] by Demod 318523 with 314880 at 2
-Id : 343753, {_}: multiply ?1701701 ?1701702 =<= multiply (divide ?1701701 (divide ?1701703 ?1701702)) ?1701703 [1701703, 1701702, 1701701] by Super 311868 with 320415 at 1,3
-Id : 311818, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (inverse (multiply ?259 ?260))) ?258 [260, 259, 258, 256, 257] by Demod 311594 with 311604 at 2,1,3
-Id : 311820, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (multiply ?257 (multiply ?259 ?260)) ?258 [260, 259, 258, 256, 257] by Demod 311818 with 6 at 1,3
-Id : 317517, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =?= divide (multiply ?1643886 (multiply ?1643888 ?1643889)) (multiply ?1643885 (multiply ?1643888 ?1643889)) [1643889, 1643888, 1643885, 1643887, 1643886] by Super 311820 with 313818 at 1,2,2
-Id : 32072, {_}: inverse (inverse (inverse (divide (divide ?152561 (divide ?152562 (multiply ?152563 ?152564))) (divide ?152565 ?152562)))) =>= inverse (divide (divide ?152561 (divide (inverse ?152564) ?152563)) ?152565) [152565, 152564, 152563, 152562, 152561] by Super 31662 with 6 at 2,2,1,1,1,1,2
-Id : 691, {_}: inverse (inverse (divide ?3011 (divide ?3010 (divide (inverse (divide (divide (inverse ?3013) ?3012) ?3010)) (multiply ?3012 ?3013))))) =>= ?3011 [3012, 3013, 3010, 3011] by Super 673 with 10 at 1,2
-Id : 32186, {_}: inverse (divide ?153559 (divide (divide (inverse (divide (divide (inverse ?153557) ?153558) ?153562)) (multiply ?153558 ?153557)) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153562, 153558, 153557, 153559] by Super 32072 with 691 at 1,2
-Id : 311187, {_}: inverse (divide ?153559 (divide (divide ?153562 (divide (multiply ?153558 ?153557) (divide ?153558 (inverse ?153557)))) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153557, 153558, 153562, 153559] by Demod 32186 with 311135 at 1,2,1,2
-Id : 311196, {_}: inverse (divide ?153559 (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153557, 153558, 153562, 153559] by Demod 311187 with 6 at 2,2,1,2,1,2
-Id : 311391, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311196 with 311017 at 2
-Id : 311392, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (divide ?153559 (divide (inverse ?153561) ?153560)) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311391 with 311017 at 3
-Id : 312039, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (divide ?153559 (inverse (multiply ?153560 ?153561))) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311392 with 311604 at 2,2,3
-Id : 312040, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (multiply ?153559 (multiply ?153560 ?153561)) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 312039 with 6 at 2,3
-Id : 312075, {_}: divide (divide ?153562 (multiply ?153560 ?153561)) ?153559 =?= divide ?153562 (multiply ?153559 (multiply ?153560 ?153561)) [153559, 153561, 153560, 153562] by Demod 312040 with 312065 at 1,1,2
-Id : 318365, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =?= divide (divide (multiply ?1643886 (multiply ?1643888 ?1643889)) (multiply ?1643888 ?1643889)) ?1643885 [1643889, 1643888, 1643885, 1643887, 1643886] by Demod 317517 with 312075 at 3
-Id : 318366, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =>= divide ?1643886 ?1643885 [1643885, 1643887, 1643886] by Demod 318365 with 313818 at 1,3
-Id : 343774, {_}: multiply ?1701846 (multiply ?1701845 ?1701844) =<= multiply (divide ?1701846 (divide ?1701843 ?1701845)) (multiply ?1701843 ?1701844) [1701843, 1701844, 1701845, 1701846] by Super 343753 with 318366 at 2,1,3
-Id : 178704, {_}: inverse (inverse (divide (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) (inverse ?1024392))) =>= inverse (inverse (inverse (divide (inverse (multiply (divide ?1024396 ?1024395) ?1024392)) (divide ?1024394 ?1024393)))) [1024392, 1024396, 1024395, 1024394, 1024393] by Super 178625 with 6 at 1,1,1,1,1,3
-Id : 179107, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide ?1024396 ?1024395) ?1024392)) (divide ?1024394 ?1024393)))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 178704 with 6 at 1,1,2
-Id : 300345, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =<= inverse (inverse (inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 179107 with 299719 at 3
-Id : 309518, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =>= inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 300345 with 305044 at 3
-Id : 311123, {_}: multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392 =<= inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 309518 with 310837 at 2
-Id : 311124, {_}: multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392 =>= multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 311123 with 310837 at 3
-Id : 311459, {_}: multiply (divide (divide ?1024394 ?1024393) (divide ?1024395 ?1024396)) ?1024392 =?= multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392) [1024392, 1024396, 1024395, 1024393, 1024394] by Demod 311124 with 311017 at 1,1,2
-Id : 314145, {_}: multiply (divide (divide ?1636195 ?1636196) (inverse ?1636193)) ?1636197 =<= multiply (divide ?1636195 ?1636196) (multiply (divide ?1636193 (divide ?1636194 ?1636194)) ?1636197) [1636194, 1636197, 1636193, 1636196, 1636195] by Super 311459 with 312719 at 2,1,2
-Id : 315602, {_}: multiply (multiply (divide ?1636195 ?1636196) ?1636193) ?1636197 =<= multiply (divide ?1636195 ?1636196) (multiply (divide ?1636193 (divide ?1636194 ?1636194)) ?1636197) [1636194, 1636197, 1636193, 1636196, 1636195] by Demod 314145 with 6 at 1,2
-Id : 315603, {_}: multiply (multiply (divide ?1636195 ?1636196) ?1636193) ?1636197 =>= multiply (divide ?1636195 ?1636196) (multiply ?1636193 ?1636197) [1636197, 1636193, 1636196, 1636195] by Demod 315602 with 312065 at 1,2,3
-Id : 320945, {_}: multiply ?1653480 ?1653482 =<= multiply (divide ?1653480 (divide ?1653481 ?1653482)) ?1653481 [1653481, 1653482, 1653480] by Super 311868 with 320415 at 1,3
-Id : 343542, {_}: multiply (multiply ?1699948 ?1699949) ?1699951 =<= multiply (divide ?1699948 (divide ?1699950 ?1699949)) (multiply ?1699950 ?1699951) [1699950, 1699951, 1699949, 1699948] by Super 315603 with 320945 at 1,2
-Id : 394401, {_}: multiply ?1701846 (multiply ?1701845 ?1701844) =?= multiply (multiply ?1701846 ?1701845) ?1701844 [1701844, 1701845, 1701846] by Demod 343774 with 343542 at 3
-Id : 395259, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 394401 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP471-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 10.874059s
-% SZS status Unsatisfiable for GRP477-1.p
-% SZS output start CNFRefutation for GRP477-1.p
-Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 7, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 4, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 9, {_}: divide (inverse (divide (divide (divide ?26 ?27) (divide ?23 ?22)) ?25)) (divide ?27 ?26) =?= inverse (divide (divide (divide ?22 ?23) ?24) (divide ?25 ?24)) [24, 25, 22, 23, 27, 26] by Super 7 with 4 at 2,1,1,2
-Id : 8947, {_}: inverse (divide (divide (divide ?66899 ?66900) ?66901) (divide (divide ?66902 (divide ?66900 ?66899)) ?66901)) =>= ?66902 [66902, 66901, 66900, 66899] by Super 4 with 9 at 2
-Id : 9487, {_}: inverse (divide (divide (divide (inverse ?70062) ?70063) ?70064) (divide (divide ?70065 (multiply ?70063 ?70062)) ?70064)) =>= ?70065 [70065, 70064, 70063, 70062] by Super 8947 with 6 at 2,1,2,1,2
-Id : 13, {_}: divide (inverse (divide (divide (divide ?48 ?49) (inverse ?47)) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Super 4 with 6 at 2,1,1,2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?88 ?89) ?90) (multiply ?91 ?90))) (divide ?89 ?88) =>= ?91 [91, 90, 89, 88] by Demod 13 with 6 at 1,1,1,2
-Id : 27, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (divide (divide ?113 ?112) (inverse (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114)))) =>= ?117 [114, 112, 113, 117, 116, 115] by Super 23 with 4 at 1,1,1,1,2
-Id : 35, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (multiply (divide ?113 ?112) (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114))) =>= ?117 [114, 112, 113, 117, 116, 115] by Demod 27 with 6 at 2,2
-Id : 9506, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?70226 ?70225) ?70227) (divide ?70222 ?70227))) (divide ?70225 ?70226)) ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222, 70227, 70225, 70226] by Super 9487 with 35 at 1,2,1,2
-Id : 9604, {_}: inverse (divide (divide ?70222 ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222] by Demod 9506 with 4 at 1,1,1,2
-Id : 27713, {_}: divide (divide (inverse (divide (divide (divide ?169617 ?169618) (divide ?169619 ?169620)) ?169621)) (divide ?169618 ?169617)) (divide ?169619 ?169620) =>= ?169621 [169621, 169620, 169619, 169618, 169617] by Super 4 with 9 at 1,2
-Id : 27714, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) (divide (inverse (divide (divide (divide ?169623 ?169624) ?169625) (divide ?169626 ?169625))) (divide ?169624 ?169623))) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169625, 169624, 169623, 169628, 169627] by Super 27713 with 4 at 2,2
-Id : 28344, {_}: divide (divide (inverse (divide (divide (divide ?173215 ?173216) ?173217) ?173218)) (divide ?173216 ?173215)) ?173217 =>= ?173218 [173218, 173217, 173216, 173215] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28449, {_}: divide (divide (inverse (multiply (divide (divide ?174106 ?174107) ?174108) ?174105)) (divide ?174107 ?174106)) ?174108 =>= inverse ?174105 [174105, 174108, 174107, 174106] by Super 28344 with 6 at 1,1,1,2
-Id : 28805, {_}: multiply (divide (inverse (multiply (divide (divide ?175142 ?175143) (inverse ?175145)) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Super 6 with 28449 at 3
-Id : 29852, {_}: multiply (divide (inverse (multiply (multiply (divide ?180549 ?180550) ?180551) ?180552)) (divide ?180550 ?180549)) ?180551 =>= inverse ?180552 [180552, 180551, 180550, 180549] by Demod 28805 with 6 at 1,1,1,1,2
-Id : 33202, {_}: multiply (divide (inverse (multiply (multiply (divide (inverse ?199058) ?199059) ?199060) ?199061)) (multiply ?199059 ?199058)) ?199060 =>= inverse ?199061 [199061, 199060, 199059, 199058] by Super 29852 with 6 at 2,1,2
-Id : 33304, {_}: multiply (divide (inverse (multiply (multiply (multiply (inverse ?199942) ?199941) ?199943) ?199944)) (multiply (inverse ?199941) ?199942)) ?199943 =>= inverse ?199944 [199944, 199943, 199941, 199942] by Super 33202 with 6 at 1,1,1,1,1,2
-Id : 43, {_}: divide (inverse (divide (divide (divide (inverse ?171) ?172) ?173) (divide ?174 ?173))) (multiply ?172 ?171) =>= ?174 [174, 173, 172, 171] by Super 4 with 6 at 2,2
-Id : 48, {_}: divide (inverse (divide (divide ?205 ?206) (divide ?207 ?206))) (multiply (divide ?203 ?202) (divide (divide (divide ?202 ?203) ?204) (divide ?205 ?204))) =>= ?207 [204, 202, 203, 207, 206, 205] by Super 43 with 4 at 1,1,1,1,2
-Id : 8271, {_}: inverse (divide (divide (divide ?62998 ?62997) ?62999) (divide (divide ?63000 (divide ?62997 ?62998)) ?62999)) =>= ?63000 [63000, 62999, 62997, 62998] by Super 4 with 9 at 2
-Id : 8914, {_}: divide ?66588 (multiply (divide ?66589 ?66590) (divide (divide (divide ?66590 ?66589) ?66591) (divide (divide ?66585 ?66586) ?66591))) =>= divide ?66588 (divide ?66586 ?66585) [66586, 66585, 66591, 66590, 66589, 66588] by Super 48 with 8271 at 1,2
-Id : 27904, {_}: divide (divide (inverse (divide (divide (divide ?171441 ?171442) (divide ?171443 ?171444)) (divide ?171440 ?171439))) (divide ?171442 ?171441)) (divide ?171443 ?171444) =?= multiply (divide ?171436 ?171437) (divide (divide (divide ?171437 ?171436) ?171438) (divide (divide ?171439 ?171440) ?171438)) [171438, 171437, 171436, 171439, 171440, 171444, 171443, 171442, 171441] by Super 27713 with 8914 at 1,1,1,2
-Id : 8270, {_}: divide (divide (inverse (divide (divide (divide ?62988 ?62989) (divide ?62990 ?62991)) ?62992)) (divide ?62989 ?62988)) (divide ?62990 ?62991) =>= ?62992 [62992, 62991, 62990, 62989, 62988] by Super 4 with 9 at 1,2
-Id : 28135, {_}: divide ?171440 ?171439 =<= multiply (divide ?171436 ?171437) (divide (divide (divide ?171437 ?171436) ?171438) (divide (divide ?171439 ?171440) ?171438)) [171438, 171437, 171436, 171439, 171440] by Demod 27904 with 8270 at 2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?48 ?49) ?47) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Demod 13 with 6 at 1,1,1,2
-Id : 22, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (divide (divide ?82 ?81) (inverse (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83)))) =>= ?86 [83, 81, 82, 86, 85, 84] by Super 4 with 18 at 1,1,1,1,2
-Id : 32, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (multiply (divide ?82 ?81) (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83))) =>= ?86 [83, 81, 82, 86, 85, 84] by Demod 22 with 6 at 2,2
-Id : 8902, {_}: divide ?66500 (multiply (divide ?66501 ?66502) (divide (multiply (divide ?66502 ?66501) ?66503) (multiply (divide ?66497 ?66498) ?66503))) =>= divide ?66500 (divide ?66498 ?66497) [66498, 66497, 66503, 66502, 66501, 66500] by Super 32 with 8271 at 1,2
-Id : 27903, {_}: divide (divide (inverse (divide (divide (divide ?171431 ?171432) (divide ?171433 ?171434)) (divide ?171430 ?171429))) (divide ?171432 ?171431)) (divide ?171433 ?171434) =?= multiply (divide ?171426 ?171427) (divide (multiply (divide ?171427 ?171426) ?171428) (multiply (divide ?171429 ?171430) ?171428)) [171428, 171427, 171426, 171429, 171430, 171434, 171433, 171432, 171431] by Super 27713 with 8902 at 1,1,1,2
-Id : 28134, {_}: divide ?171430 ?171429 =<= multiply (divide ?171426 ?171427) (divide (multiply (divide ?171427 ?171426) ?171428) (multiply (divide ?171429 ?171430) ?171428)) [171428, 171427, 171426, 171429, 171430] by Demod 27903 with 8270 at 2
-Id : 34242, {_}: divide (divide (inverse (divide ?204167 ?204168)) (divide ?204171 ?204170)) ?204172 =<= inverse (divide (multiply (divide ?204172 (divide ?204170 ?204171)) ?204169) (multiply (divide ?204168 ?204167) ?204169)) [204169, 204172, 204170, 204171, 204168, 204167] by Super 28449 with 28134 at 1,1,1,2
-Id : 34778, {_}: divide (divide (divide (inverse (divide ?206532 ?206533)) (divide ?206534 ?206535)) ?206536) (divide (divide ?206535 ?206534) ?206536) =>= divide ?206533 ?206532 [206536, 206535, 206534, 206533, 206532] by Super 18 with 34242 at 1,2
-Id : 54527, {_}: divide ?300655 ?300656 =<= multiply (divide (divide ?300655 ?300656) (inverse (divide ?300653 ?300654))) (divide ?300654 ?300653) [300654, 300653, 300656, 300655] by Super 28135 with 34778 at 2,3
-Id : 55213, {_}: divide ?304381 ?304382 =<= multiply (multiply (divide ?304381 ?304382) (divide ?304383 ?304384)) (divide ?304384 ?304383) [304384, 304383, 304382, 304381] by Demod 54527 with 6 at 1,3
-Id : 55316, {_}: divide (inverse (divide (divide (divide ?305230 ?305231) ?305232) (divide ?305233 ?305232))) (divide ?305231 ?305230) =?= multiply (multiply ?305233 (divide ?305234 ?305235)) (divide ?305235 ?305234) [305235, 305234, 305233, 305232, 305231, 305230] by Super 55213 with 4 at 1,1,3
-Id : 55555, {_}: ?305233 =<= multiply (multiply ?305233 (divide ?305234 ?305235)) (divide ?305235 ?305234) [305235, 305234, 305233] by Demod 55316 with 4 at 2
-Id : 27948, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) ?169626) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169628, 169627] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28234, {_}: multiply (divide (inverse (divide (divide (divide ?172298 ?172299) (inverse ?172301)) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Super 6 with 27948 at 3
-Id : 28487, {_}: multiply (divide (inverse (divide (multiply (divide ?172298 ?172299) ?172301) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 9011, {_}: inverse (divide (divide (divide ?67439 ?67440) (inverse ?67438)) (multiply (divide ?67441 (divide ?67440 ?67439)) ?67438)) =>= ?67441 [67441, 67438, 67440, 67439] by Super 8947 with 6 at 2,1,2
-Id : 9220, {_}: inverse (divide (multiply (divide ?68482 ?68483) ?68484) (multiply (divide ?68485 (divide ?68483 ?68482)) ?68484)) =>= ?68485 [68485, 68484, 68483, 68482] by Demod 9011 with 6 at 1,1,2
-Id : 9262, {_}: inverse (divide (multiply (divide (inverse ?68840) ?68841) ?68842) (multiply (divide ?68843 (multiply ?68841 ?68840)) ?68842)) =>= ?68843 [68843, 68842, 68841, 68840] by Super 9220 with 6 at 2,1,2,1,2
-Id : 34818, {_}: inverse (divide (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) (divide (divide ?206979 ?206978) ?206984)) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206978, 206979, 206984, 206980, 206981, 206982] by Super 9604 with 34242 at 3
-Id : 54516, {_}: inverse (divide ?300558 ?300557) =<= divide (divide (inverse (divide ?300559 ?300560)) (divide ?300560 ?300559)) (inverse (divide ?300557 ?300558)) [300560, 300559, 300557, 300558] by Super 34818 with 34778 at 1,2
-Id : 54778, {_}: inverse (divide ?300558 ?300557) =<= multiply (divide (inverse (divide ?300559 ?300560)) (divide ?300560 ?300559)) (divide ?300557 ?300558) [300560, 300559, 300557, 300558] by Demod 54516 with 6 at 3
-Id : 58787, {_}: inverse (divide (inverse (divide ?321392 ?321393)) (multiply (divide ?321396 (multiply (divide ?321395 ?321394) (divide ?321394 ?321395))) (divide ?321393 ?321392))) =>= ?321396 [321394, 321395, 321396, 321393, 321392] by Super 9262 with 54778 at 1,1,2
-Id : 12, {_}: divide (inverse (divide (divide (divide (inverse ?42) ?41) ?43) (divide ?44 ?43))) (multiply ?41 ?42) =>= ?44 [44, 43, 41, 42] by Super 4 with 6 at 2,2
-Id : 54402, {_}: divide (inverse (divide ?299508 ?299507)) (multiply (divide ?299509 ?299510) (divide ?299507 ?299508)) =>= divide ?299510 ?299509 [299510, 299509, 299507, 299508] by Super 12 with 34778 at 1,1,2
-Id : 59136, {_}: inverse (divide (multiply (divide ?321395 ?321394) (divide ?321394 ?321395)) ?321396) =>= ?321396 [321396, 321394, 321395] by Demod 58787 with 54402 at 1,2
-Id : 59503, {_}: multiply (divide ?323772 (divide ?323771 ?323770)) (divide ?323771 ?323770) =>= ?323772 [323770, 323771, 323772] by Super 28487 with 59136 at 1,1,2
-Id : 60069, {_}: divide ?327147 (divide ?327148 ?327149) =<= multiply ?327147 (divide ?327149 ?327148) [327149, 327148, 327147] by Super 55555 with 59503 at 1,3
-Id : 60669, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?329868) ?329869) ?329870) (divide ?329866 ?329867))) (multiply (inverse ?329869) ?329868)) ?329870 =>= inverse (divide ?329867 ?329866) [329867, 329866, 329870, 329869, 329868] by Super 33304 with 60069 at 1,1,1,2
-Id : 29399, {_}: multiply (divide (inverse (divide (multiply (divide ?178179 ?178180) ?178181) ?178182)) (divide ?178180 ?178179)) ?178181 =>= ?178182 [178182, 178181, 178180, 178179] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 32341, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?194066) ?194067) ?194068) ?194069)) (multiply ?194067 ?194066)) ?194068 =>= ?194069 [194069, 194068, 194067, 194066] by Super 29399 with 6 at 2,1,2
-Id : 32441, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?194936) ?194935) ?194937) ?194938)) (multiply (inverse ?194935) ?194936)) ?194937 =>= ?194938 [194938, 194937, 194935, 194936] by Super 32341 with 6 at 1,1,1,1,1,2
-Id : 61017, {_}: divide ?329866 ?329867 =<= inverse (divide ?329867 ?329866) [329867, 329866] by Demod 60669 with 32441 at 2
-Id : 61512, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70222, 70228, 70224] by Demod 9604 with 61017 at 2
-Id : 61513, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= divide (multiply ?70224 ?70223) (multiply ?70222 ?70223) [70223, 70222, 70228, 70224] by Demod 61512 with 61017 at 3
-Id : 60072, {_}: multiply (divide ?327160 (divide ?327161 ?327162)) (divide ?327161 ?327162) =>= ?327160 [327162, 327161, 327160] by Super 28487 with 59136 at 1,1,2
-Id : 60073, {_}: multiply (divide ?327168 (divide (inverse (divide (divide (divide ?327164 ?327165) ?327166) (divide ?327167 ?327166))) (divide ?327165 ?327164))) ?327167 =>= ?327168 [327167, 327166, 327165, 327164, 327168] by Super 60072 with 4 at 2,2
-Id : 64649, {_}: multiply (divide ?338211 ?338212) ?338212 =>= ?338211 [338212, 338211] by Demod 60073 with 4 at 2,1,2
-Id : 61711, {_}: divide ?332019 ?332020 =<= inverse (divide ?332020 ?332019) [332020, 332019] by Demod 60669 with 32441 at 2
-Id : 61786, {_}: divide (inverse ?332481) ?332482 =>= inverse (multiply ?332482 ?332481) [332482, 332481] by Super 61711 with 6 at 1,3
-Id : 64688, {_}: multiply (inverse (multiply ?338450 ?338449)) ?338450 =>= inverse ?338449 [338449, 338450] by Super 64649 with 61786 at 1,2
-Id : 70472, {_}: divide (divide ?351323 ?351324) (divide (inverse (multiply ?351321 ?351322)) ?351324) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Super 61513 with 64688 at 2,3
-Id : 70841, {_}: divide (divide ?351323 ?351324) (inverse (multiply ?351324 (multiply ?351321 ?351322))) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Demod 70472 with 61786 at 2,2
-Id : 70842, {_}: multiply (divide ?351323 ?351324) (multiply ?351324 (multiply ?351321 ?351322)) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Demod 70841 with 6 at 2
-Id : 70843, {_}: multiply (divide ?351323 ?351324) (multiply ?351324 (multiply ?351321 ?351322)) =>= multiply (multiply ?351323 ?351321) ?351322 [351322, 351321, 351324, 351323] by Demod 70842 with 6 at 3
-Id : 67, {_}: divide (inverse (divide (divide (multiply ?287 ?288) ?289) (divide ?290 ?289))) (divide (inverse ?288) ?287) =>= ?290 [290, 289, 288, 287] by Super 4 with 6 at 1,1,1,1,2
-Id : 14, {_}: divide (inverse (divide (divide (multiply ?51 ?52) ?53) (divide ?54 ?53))) (divide (inverse ?52) ?51) =>= ?54 [54, 53, 52, 51] by Super 4 with 6 at 1,1,1,1,2
-Id : 70, {_}: divide (inverse (divide (divide (multiply (divide (inverse ?307) ?306) (divide (divide (multiply ?306 ?307) ?308) (divide ?309 ?308))) ?310) (divide ?311 ?310))) ?309 =>= ?311 [311, 310, 309, 308, 306, 307] by Super 67 with 14 at 2,2
-Id : 60413, {_}: divide (inverse (divide (divide (divide (divide (inverse ?307) ?306) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310) (divide ?311 ?310))) ?309 =>= ?311 [311, 310, 308, 309, 306, 307] by Demod 70 with 60069 at 1,1,1,1,2
-Id : 61462, {_}: divide (divide (divide ?311 ?310) (divide (divide (divide (inverse ?307) ?306) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310)) ?309 =>= ?311 [308, 309, 306, 307, 310, 311] by Demod 60413 with 61017 at 1,2
-Id : 62183, {_}: divide (divide (divide ?311 ?310) (divide (divide (inverse (multiply ?306 ?307)) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310)) ?309 =>= ?311 [308, 309, 307, 306, 310, 311] by Demod 61462 with 61786 at 1,1,2,1,2
-Id : 62184, {_}: divide (divide (divide ?311 ?310) (divide (inverse (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307))) ?310)) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62183 with 61786 at 1,2,1,2
-Id : 62185, {_}: divide (divide (divide ?311 ?310) (inverse (multiply ?310 (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307))))) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62184 with 61786 at 2,1,2
-Id : 62194, {_}: divide (multiply (divide ?311 ?310) (multiply ?310 (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307)))) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62185 with 6 at 1,2
-Id : 61520, {_}: divide (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (divide (inverse ?52) ?51) =>= ?54 [52, 51, 53, 54] by Demod 14 with 61017 at 1,2
-Id : 62166, {_}: divide (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (inverse (multiply ?51 ?52)) =>= ?54 [52, 51, 53, 54] by Demod 61520 with 61786 at 2,2
-Id : 62205, {_}: multiply (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (multiply ?51 ?52) =>= ?54 [52, 51, 53, 54] by Demod 62166 with 6 at 2
-Id : 62206, {_}: divide (multiply (divide ?311 ?310) (multiply ?310 ?309)) ?309 =>= ?311 [309, 310, 311] by Demod 62194 with 62205 at 2,2,1,2
-Id : 64698, {_}: multiply ?338511 ?338513 =<= multiply (divide ?338511 ?338512) (multiply ?338512 ?338513) [338512, 338513, 338511] by Super 64649 with 62206 at 1,2
-Id : 88169, {_}: multiply ?351323 (multiply ?351321 ?351322) =?= multiply (multiply ?351323 ?351321) ?351322 [351322, 351321, 351323] by Demod 70843 with 64698 at 2
-Id : 88454, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 88169 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP477-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Last chance: 1246072731.81
-Last chance: all is indexed 1246074535.38
-Last chance: failed over 100 goal 1246074535.38
-FAILURE in 0 iterations
-% SZS status Timeout for GRP506-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- inverse is 94
- multiply is 96
- prove_these_axioms_4 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-Last chance: 1246074836.94
-Last chance: all is indexed 1246076623.31
-Last chance: failed over 100 goal 1246076623.31
-FAILURE in 0 iterations
-% SZS status Timeout for GRP508-1.p
-Order
- == is 100
- _ is 99
- a is 98
- join is 95
- meet is 97
- prove_normal_axioms_1 is 96
- single_axiom is 94
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-Found proof, 13.503938s
-% SZS status Unsatisfiable for LAT080-1.p
-% SZS output start CNFRefutation for LAT080-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) (meet (join (meet ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) (meet ?8 (join ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Id : 5, {_}: join (meet (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12) (meet (join (meet ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)) (meet (join (meet ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)) (meet ?16 (join ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)))) (join ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)))) (join (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12)) =>= ?11 [16, 15, 14, 13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 ?14 ?15 ?16
-Id : 39, {_}: join (meet (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290) (meet (join (meet ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))) (meet ?289 (join ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))))) (join (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290)) =>= join (meet ?288 ?289) (meet ?289 (join ?288 ?289)) [292, 291, 290, 289, 288, 287] by Super 5 with 4 at 1,2,1,2,2
-Id : 42, {_}: join (meet (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))))) ?324) (meet (join (meet ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join 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?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 317, 318, 323] by Demod 42 with 4 at 2,1,1,1,2
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(join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 317, 318, 323] by Demod 126 with 4 at 1,2,1,1,2
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(meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 322, 321, 320, 319, 317, 325, 324, 318, 323] by Demod 127 with 4 at 2,2,2,1,1,2
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(join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 129 with 4 at 1,2,1,2,1,1,2,2
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(meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) 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?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 130 with 4 at 2,2,1,1,2,2
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?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 131 with 4 at 2,1,1,2,2,2,1,2,2
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?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 132 with 4 at 1,2,1,2,2,2,1,2,2
-Id : 134, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 133 with 4 at 2,2,2,2,1,2,2
-Id : 135, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 134 with 4 at 2,1,1,2,2,2
-Id : 136, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324)) =?= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 135 with 4 at 1,2,1,2,2,2
-Id : 714, {_}: join (meet (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383) (meet (join (meet ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)) (meet (join (meet ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)) (meet (join (meet ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)) (meet ?1390 (join ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)))) (join ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)))) (join ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)))) (join (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383)) =>= ?1382 [1390, 1389, 1388, 1387, 1386, 1385, 1384, 1383, 1382, 1381] by Demod 136 with 4 at 3
-Id : 1147, {_}: join (meet (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512) (meet ?2511 (join (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512)) =>= ?2511 [2512, 2511, 2510] by Super 714 with 4 at 1,2,2
-Id : 748, {_}: join (meet (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913) (meet ?1912 (join (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913)) =>= ?1912 [1913, 1912, 1916] by Super 714 with 4 at 1,2,2
-Id : 1164, {_}: join (meet (join (meet (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643) (meet ?2643 (join (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643))) ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643, 2642] by Super 1147 with 748 at 1,2,2,2
-Id : 1544, {_}: join (meet ?2643 ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643] by Demod 1164 with 748 at 1,1,2
-Id : 13, {_}: join (meet (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113) (meet (join (meet ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))) (meet ?107 (join ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))))) (join (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113)) =>= join (meet ?106 ?107) (meet ?107 (join ?106 ?107)) [115, 114, 113, 107, 106, 112] by Super 5 with 4 at 1,2,1,2,2
-Id : 1092, {_}: join (meet (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2039, 2038, 2040] by Super 13 with 748 at 2,2,2,1,2,2,2
-Id : 1218, {_}: join (meet (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1092 with 748 at 2,1,1,1,2
-Id : 1219, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1218 with 748 at 1,2,1,1,2
-Id : 1220, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1219 with 748 at 2,2,2,1,1,2
-Id : 1221, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1220 with 748 at 2,1,1,2,1,1,2,2
-Id : 1222, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1221 with 748 at 1,2,1,2,1,1,2,2
-Id : 1223, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1222 with 748 at 2,2,1,1,2,2
-Id : 1224, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1223 with 748 at 2,1,1,2,2,2,1,2,2
-Id : 1225, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1224 with 748 at 1,2,1,2,2,2,1,2,2
-Id : 1226, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1225 with 748 at 2,2,2,2,1,2,2
-Id : 1227, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1226 with 748 at 2,1,1,2,2,2
-Id : 1228, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =?= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1227 with 748 at 1,2,1,2,2,2
-Id : 2531, {_}: join (meet (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436) (meet (join (meet ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)) (meet ?4435 (join ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)))) (join (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436)) =>= ?4435 [4438, 4437, 4436, 4435, 4434] by Demod 1228 with 748 at 3
-Id : 2540, {_}: join (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))))) ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4516, 4515, 4514, 4513, 4512, 4511, 4510, 4509] by Super 2531 with 4 at 1,2,2,2
-Id : 2926, {_}: join (meet ?4510 ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4514, 4513, 4512, 4511, 4516, 4509, 4515, 4510] by Demod 2540 with 4 at 1,1,2
-Id : 2927, {_}: join (meet ?4510 ?4515) (meet ?4510 (join ?4510 ?4515)) =?= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4515, 4510] by Demod 2926 with 4 at 1,2,2
-Id : 2928, {_}: ?4510 =<= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4510] by Demod 2927 with 1544 at 2
-Id : 4152, {_}: ?6409 =<= join (meet ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409)) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6413, 6412, 6411, 6410, 6409] by Super 1544 with 2928 at 2
-Id : 1229, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2043, 2042, 2041, 2039, 2040] by Demod 1228 with 748 at 3
-Id : 2544, {_}: join (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))))) ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4552, 4551, 4550, 4549, 4548, 4547] by Super 2531 with 1229 at 1,2,2,2
-Id : 2938, {_}: join (meet ?4548 ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4550, 4549, 4552, 4547, 4551, 4548] by Demod 2544 with 1229 at 1,1,2
-Id : 2939, {_}: join (meet ?4548 ?4551) (meet ?4548 (join ?4548 ?4551)) =?= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4551, 4548] by Demod 2938 with 1229 at 1,2,2
-Id : 2940, {_}: ?4548 =<= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4548] by Demod 2939 with 1544 at 2
-Id : 2998, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet ?2039 (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2041, 2039, 2040] by Demod 1229 with 2940 at 1,2,2
-Id : 4435, {_}: join (meet ?7069 ?7068) (meet ?7068 (join ?7069 ?7068)) =>= ?7068 [7068, 7069] by Super 2998 with 4152 at 2
-Id : 4973, {_}: ?7997 =<= meet (meet (join ?7998 (join ?7997 ?7999)) (join ?8000 ?7997)) ?7997 [8000, 7999, 7998, 7997] by Super 4152 with 4435 at 3
-Id : 7418, {_}: meet ?10627 ?10628 =<= meet (meet (join ?10629 ?10627) (join ?10630 (meet ?10627 ?10628))) (meet ?10627 ?10628) [10630, 10629, 10628, 10627] by Super 4973 with 1544 at 2,1,1,3
-Id : 3035, {_}: ?5143 =<= join (meet ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143)) (meet ?5143 (join ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143))) [5146, 5145, 5144, 5143] by Demod 2939 with 1544 at 2
-Id : 3039, {_}: ?5175 =<= join (meet ?5174 (join (join (meet ?5175 ?5175) (meet ?5175 (join ?5175 ?5175))) ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Super 3035 with 1544 at 1,2,2,2,3
-Id : 3217, {_}: ?5175 =<= join (meet ?5174 (join ?5175 ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Demod 3039 with 1544 at 1,2,1,3
-Id : 4899, {_}: ?7757 =<= meet (meet (join ?7758 (join ?7757 ?7759)) (join ?7760 ?7757)) ?7757 [7760, 7759, 7758, 7757] by Super 4152 with 4435 at 3
-Id : 4939, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6412, 6411, 6410, 6413, 6409] by Demod 4152 with 4899 at 2,1,3
-Id : 4940, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 ?6409)) [6413, 6409] by Demod 4939 with 4899 at 2,2,2,3
-Id : 4941, {_}: ?7815 =<= join (meet ?7815 ?7815) (join ?7815 ?7815) [7815] by Super 4940 with 4899 at 2,3
-Id : 5068, {_}: ?8129 =<= join (meet (meet ?8129 ?8129) (join ?8129 ?8129)) (meet ?8129 ?8129) [8129] by Super 3217 with 4941 at 2,2,3
-Id : 5072, {_}: ?8141 =<= meet (meet ?8141 (join ?8142 ?8141)) ?8141 [8142, 8141] by Super 4899 with 4941 at 1,1,3
-Id : 5084, {_}: join ?8151 (meet ?8151 (join (meet ?8151 (join ?8152 ?8151)) ?8151)) =>= ?8151 [8152, 8151] by Super 4435 with 5072 at 1,2
-Id : 5705, {_}: ?8954 =<= meet (meet (join ?8955 ?8954) (join ?8956 ?8954)) ?8954 [8956, 8955, 8954] by Super 4899 with 5084 at 2,1,1,3
-Id : 5955, {_}: join ?9293 ?9293 =<= meet (meet (join ?9294 (join ?9293 ?9293)) ?9293) (join ?9293 ?9293) [9294, 9293] by Super 5705 with 4941 at 2,1,3
-Id : 5957, {_}: join ?9299 ?9299 =<= meet (meet ?9299 ?9299) (join ?9299 ?9299) [9299] by Super 5955 with 4941 at 1,1,3
-Id : 6022, {_}: ?8129 =<= join (join ?8129 ?8129) (meet ?8129 ?8129) [8129] by Demod 5068 with 5957 at 1,3
-Id : 7628, {_}: meet ?11050 ?11050 =<= meet (meet (join ?11051 ?11050) ?11050) (meet ?11050 ?11050) [11051, 11050] by Super 7418 with 6022 at 2,1,3
-Id : 6024, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) (join (meet ?9306 ?9306) (join ?9306 ?9306))) =>= join ?9306 ?9306 [9306] by Super 4435 with 5957 at 1,2
-Id : 6144, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) ?9306) =>= join ?9306 ?9306 [9306] by Demod 6024 with 4941 at 2,2,2
-Id : 6187, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Super 5084 with 6144 at 2,1,2,2,2
-Id : 5117, {_}: ?8275 =<= meet (meet ?8275 (join ?8276 ?8275)) ?8275 [8276, 8275] by Super 4899 with 4941 at 1,1,3
-Id : 5128, {_}: join ?8312 ?8312 =<= meet (meet (join ?8312 ?8312) ?8312) (join ?8312 ?8312) [8312] by Super 5117 with 4941 at 2,1,3
-Id : 6199, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (join ?9444 ?9444) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6187 with 5128 at 1,2,2,2
-Id : 6200, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6199 with 6144 at 2,2,2
-Id : 6201, {_}: join (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6200 with 5128 at 2,2
-Id : 6718, {_}: ?10018 =<= meet (meet (meet (join ?10018 ?10018) ?10018) (join ?10019 ?10018)) ?10018 [10019, 10018] by Super 4899 with 6201 at 1,1,3
-Id : 6736, {_}: ?10071 =<= meet (join ?10071 ?10071) ?10071 [10071] by Super 6718 with 5128 at 1,3
-Id : 7650, {_}: meet ?11113 ?11113 =<= meet ?11113 (meet ?11113 ?11113) [11113] by Super 7628 with 6736 at 1,3
-Id : 7731, {_}: join (meet ?11160 ?11160) (meet ?11160 (join ?11160 (meet ?11160 ?11160))) =>= ?11160 [11160] by Super 1544 with 7650 at 1,2
-Id : 6841, {_}: join ?10124 (meet (join ?10124 ?10124) (join (join ?10124 ?10124) ?10124)) =>= join ?10124 ?10124 [10124] by Super 1544 with 6736 at 1,2
-Id : 6817, {_}: join (join ?9306 ?9306) ?9306 =>= join ?9306 ?9306 [9306] by Demod 6144 with 6736 at 2,2
-Id : 6906, {_}: join ?10124 (meet (join ?10124 ?10124) (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6841 with 6817 at 2,2,2
-Id : 1656, {_}: join (meet ?3234 ?3235) (meet ?3234 (join ?3234 ?3235)) =>= ?3234 [3235, 3234] by Demod 1164 with 748 at 1,1,2
-Id : 1661, {_}: join (meet (meet ?3267 ?3268) (meet ?3267 (join ?3267 ?3268))) (meet (meet ?3267 ?3268) ?3267) =>= meet ?3267 ?3268 [3268, 3267] by Super 1656 with 1544 at 2,2,2
-Id : 8992, {_}: meet ?12671 (join ?12672 ?12672) =<= meet (meet (join ?12673 ?12671) ?12672) (meet ?12671 (join ?12672 ?12672)) [12673, 12672, 12671] by Super 7418 with 4940 at 2,1,3
-Id : 6822, {_}: join ?9444 (join ?9444 ?9444) =<= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6201 with 6736 at 1,2
-Id : 6823, {_}: join ?9444 (join ?9444 ?9444) =>= ?9444 [9444] by Demod 6822 with 6736 at 3
-Id : 9646, {_}: meet (join ?13551 ?13551) (join ?13552 ?13552) =<= meet (meet ?13551 ?13552) (meet (join ?13551 ?13551) (join ?13552 ?13552)) [13552, 13551] by Super 8992 with 6823 at 1,1,3
-Id : 9670, {_}: meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624)) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Super 9646 with 7650 at 1,3
-Id : 6333, {_}: meet ?9575 ?9575 =<= meet (meet (join ?9576 (meet ?9575 ?9575)) ?9575) (meet ?9575 ?9575) [9576, 9575] by Super 5705 with 5068 at 2,1,3
-Id : 6336, {_}: meet ?9583 ?9583 =<= meet (meet ?9583 ?9583) (meet ?9583 ?9583) [9583] by Super 6333 with 6022 at 1,1,3
-Id : 6405, {_}: meet ?9659 ?9659 =<= join (join (meet ?9659 ?9659) (meet ?9659 ?9659)) (meet ?9659 ?9659) [9659] by Super 6022 with 6336 at 2,3
-Id : 7013, {_}: meet ?9659 ?9659 =<= join (meet ?9659 ?9659) (meet ?9659 ?9659) [9659] by Demod 6405 with 6817 at 3
-Id : 9768, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Demod 9670 with 7013 at 2,2
-Id : 9769, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (meet ?13624 ?13624)) [13624] by Demod 9768 with 7013 at 2,2,3
-Id : 10286, {_}: join (meet (meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Super 1661 with 9769 at 1,2,2
-Id : 10416, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10286 with 9769 at 1,1,2
-Id : 7044, {_}: meet ?10282 ?10282 =<= join (meet (meet ?10282 ?10282) (meet ?10282 ?10282)) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Super 4940 with 7013 at 2,2,3
-Id : 7086, {_}: meet ?10282 ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7044 with 6336 at 1,3
-Id : 10417, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10416 with 7086 at 2,2,1,2
-Id : 10418, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10417 with 6336 at 2,1,2
-Id : 7467, {_}: meet ?10854 ?10854 =<= meet (meet (join ?10855 ?10854) (meet ?10854 ?10854)) (meet ?10854 ?10854) [10855, 10854] by Super 7418 with 7013 at 2,1,3
-Id : 10419, {_}: join (meet ?14243 ?14243) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10418 with 7467 at 1,2
-Id : 10420, {_}: meet ?14243 ?14243 =<= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10419 with 7086 at 2
-Id : 10421, {_}: meet ?14243 ?14243 =<= meet (join ?14243 ?14243) (meet ?14243 ?14243) [14243] by Demod 10420 with 9769 at 3
-Id : 10483, {_}: join (meet (meet (join ?14359 ?14359) (meet ?14359 ?14359)) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Super 1661 with 10421 at 1,2,2
-Id : 10517, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10483 with 10421 at 1,1,2
-Id : 10518, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) ?14359)) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10517 with 6022 at 2,2,1,2
-Id : 10519, {_}: join (meet (meet ?14359 ?14359) ?14359) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10518 with 6736 at 2,1,2
-Id : 10520, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10519 with 5957 at 2,2
-Id : 10521, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet ?14359 ?14359 [14359] by Demod 10520 with 10421 at 3
-Id : 10992, {_}: join (meet (meet (meet ?14539 ?14539) ?14539) (join ?14539 ?14539)) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Super 4435 with 10521 at 2,2,2
-Id : 8999, {_}: meet (meet ?12702 ?12702) (join ?12702 ?12702) =<= meet (meet (join ?12703 (meet ?12702 ?12702)) ?12702) (join ?12702 ?12702) [12703, 12702] by Super 8992 with 5957 at 2,3
-Id : 10037, {_}: join ?14089 ?14089 =<= meet (meet (join ?14090 (meet ?14089 ?14089)) ?14089) (join ?14089 ?14089) [14090, 14089] by Demod 8999 with 5957 at 2
-Id : 10046, {_}: join ?14111 ?14111 =<= meet (meet (meet ?14111 ?14111) ?14111) (join ?14111 ?14111) [14111] by Super 10037 with 7013 at 1,1,3
-Id : 11120, {_}: join (join ?14539 ?14539) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Demod 10992 with 10046 at 1,2
-Id : 11121, {_}: join (join ?14539 ?14539) (meet ?14539 ?14539) =>= join ?14539 ?14539 [14539] by Demod 11120 with 10421 at 2,2
-Id : 11122, {_}: ?14539 =<= join ?14539 ?14539 [14539] by Demod 11121 with 6022 at 2
-Id : 11192, {_}: join ?10124 (meet ?10124 (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6906 with 11122 at 1,2,2
-Id : 11193, {_}: join ?10124 (meet ?10124 ?10124) =>= join ?10124 ?10124 [10124] by Demod 11192 with 11122 at 2,2,2
-Id : 11194, {_}: join ?10124 (meet ?10124 ?10124) =>= ?10124 [10124] by Demod 11193 with 11122 at 3
-Id : 11206, {_}: join (meet ?11160 ?11160) (meet ?11160 ?11160) =>= ?11160 [11160] by Demod 7731 with 11194 at 2,2,2
-Id : 11207, {_}: meet ?11160 ?11160 =>= ?11160 [11160] by Demod 11206 with 11122 at 2
-Id : 11456, {_}: a === a [] by Demod 2 with 11207 at 2
-Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-% SZS output end CNFRefutation for LAT080-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- join is 95
- meet is 96
- prove_normal_axioms_8 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-Found proof, 13.641729s
-% SZS status Unsatisfiable for LAT087-1.p
-% SZS output start CNFRefutation for LAT087-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) (meet (join (meet ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) (meet ?8 (join ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Id : 5, {_}: join (meet (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12) (meet (join (meet ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)) (meet (join (meet ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)) (meet ?16 (join ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)))) (join ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)))) (join (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12)) =>= ?11 [16, 15, 14, 13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 ?14 ?15 ?16
-Id : 39, {_}: join (meet (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290) (meet (join (meet ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))) (meet ?289 (join ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))))) (join (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290)) =>= join (meet ?288 ?289) (meet ?289 (join ?288 ?289)) [292, 291, 290, 289, 288, 287] by Super 5 with 4 at 1,2,1,2,2
-Id : 42, {_}: join (meet (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))))) ?324) (meet (join (meet ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 318, 317, 323] by Super 39 with 4 at 2,2,2,1,2,2,2
-Id : 126, {_}: join (meet (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet 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(join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 317, 318, 323] by Demod 126 with 4 at 1,2,1,1,2
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?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 322, 321, 320, 319, 317, 325, 324, 318, 323] by Demod 128 with 4 at 2,1,1,2,1,1,2,2
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?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet 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?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 131 with 4 at 2,1,1,2,2,2,1,2,2
-Id : 133, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 132 with 4 at 1,2,1,2,2,2,1,2,2
-Id : 134, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 133 with 4 at 2,2,2,2,1,2,2
-Id : 135, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 134 with 4 at 2,1,1,2,2,2
-Id : 136, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324)) =?= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 135 with 4 at 1,2,1,2,2,2
-Id : 714, {_}: join (meet (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383) (meet (join (meet ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)) (meet (join (meet ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)) (meet (join (meet ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)) (meet ?1390 (join ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)))) (join ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)))) (join ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)))) (join (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383)) =>= ?1382 [1390, 1389, 1388, 1387, 1386, 1385, 1384, 1383, 1382, 1381] by Demod 136 with 4 at 3
-Id : 1147, {_}: join (meet (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512) (meet ?2511 (join (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512)) =>= ?2511 [2512, 2511, 2510] by Super 714 with 4 at 1,2,2
-Id : 748, {_}: join (meet (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913) (meet ?1912 (join (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913)) =>= ?1912 [1913, 1912, 1916] by Super 714 with 4 at 1,2,2
-Id : 1164, {_}: join (meet (join (meet (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643) (meet ?2643 (join (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643))) ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643, 2642] by Super 1147 with 748 at 1,2,2,2
-Id : 1544, {_}: join (meet ?2643 ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643] by Demod 1164 with 748 at 1,1,2
-Id : 13, {_}: join (meet (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113) (meet (join (meet ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))) (meet ?107 (join ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))))) (join (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113)) =>= join (meet ?106 ?107) (meet ?107 (join ?106 ?107)) [115, 114, 113, 107, 106, 112] by Super 5 with 4 at 1,2,1,2,2
-Id : 1092, {_}: join (meet (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2039, 2038, 2040] by Super 13 with 748 at 2,2,2,1,2,2,2
-Id : 1218, {_}: join (meet (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1092 with 748 at 2,1,1,1,2
-Id : 1219, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1218 with 748 at 1,2,1,1,2
-Id : 1220, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1219 with 748 at 2,2,2,1,1,2
-Id : 1221, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1220 with 748 at 2,1,1,2,1,1,2,2
-Id : 1222, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1221 with 748 at 1,2,1,2,1,1,2,2
-Id : 1223, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1222 with 748 at 2,2,1,1,2,2
-Id : 1224, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1223 with 748 at 2,1,1,2,2,2,1,2,2
-Id : 1225, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1224 with 748 at 1,2,1,2,2,2,1,2,2
-Id : 1226, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1225 with 748 at 2,2,2,2,1,2,2
-Id : 1227, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1226 with 748 at 2,1,1,2,2,2
-Id : 1228, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =?= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1227 with 748 at 1,2,1,2,2,2
-Id : 2531, {_}: join (meet (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436) (meet (join (meet ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)) (meet ?4435 (join ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)))) (join (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436)) =>= ?4435 [4438, 4437, 4436, 4435, 4434] by Demod 1228 with 748 at 3
-Id : 1229, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2043, 2042, 2041, 2039, 2040] by Demod 1228 with 748 at 3
-Id : 2544, {_}: join (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))))) ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4552, 4551, 4550, 4549, 4548, 4547] by Super 2531 with 1229 at 1,2,2,2
-Id : 2938, {_}: join (meet ?4548 ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4550, 4549, 4552, 4547, 4551, 4548] by Demod 2544 with 1229 at 1,1,2
-Id : 2939, {_}: join (meet ?4548 ?4551) (meet ?4548 (join ?4548 ?4551)) =?= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4551, 4548] by Demod 2938 with 1229 at 1,2,2
-Id : 2940, {_}: ?4548 =<= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4548] by Demod 2939 with 1544 at 2
-Id : 2998, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet ?2039 (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2041, 2039, 2040] by Demod 1229 with 2940 at 1,2,2
-Id : 2540, {_}: join (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))))) ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4516, 4515, 4514, 4513, 4512, 4511, 4510, 4509] by Super 2531 with 4 at 1,2,2,2
-Id : 2926, {_}: join (meet ?4510 ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4514, 4513, 4512, 4511, 4516, 4509, 4515, 4510] by Demod 2540 with 4 at 1,1,2
-Id : 2927, {_}: join (meet ?4510 ?4515) (meet ?4510 (join ?4510 ?4515)) =?= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4515, 4510] by Demod 2926 with 4 at 1,2,2
-Id : 2928, {_}: ?4510 =<= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4510] by Demod 2927 with 1544 at 2
-Id : 4152, {_}: ?6409 =<= join (meet ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409)) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6413, 6412, 6411, 6410, 6409] by Super 1544 with 2928 at 2
-Id : 4435, {_}: join (meet ?7069 ?7068) (meet ?7068 (join ?7069 ?7068)) =>= ?7068 [7068, 7069] by Super 2998 with 4152 at 2
-Id : 1656, {_}: join (meet ?3234 ?3235) (meet ?3234 (join ?3234 ?3235)) =>= ?3234 [3235, 3234] by Demod 1164 with 748 at 1,1,2
-Id : 1661, {_}: join (meet (meet ?3267 ?3268) (meet ?3267 (join ?3267 ?3268))) (meet (meet ?3267 ?3268) ?3267) =>= meet ?3267 ?3268 [3268, 3267] by Super 1656 with 1544 at 2,2,2
-Id : 4973, {_}: ?7997 =<= meet (meet (join ?7998 (join ?7997 ?7999)) (join ?8000 ?7997)) ?7997 [8000, 7999, 7998, 7997] by Super 4152 with 4435 at 3
-Id : 7418, {_}: meet ?10627 ?10628 =<= meet (meet (join ?10629 ?10627) (join ?10630 (meet ?10627 ?10628))) (meet ?10627 ?10628) [10630, 10629, 10628, 10627] by Super 4973 with 1544 at 2,1,1,3
-Id : 4899, {_}: ?7757 =<= meet (meet (join ?7758 (join ?7757 ?7759)) (join ?7760 ?7757)) ?7757 [7760, 7759, 7758, 7757] by Super 4152 with 4435 at 3
-Id : 4939, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6412, 6411, 6410, 6413, 6409] by Demod 4152 with 4899 at 2,1,3
-Id : 4940, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 ?6409)) [6413, 6409] by Demod 4939 with 4899 at 2,2,2,3
-Id : 8992, {_}: meet ?12671 (join ?12672 ?12672) =<= meet (meet (join ?12673 ?12671) ?12672) (meet ?12671 (join ?12672 ?12672)) [12673, 12672, 12671] by Super 7418 with 4940 at 2,1,3
-Id : 4941, {_}: ?7815 =<= join (meet ?7815 ?7815) (join ?7815 ?7815) [7815] by Super 4940 with 4899 at 2,3
-Id : 5072, {_}: ?8141 =<= meet (meet ?8141 (join ?8142 ?8141)) ?8141 [8142, 8141] by Super 4899 with 4941 at 1,1,3
-Id : 5084, {_}: join ?8151 (meet ?8151 (join (meet ?8151 (join ?8152 ?8151)) ?8151)) =>= ?8151 [8152, 8151] by Super 4435 with 5072 at 1,2
-Id : 5705, {_}: ?8954 =<= meet (meet (join ?8955 ?8954) (join ?8956 ?8954)) ?8954 [8956, 8955, 8954] by Super 4899 with 5084 at 2,1,1,3
-Id : 5955, {_}: join ?9293 ?9293 =<= meet (meet (join ?9294 (join ?9293 ?9293)) ?9293) (join ?9293 ?9293) [9294, 9293] by Super 5705 with 4941 at 2,1,3
-Id : 5957, {_}: join ?9299 ?9299 =<= meet (meet ?9299 ?9299) (join ?9299 ?9299) [9299] by Super 5955 with 4941 at 1,1,3
-Id : 6024, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) (join (meet ?9306 ?9306) (join ?9306 ?9306))) =>= join ?9306 ?9306 [9306] by Super 4435 with 5957 at 1,2
-Id : 6144, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) ?9306) =>= join ?9306 ?9306 [9306] by Demod 6024 with 4941 at 2,2,2
-Id : 6187, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Super 5084 with 6144 at 2,1,2,2,2
-Id : 5117, {_}: ?8275 =<= meet (meet ?8275 (join ?8276 ?8275)) ?8275 [8276, 8275] by Super 4899 with 4941 at 1,1,3
-Id : 5128, {_}: join ?8312 ?8312 =<= meet (meet (join ?8312 ?8312) ?8312) (join ?8312 ?8312) [8312] by Super 5117 with 4941 at 2,1,3
-Id : 6199, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (join ?9444 ?9444) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6187 with 5128 at 1,2,2,2
-Id : 6200, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6199 with 6144 at 2,2,2
-Id : 6201, {_}: join (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6200 with 5128 at 2,2
-Id : 6718, {_}: ?10018 =<= meet (meet (meet (join ?10018 ?10018) ?10018) (join ?10019 ?10018)) ?10018 [10019, 10018] by Super 4899 with 6201 at 1,1,3
-Id : 6736, {_}: ?10071 =<= meet (join ?10071 ?10071) ?10071 [10071] by Super 6718 with 5128 at 1,3
-Id : 6822, {_}: join ?9444 (join ?9444 ?9444) =<= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6201 with 6736 at 1,2
-Id : 6823, {_}: join ?9444 (join ?9444 ?9444) =>= ?9444 [9444] by Demod 6822 with 6736 at 3
-Id : 9646, {_}: meet (join ?13551 ?13551) (join ?13552 ?13552) =<= meet (meet ?13551 ?13552) (meet (join ?13551 ?13551) (join ?13552 ?13552)) [13552, 13551] by Super 8992 with 6823 at 1,1,3
-Id : 3035, {_}: ?5143 =<= join (meet ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143)) (meet ?5143 (join ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143))) [5146, 5145, 5144, 5143] by Demod 2939 with 1544 at 2
-Id : 3039, {_}: ?5175 =<= join (meet ?5174 (join (join (meet ?5175 ?5175) (meet ?5175 (join ?5175 ?5175))) ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Super 3035 with 1544 at 1,2,2,2,3
-Id : 3217, {_}: ?5175 =<= join (meet ?5174 (join ?5175 ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Demod 3039 with 1544 at 1,2,1,3
-Id : 5068, {_}: ?8129 =<= join (meet (meet ?8129 ?8129) (join ?8129 ?8129)) (meet ?8129 ?8129) [8129] by Super 3217 with 4941 at 2,2,3
-Id : 6022, {_}: ?8129 =<= join (join ?8129 ?8129) (meet ?8129 ?8129) [8129] by Demod 5068 with 5957 at 1,3
-Id : 7628, {_}: meet ?11050 ?11050 =<= meet (meet (join ?11051 ?11050) ?11050) (meet ?11050 ?11050) [11051, 11050] by Super 7418 with 6022 at 2,1,3
-Id : 7650, {_}: meet ?11113 ?11113 =<= meet ?11113 (meet ?11113 ?11113) [11113] by Super 7628 with 6736 at 1,3
-Id : 9670, {_}: meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624)) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Super 9646 with 7650 at 1,3
-Id : 6333, {_}: meet ?9575 ?9575 =<= meet (meet (join ?9576 (meet ?9575 ?9575)) ?9575) (meet ?9575 ?9575) [9576, 9575] by Super 5705 with 5068 at 2,1,3
-Id : 6336, {_}: meet ?9583 ?9583 =<= meet (meet ?9583 ?9583) (meet ?9583 ?9583) [9583] by Super 6333 with 6022 at 1,1,3
-Id : 6405, {_}: meet ?9659 ?9659 =<= join (join (meet ?9659 ?9659) (meet ?9659 ?9659)) (meet ?9659 ?9659) [9659] by Super 6022 with 6336 at 2,3
-Id : 6817, {_}: join (join ?9306 ?9306) ?9306 =>= join ?9306 ?9306 [9306] by Demod 6144 with 6736 at 2,2
-Id : 7013, {_}: meet ?9659 ?9659 =<= join (meet ?9659 ?9659) (meet ?9659 ?9659) [9659] by Demod 6405 with 6817 at 3
-Id : 9768, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Demod 9670 with 7013 at 2,2
-Id : 9769, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (meet ?13624 ?13624)) [13624] by Demod 9768 with 7013 at 2,2,3
-Id : 10286, {_}: join (meet (meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Super 1661 with 9769 at 1,2,2
-Id : 10416, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10286 with 9769 at 1,1,2
-Id : 7044, {_}: meet ?10282 ?10282 =<= join (meet (meet ?10282 ?10282) (meet ?10282 ?10282)) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Super 4940 with 7013 at 2,2,3
-Id : 7086, {_}: meet ?10282 ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7044 with 6336 at 1,3
-Id : 10417, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10416 with 7086 at 2,2,1,2
-Id : 10418, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10417 with 6336 at 2,1,2
-Id : 7467, {_}: meet ?10854 ?10854 =<= meet (meet (join ?10855 ?10854) (meet ?10854 ?10854)) (meet ?10854 ?10854) [10855, 10854] by Super 7418 with 7013 at 2,1,3
-Id : 10419, {_}: join (meet ?14243 ?14243) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10418 with 7467 at 1,2
-Id : 10420, {_}: meet ?14243 ?14243 =<= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10419 with 7086 at 2
-Id : 10421, {_}: meet ?14243 ?14243 =<= meet (join ?14243 ?14243) (meet ?14243 ?14243) [14243] by Demod 10420 with 9769 at 3
-Id : 10483, {_}: join (meet (meet (join ?14359 ?14359) (meet ?14359 ?14359)) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Super 1661 with 10421 at 1,2,2
-Id : 10517, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10483 with 10421 at 1,1,2
-Id : 10518, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) ?14359)) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10517 with 6022 at 2,2,1,2
-Id : 10519, {_}: join (meet (meet ?14359 ?14359) ?14359) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10518 with 6736 at 2,1,2
-Id : 10520, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10519 with 5957 at 2,2
-Id : 10521, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet ?14359 ?14359 [14359] by Demod 10520 with 10421 at 3
-Id : 10992, {_}: join (meet (meet (meet ?14539 ?14539) ?14539) (join ?14539 ?14539)) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Super 4435 with 10521 at 2,2,2
-Id : 8999, {_}: meet (meet ?12702 ?12702) (join ?12702 ?12702) =<= meet (meet (join ?12703 (meet ?12702 ?12702)) ?12702) (join ?12702 ?12702) [12703, 12702] by Super 8992 with 5957 at 2,3
-Id : 10037, {_}: join ?14089 ?14089 =<= meet (meet (join ?14090 (meet ?14089 ?14089)) ?14089) (join ?14089 ?14089) [14090, 14089] by Demod 8999 with 5957 at 2
-Id : 10046, {_}: join ?14111 ?14111 =<= meet (meet (meet ?14111 ?14111) ?14111) (join ?14111 ?14111) [14111] by Super 10037 with 7013 at 1,1,3
-Id : 11120, {_}: join (join ?14539 ?14539) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Demod 10992 with 10046 at 1,2
-Id : 11121, {_}: join (join ?14539 ?14539) (meet ?14539 ?14539) =>= join ?14539 ?14539 [14539] by Demod 11120 with 10421 at 2,2
-Id : 11122, {_}: ?14539 =<= join ?14539 ?14539 [14539] by Demod 11121 with 6022 at 2
-Id : 11280, {_}: ?14616 =<= join (meet (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616) (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) (meet ?14616 (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) [14618, 14617, 14616] by Super 2940 with 11122 at 2,2,3
-Id : 7731, {_}: join (meet ?11160 ?11160) (meet ?11160 (join ?11160 (meet ?11160 ?11160))) =>= ?11160 [11160] by Super 1544 with 7650 at 1,2
-Id : 6841, {_}: join ?10124 (meet (join ?10124 ?10124) (join (join ?10124 ?10124) ?10124)) =>= join ?10124 ?10124 [10124] by Super 1544 with 6736 at 1,2
-Id : 6906, {_}: join ?10124 (meet (join ?10124 ?10124) (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6841 with 6817 at 2,2,2
-Id : 11192, {_}: join ?10124 (meet ?10124 (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6906 with 11122 at 1,2,2
-Id : 11193, {_}: join ?10124 (meet ?10124 ?10124) =>= join ?10124 ?10124 [10124] by Demod 11192 with 11122 at 2,2,2
-Id : 11194, {_}: join ?10124 (meet ?10124 ?10124) =>= ?10124 [10124] by Demod 11193 with 11122 at 3
-Id : 11206, {_}: join (meet ?11160 ?11160) (meet ?11160 ?11160) =>= ?11160 [11160] by Demod 7731 with 11194 at 2,2,2
-Id : 11207, {_}: meet ?11160 ?11160 =>= ?11160 [11160] by Demod 11206 with 11122 at 2
-Id : 11417, {_}: ?14616 =<= join (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616) (meet ?14616 (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) [14618, 14617, 14616] by Demod 11280 with 11207 at 1,3
-Id : 11210, {_}: ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7086 with 11207 at 2
-Id : 11211, {_}: ?10282 =<= join ?10282 (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 11210 with 11207 at 1,3
-Id : 11212, {_}: ?10282 =<= join ?10282 (meet ?10283 ?10282) [10283, 10282] by Demod 11211 with 11207 at 2,2,3
-Id : 12052, {_}: ?15606 =<= join (join (meet ?15607 ?15606) (meet ?15606 ?15608)) ?15606 [15608, 15607, 15606] by Demod 11417 with 11212 at 3
-Id : 12070, {_}: ?15688 =<= join (join ?15688 (meet ?15688 ?15689)) ?15688 [15689, 15688] by Super 12052 with 11207 at 1,1,3
-Id : 12545, {_}: join (meet (join ?16137 (meet ?16137 ?16138)) ?16137) (meet (join ?16137 (meet ?16137 ?16138)) ?16137) =>= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Super 1544 with 12070 at 2,2,2
-Id : 12628, {_}: meet (join ?16137 (meet ?16137 ?16138)) ?16137 =>= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Demod 12545 with 11122 at 2
-Id : 11515, {_}: ?14875 =<= meet (meet (join ?14876 (join ?14875 ?14877)) ?14875) ?14875 [14877, 14876, 14875] by Super 4899 with 11122 at 2,1,3
-Id : 11529, {_}: ?14934 =<= meet (meet (join ?14934 ?14935) ?14934) ?14934 [14935, 14934] by Super 11515 with 11122 at 1,1,3
-Id : 12090, {_}: ?15773 =<= join (meet ?15774 ?15773) ?15773 [15774, 15773] by Super 12052 with 11212 at 1,3
-Id : 12194, {_}: join (meet (meet ?15862 ?15861) ?15861) (meet (meet ?15862 ?15861) ?15861) =>= meet ?15862 ?15861 [15861, 15862] by Super 1544 with 12090 at 2,2,2
-Id : 12248, {_}: meet (meet ?15862 ?15861) ?15861 =>= meet ?15862 ?15861 [15861, 15862] by Demod 12194 with 11122 at 2
-Id : 12318, {_}: ?14934 =<= meet (join ?14934 ?14935) ?14934 [14935, 14934] by Demod 11529 with 12248 at 3
-Id : 12629, {_}: ?16137 =<= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Demod 12628 with 12318 at 2
-Id : 12769, {_}: a === a [] by Demod 2 with 12629 at 2
-Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-% SZS output end CNFRefutation for LAT087-1.p
-Order
- == is 100
- _ is 99
- a is 97
- b is 98
- join is 94
- meet is 96
- prove_wal_axioms_2 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-Found proof, 13.145365s
-% SZS status Unsatisfiable for LAT093-1.p
-% SZS output start CNFRefutation for LAT093-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) (meet (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) (meet ?7 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Id : 5, {_}: join (meet (join (meet ?9 ?10) (meet ?10 (join ?9 ?10))) ?11) (meet (join (meet ?9 (join (join (meet ?10 ?12) (meet ?13 ?10)) ?10)) (meet (join (meet ?10 (meet (meet (join ?10 ?12) (join ?13 ?10)) ?10)) (meet ?14 (join ?10 (meet (meet (join ?10 ?12) (join ?13 ?10)) ?10)))) (join ?9 (join (join (meet ?10 ?12) (meet ?13 ?10)) ?10)))) (join (join (meet ?9 ?10) (meet ?10 (join ?9 ?10))) ?11)) =>= ?10 [14, 13, 12, 11, 10, 9] by single_axiom ?9 ?10 ?11 ?12 ?13 ?14
-Id : 33, {_}: join (meet (join (meet ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))) (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) (join ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))))) ?218) (meet (join (meet ?215 (join (join (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) ?219) (meet ?220 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (meet ?217 (join ?215 (join (join (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) ?219) (meet ?220 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))))) (join (join (meet ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))) (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) (join ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))))) ?218)) =>= join (meet ?216 ?217) (meet ?217 (join ?216 ?217)) [220, 219, 218, 217, 216, 215] by Super 5 with 4 at 1,2,1,2,2
-Id : 36, {_}: join (meet (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))))) ?250) (meet (join (meet ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join 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?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 245, 244, 249] by Super 33 with 4 at 2,2,2,1,2,2,2
-Id : 118, {_}: join (meet (join (meet ?249 ?245) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) 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?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 244, 245, 249] by Demod 36 with 4 at 2,1,1,1,2
-Id : 119, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 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(meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 244, 245, 249] by Demod 118 with 4 at 1,2,1,1,2
-Id : 120, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet 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(join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 248, 247, 246, 244, 250, 245, 249] by Demod 119 with 4 at 2,2,2,1,1,2
-Id : 121, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 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?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 120 with 4 at 1,1,1,2,1,1,2,2
-Id : 122, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) 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?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 121 with 4 at 2,2,1,2,1,1,2,2
-Id : 123, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join 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(meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 122 with 4 at 2,2,1,1,2,2
-Id : 124, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 123 with 4 at 1,1,1,2,2,2,1,2,2
-Id : 125, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 124 with 4 at 2,2,1,2,2,2,1,2,2
-Id : 126, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 125 with 4 at 2,2,2,2,1,2,2
-Id : 127, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 ?245) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 126 with 4 at 2,1,1,2,2,2
-Id : 128, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250)) =?= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 127 with 4 at 1,2,1,2,2,2
-Id : 704, {_}: join (meet (join (meet ?1213 ?1214) (meet ?1214 (join ?1213 ?1214))) ?1215) (meet (join (meet ?1213 (join (join (meet ?1214 ?1216) (meet ?1217 ?1214)) ?1214)) (meet (join (meet ?1218 (join (join (meet ?1214 ?1219) (meet ?1220 ?1214)) ?1214)) (meet (join (meet ?1214 (meet (meet (join ?1214 ?1219) (join ?1220 ?1214)) ?1214)) (meet ?1221 (join ?1214 (meet (meet (join ?1214 ?1219) (join ?1220 ?1214)) ?1214)))) (join ?1218 (join (join (meet ?1214 ?1219) (meet ?1220 ?1214)) ?1214)))) (join ?1213 (join (join (meet ?1214 ?1216) (meet ?1217 ?1214)) ?1214)))) (join (join (meet ?1213 ?1214) (meet ?1214 (join ?1213 ?1214))) ?1215)) =>= ?1214 [1221, 1220, 1219, 1218, 1217, 1216, 1215, 1214, 1213] by Demod 128 with 4 at 3
-Id : 1103, {_}: join (meet (join (meet (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032) (meet ?2032 (join (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032))) ?2033) (meet ?2032 (join (join (meet (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032) (meet ?2032 (join (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032))) ?2033)) =>= ?2032 [2033, 2032, 2031] by Super 704 with 4 at 1,2,2
-Id : 726, {_}: join (meet (join (meet (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532) (meet ?1532 (join (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532))) ?1533) (meet ?1532 (join (join (meet (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532) (meet ?1532 (join (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532))) ?1533)) =>= ?1532 [1533, 1532, 1536] by Super 704 with 4 at 1,2,2
-Id : 1120, {_}: join (meet (join (meet (join (meet (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156) (meet ?2156 (join (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156))) ?2156) (meet ?2156 (join (join (meet (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156) (meet ?2156 (join (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156))) ?2156))) ?2157) (meet ?2156 (join ?2156 ?2157)) =>= ?2156 [2157, 2156, 2155] by Super 1103 with 726 at 1,2,2,2
-Id : 1492, {_}: join (meet ?2156 ?2157) (meet ?2156 (join ?2156 ?2157)) =>= ?2156 [2157, 2156] by Demod 1120 with 726 at 1,1,2
-Id : 12, {_}: join (meet (join (meet ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))) (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) (join ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))))) ?87) (meet (join (meet ?86 (join (join (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) ?88) (meet ?89 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (meet ?82 (join ?86 (join (join (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) ?88) (meet ?89 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))))) (join (join (meet ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))) (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) (join ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))))) ?87)) =>= join (meet ?81 ?82) (meet ?82 (join ?81 ?82)) [89, 88, 87, 82, 81, 86] by Super 5 with 4 at 1,2,1,2,2
-Id : 1056, {_}: join (meet (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1647, 1646, 1648] by Super 12 with 726 at 2,2,2,1,2,2,2
-Id : 1168, {_}: join (meet (join (meet ?1648 ?1647) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1646, 1647, 1648] by Demod 1056 with 726 at 2,1,1,1,2
-Id : 1169, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1646, 1647, 1648] by Demod 1168 with 726 at 1,2,1,1,2
-Id : 1170, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1646, 1649, 1647, 1648] by Demod 1169 with 726 at 2,2,2,1,1,2
-Id : 1171, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1170 with 726 at 1,1,1,2,1,1,2,2
-Id : 1172, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1171 with 726 at 2,2,1,2,1,1,2,2
-Id : 1173, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1172 with 726 at 2,2,1,1,2,2
-Id : 1174, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1173 with 726 at 1,1,1,2,2,2,1,2,2
-Id : 1175, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1174 with 726 at 2,2,1,2,2,2,1,2,2
-Id : 1176, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1175 with 726 at 2,2,2,2,1,2,2
-Id : 1177, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1176 with 726 at 2,1,1,2,2,2
-Id : 1178, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =?= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1177 with 726 at 1,2,1,2,2,2
-Id : 1179, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =>= ?1647 [1651, 1650, 1649, 1647, 1648] by Demod 1178 with 726 at 3
-Id : 2457, {_}: join (meet (join (meet ?3744 ?3745) (meet ?3745 (join ?3744 ?3745))) ?3746) (meet (join (meet ?3744 (join (join (meet ?3745 ?3747) (meet ?3748 ?3745)) ?3745)) (meet ?3745 (join ?3744 (join (join (meet ?3745 ?3747) (meet ?3748 ?3745)) ?3745)))) (join (join (meet ?3744 ?3745) (meet ?3745 (join ?3744 ?3745))) ?3746)) =>= ?3745 [3748, 3747, 3746, 3745, 3744] by Demod 1178 with 726 at 3
-Id : 2470, {_}: join (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))))))) ?3857) (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))))) (join ?3854 ?3857)) =>= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3859, 3858, 3857, 3856, 3855, 3854, 3853] by Super 2457 with 1179 at 1,2,2,2
-Id : 2846, {_}: join (meet ?3854 ?3857) (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))))) (join ?3854 ?3857)) =>= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3859, 3858, 3856, 3855, 3853, 3857, 3854] by Demod 2470 with 1179 at 1,1,2
-Id : 2847, {_}: join (meet ?3854 ?3857) (meet ?3854 (join ?3854 ?3857)) =?= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3856, 3855, 3853, 3857, 3854] by Demod 2846 with 1179 at 1,2,2
-Id : 2848, {_}: ?3854 =<= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3856, 3855, 3853, 3854] by Demod 2847 with 1492 at 2
-Id : 2894, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet ?1647 (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =>= ?1647 [1649, 1647, 1648] by Demod 1179 with 2848 at 1,2,2
-Id : 2466, {_}: join (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))))))) ?3822) (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))))) (join ?3818 ?3822)) =>= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3824, 3823, 3822, 3821, 3820, 3819, 3818, 3817] by Super 2457 with 4 at 1,2,2,2
-Id : 2834, {_}: join (meet ?3818 ?3822) (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))))) (join ?3818 ?3822)) =>= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3824, 3823, 3821, 3820, 3819, 3817, 3822, 3818] by Demod 2466 with 4 at 1,1,2
-Id : 2835, {_}: join (meet ?3818 ?3822) (meet ?3818 (join ?3818 ?3822)) =?= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3821, 3820, 3819, 3817, 3822, 3818] by Demod 2834 with 4 at 1,2,2
-Id : 2836, {_}: ?3818 =<= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3821, 3820, 3819, 3817, 3818] by Demod 2835 with 1492 at 2
-Id : 3353, {_}: ?4683 =<= join (meet ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683)) (meet ?4686 (join ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683))) [4686, 4685, 4684, 4683] by Super 2894 with 2836 at 2
-Id : 3629, {_}: join (meet ?5382 ?5381) (meet ?5381 (join ?5382 ?5381)) =>= ?5381 [5381, 5382] by Super 2894 with 3353 at 2
-Id : 4066, {_}: ?5811 =<= meet (meet (join ?5811 ?5812) (join ?5813 ?5811)) ?5811 [5813, 5812, 5811] by Super 3353 with 3629 at 3
-Id : 4517, {_}: meet ?6536 ?6537 =<= meet (meet ?6537 (join ?6538 (meet ?6536 ?6537))) (meet ?6536 ?6537) [6538, 6537, 6536] by Super 4066 with 3629 at 1,1,3
-Id : 4020, {_}: ?5649 =<= meet (meet (join ?5649 ?5650) (join ?5651 ?5649)) ?5649 [5651, 5650, 5649] by Super 3353 with 3629 at 3
-Id : 4518, {_}: meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542 =<= meet (meet ?6542 (join ?6543 (meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542))) ?6542 [6543, 6541, 6540, 6542] by Super 4517 with 4020 at 2,3
-Id : 4585, {_}: ?6542 =<= meet (meet ?6542 (join ?6543 (meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542))) ?6542 [6541, 6540, 6543, 6542] by Demod 4518 with 4020 at 2
-Id : 4586, {_}: ?6542 =<= meet (meet ?6542 (join ?6543 ?6542)) ?6542 [6543, 6542] by Demod 4585 with 4020 at 2,2,1,3
-Id : 1596, {_}: join (meet ?2660 ?2661) (meet ?2660 (join ?2660 ?2661)) =>= ?2660 [2661, 2660] by Demod 1120 with 726 at 1,1,2
-Id : 1601, {_}: join (meet (meet ?2691 ?2692) (meet ?2691 (join ?2691 ?2692))) (meet (meet ?2691 ?2692) ?2691) =>= meet ?2691 ?2692 [2692, 2691] by Super 1596 with 1492 at 2,2,2
-Id : 4161, {_}: meet ?6000 ?6001 =<= meet (meet ?6000 (join ?6002 (meet ?6000 ?6001))) (meet ?6000 ?6001) [6002, 6001, 6000] by Super 4066 with 1492 at 1,1,3
-Id : 4166, {_}: meet ?6025 (join ?6025 ?6024) =<= meet (meet ?6025 ?6025) (meet ?6025 (join ?6025 ?6024)) [6024, 6025] by Super 4161 with 1492 at 2,1,3
-Id : 4239, {_}: join (meet ?6108 (join ?6108 ?6108)) (meet (meet ?6108 ?6108) ?6108) =>= meet ?6108 ?6108 [6108] by Super 1601 with 4166 at 1,2
-Id : 1974, {_}: join (meet (meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900))) (meet (meet ?2899 ?2900) ?2899)) (meet (meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900))) (meet ?2899 ?2900)) =>= meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900)) [2900, 2899] by Super 1492 with 1601 at 2,2,2
-Id : 4530, {_}: meet ?6595 (join ?6595 ?6594) =<= meet (meet (join ?6595 ?6594) ?6595) (meet ?6595 (join ?6595 ?6594)) [6594, 6595] by Super 4517 with 1492 at 2,1,3
-Id : 4634, {_}: join ?6728 (meet ?6728 (join (meet ?6728 (join ?6729 ?6728)) ?6728)) =>= ?6728 [6729, 6728] by Super 3629 with 4586 at 1,2
-Id : 5854, {_}: meet ?8039 (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) =<= meet (meet (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) ?8039) (meet ?8039 ?8039) [8040, 8039] by Super 4530 with 4634 at 2,2,3
-Id : 5885, {_}: meet ?8039 ?8039 =<= meet (meet (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) ?8039) (meet ?8039 ?8039) [8040, 8039] by Demod 5854 with 4634 at 2,2
-Id : 5886, {_}: meet ?8039 ?8039 =<= meet (meet ?8039 ?8039) (meet ?8039 ?8039) [8039] by Demod 5885 with 4634 at 1,1,3
-Id : 5940, {_}: join (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Super 1974 with 5886 at 2,2,2
-Id : 6002, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 5940 with 4166 at 1,1,2
-Id : 6003, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6002 with 5886 at 1,2,1,2
-Id : 6004, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet ?8123 ?8123)) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6003 with 5886 at 2,1,2
-Id : 6005, {_}: join (meet ?8123 ?8123) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6004 with 4586 at 1,2
-Id : 6006, {_}: join (meet ?8123 ?8123) (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet ?8123 ?8123)) =<= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6005 with 4166 at 1,2,2
-Id : 6007, {_}: join (meet ?8123 ?8123) (meet ?8123 ?8123) =<= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6006 with 4586 at 2,2
-Id : 6008, {_}: join (meet ?8123 ?8123) (meet ?8123 ?8123) =<= meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)) [8123] by Demod 6007 with 4166 at 3
-Id : 7068, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet (meet (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355)) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Super 4239 with 6008 at 1,2
-Id : 7098, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet (meet ?9355 ?9355) (meet ?9355 ?9355)) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Demod 7068 with 5886 at 1,2,2
-Id : 7099, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Demod 7098 with 5886 at 2,2
-Id : 7100, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355) =>= meet ?9355 ?9355 [9355] by Demod 7099 with 5886 at 3
-Id : 7401, {_}: meet ?9521 ?9521 =<= meet (meet (join (meet ?9521 ?9521) ?9522) (meet ?9521 ?9521)) (meet ?9521 ?9521) [9522, 9521] by Super 4020 with 7100 at 2,1,3
-Id : 13724, {_}: join (meet ?15407 ?15407) (meet (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (join (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (meet ?15407 ?15407))) =>= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Super 1492 with 7401 at 1,2
-Id : 4041, {_}: ?4683 =<= join (meet ?4683 ?4683) (meet ?4686 (join ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683))) [4685, 4684, 4686, 4683] by Demod 3353 with 4020 at 2,1,3
-Id : 4042, {_}: ?4683 =<= join (meet ?4683 ?4683) (meet ?4686 (join ?4683 ?4683)) [4686, 4683] by Demod 4041 with 4020 at 2,2,2,3
-Id : 4536, {_}: meet ?6617 (join ?6616 ?6616) =<= meet (meet (join ?6616 ?6616) ?6616) (meet ?6617 (join ?6616 ?6616)) [6616, 6617] by Super 4517 with 4042 at 2,1,3
-Id : 7400, {_}: join (meet (join (meet ?9519 ?9519) (meet ?9519 ?9519)) (meet ?9519 ?9519)) (meet (meet ?9519 ?9519) (meet ?9519 ?9519)) =>= meet ?9519 ?9519 [9519] by Super 3629 with 7100 at 2,2,2
-Id : 7034, {_}: meet ?9263 ?9263 =<= meet (join (meet ?9263 ?9263) (meet ?9263 ?9263)) (meet ?9263 ?9263) [9263] by Super 4586 with 6008 at 1,3
-Id : 7430, {_}: join (meet ?9519 ?9519) (meet (meet ?9519 ?9519) (meet ?9519 ?9519)) =>= meet ?9519 ?9519 [9519] by Demod 7400 with 7034 at 1,2
-Id : 7431, {_}: join (meet ?9519 ?9519) (meet ?9519 ?9519) =>= meet ?9519 ?9519 [9519] by Demod 7430 with 5886 at 2,2
-Id : 7539, {_}: meet ?9566 (join (meet ?9565 ?9565) (meet ?9565 ?9565)) =<= meet (meet (join (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Super 4536 with 7431 at 2,2,3
-Id : 7732, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet (join (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7539 with 7431 at 2,2
-Id : 7733, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7732 with 7431 at 1,1,3
-Id : 7734, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet ?9565 ?9565) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7733 with 5886 at 1,3
-Id : 7988, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet (meet ?9922 ?9922) (join (meet ?9922 ?9922) (meet ?9921 (meet ?9922 ?9922)))) =>= meet ?9922 ?9922 [9922, 9921] by Super 1492 with 7734 at 1,2
-Id : 7550, {_}: meet ?9591 ?9591 =<= join (meet (meet ?9591 ?9591) (meet ?9591 ?9591)) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Super 4042 with 7431 at 2,2,3
-Id : 7707, {_}: meet ?9591 ?9591 =<= join (meet ?9591 ?9591) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 7550 with 5886 at 1,3
-Id : 8067, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet (meet ?9922 ?9922) (meet ?9922 ?9922)) =>= meet ?9922 ?9922 [9922, 9921] by Demod 7988 with 7707 at 2,2,2
-Id : 8068, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet ?9922 ?9922) =>= meet ?9922 ?9922 [9922, 9921] by Demod 8067 with 5886 at 2,2
-Id : 13909, {_}: join (meet ?15407 ?15407) (meet (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (meet ?15407 ?15407)) =>= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13724 with 8068 at 2,2,2
-Id : 13910, {_}: meet ?15407 ?15407 =<= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13909 with 7707 at 2
-Id : 5848, {_}: join (meet ?8021 (meet ?8021 (join (meet ?8021 (join ?8022 ?8021)) ?8021))) (meet ?8021 ?8021) =>= ?8021 [8022, 8021] by Super 1492 with 4634 at 2,2,2
-Id : 4640, {_}: ?6750 =<= meet (meet ?6750 (join ?6751 ?6750)) ?6750 [6751, 6750] by Demod 4585 with 4020 at 2,2,1,3
-Id : 4645, {_}: meet ?6768 (join ?6767 ?6768) =<= meet (meet (meet ?6768 (join ?6767 ?6768)) ?6768) (meet ?6768 (join ?6767 ?6768)) [6767, 6768] by Super 4640 with 3629 at 2,1,3
-Id : 4708, {_}: meet ?6768 (join ?6767 ?6768) =<= meet ?6768 (meet ?6768 (join ?6767 ?6768)) [6767, 6768] by Demod 4645 with 4586 at 1,3
-Id : 5910, {_}: join (meet ?8021 (join (meet ?8021 (join ?8022 ?8021)) ?8021)) (meet ?8021 ?8021) =>= ?8021 [8022, 8021] by Demod 5848 with 4708 at 1,2
-Id : 9401, {_}: meet (meet ?11248 ?11249) ?11248 =<= meet (meet (meet ?11248 ?11249) (meet ?11248 ?11249)) (meet (meet ?11248 ?11249) ?11248) [11249, 11248] by Super 4161 with 1601 at 2,1,3
-Id : 9402, {_}: meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Super 9401 with 4020 at 1,2,3
-Id : 9552, {_}: meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Demod 9402 with 4020 at 1,2
-Id : 9553, {_}: meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet ?11253 (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Demod 9552 with 4020 at 1,1,3
-Id : 18238, {_}: meet ?19914 (meet (join ?19914 ?19915) (join ?19916 ?19914)) =<= meet (meet ?19914 ?19914) (meet ?19914 (meet (join ?19914 ?19915) (join ?19916 ?19914))) [19916, 19915, 19914] by Demod 9553 with 4020 at 2,1,3
-Id : 11581, {_}: meet ?13378 (join ?13379 ?13379) =<= meet (meet (meet ?13378 (join ?13379 ?13379)) ?13379) (meet ?13378 (join ?13379 ?13379)) [13379, 13378] by Super 4640 with 4042 at 2,1,3
-Id : 11600, {_}: meet (join ?13442 ?13441) (join ?13442 ?13442) =<= meet ?13442 (meet (join ?13442 ?13441) (join ?13442 ?13442)) [13441, 13442] by Super 11581 with 4020 at 1,3
-Id : 18285, {_}: meet ?20107 (meet (join ?20107 ?20106) (join ?20107 ?20107)) =<= meet (meet ?20107 ?20107) (meet (join ?20107 ?20106) (join ?20107 ?20107)) [20106, 20107] by Super 18238 with 11600 at 2,3
-Id : 18491, {_}: meet (join ?20107 ?20106) (join ?20107 ?20107) =<= meet (meet ?20107 ?20107) (meet (join ?20107 ?20106) (join ?20107 ?20107)) [20106, 20107] by Demod 18285 with 11600 at 2
-Id : 18514, {_}: join (meet (join ?20180 ?20181) (join ?20180 ?20180)) (meet (meet (join ?20180 ?20181) (join ?20180 ?20180)) (join (meet ?20180 ?20180) (meet (join ?20180 ?20181) (join ?20180 ?20180)))) =>= meet (join ?20180 ?20181) (join ?20180 ?20180) [20181, 20180] by Super 3629 with 18491 at 1,2
-Id : 18667, {_}: join (meet (join ?20180 ?20181) (join ?20180 ?20180)) (meet (meet (join ?20180 ?20181) (join ?20180 ?20180)) ?20180) =>= meet (join ?20180 ?20181) (join ?20180 ?20180) [20181, 20180] by Demod 18514 with 4042 at 2,2,2
-Id : 18856, {_}: join (meet (join ?20559 ?20560) (join ?20559 ?20559)) ?20559 =>= meet (join ?20559 ?20560) (join ?20559 ?20559) [20560, 20559] by Demod 18667 with 4020 at 2,2
-Id : 4044, {_}: join ?5696 (meet ?5696 (join (meet (join ?5696 ?5697) (join ?5698 ?5696)) ?5696)) =>= ?5696 [5698, 5697, 5696] by Super 3629 with 4020 at 1,2
-Id : 18864, {_}: join (meet ?20588 (join ?20588 ?20588)) ?20588 =<= meet (join ?20588 (meet ?20588 (join (meet (join ?20588 ?20586) (join ?20587 ?20588)) ?20588))) (join ?20588 ?20588) [20587, 20586, 20588] by Super 18856 with 4044 at 1,1,2
-Id : 19017, {_}: join (meet ?20588 (join ?20588 ?20588)) ?20588 =>= meet ?20588 (join ?20588 ?20588) [20588] by Demod 18864 with 4044 at 1,3
-Id : 19112, {_}: join (meet ?20758 (meet ?20758 (join ?20758 ?20758))) (meet ?20758 ?20758) =>= ?20758 [20758] by Super 5910 with 19017 at 2,1,2
-Id : 19134, {_}: join (meet ?20758 (join ?20758 ?20758)) (meet ?20758 ?20758) =>= ?20758 [20758] by Demod 19112 with 4708 at 1,2
-Id : 12695, {_}: ?14373 =<= join (meet ?14375 (join (join (meet ?14373 (join (meet ?14373 (join ?14374 ?14373)) ?14373)) (meet ?14373 ?14373)) ?14373)) (meet ?14373 (join ?14375 (join ?14373 ?14373))) [14374, 14375, 14373] by Super 2848 with 5910 at 1,2,2,2,3
-Id : 12774, {_}: ?14373 =<= join (meet ?14375 (join ?14373 ?14373)) (meet ?14373 (join ?14375 (join ?14373 ?14373))) [14375, 14373] by Demod 12695 with 5910 at 1,2,1,3
-Id : 23235, {_}: join ?23859 ?23859 =>= ?23859 [23859] by Super 4042 with 12774 at 3
-Id : 23429, {_}: join (meet ?20758 ?20758) (meet ?20758 ?20758) =>= ?20758 [20758] by Demod 19134 with 23235 at 2,1,2
-Id : 23430, {_}: meet ?20758 ?20758 =>= ?20758 [20758] by Demod 23429 with 23235 at 2
-Id : 23444, {_}: ?15407 =<= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13910 with 23430 at 2
-Id : 23445, {_}: ?15407 =<= meet (join ?15407 ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 23444 with 23430 at 1,1,3
-Id : 23446, {_}: ?15407 =<= meet (join ?15407 ?15408) ?15407 [15408, 15407] by Demod 23445 with 23430 at 2,3
-Id : 23618, {_}: ?24079 =<= join (meet (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079) (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) (meet ?24079 (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) [24081, 24080, 24079] by Super 2848 with 23235 at 2,2,3
-Id : 23720, {_}: ?24079 =<= join (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079) (meet ?24079 (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) [24081, 24080, 24079] by Demod 23618 with 23430 at 1,3
-Id : 23476, {_}: ?9591 =<= join (meet ?9591 ?9591) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 7707 with 23430 at 2
-Id : 23477, {_}: ?9591 =<= join ?9591 (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 23476 with 23430 at 1,3
-Id : 23478, {_}: ?9591 =<= join ?9591 (meet ?9592 ?9591) [9592, 9591] by Demod 23477 with 23430 at 2,2,3
-Id : 23792, {_}: ?24251 =<= join (join (meet ?24251 ?24252) (meet ?24253 ?24251)) ?24251 [24253, 24252, 24251] by Demod 23720 with 23478 at 3
-Id : 23793, {_}: ?24256 =<= join (join (meet ?24256 ?24255) ?24256) ?24256 [24255, 24256] by Super 23792 with 23430 at 2,1,3
-Id : 23892, {_}: join (meet ?24386 ?24387) ?24386 =<= meet ?24386 (join (meet ?24386 ?24387) ?24386) [24387, 24386] by Super 23446 with 23793 at 1,3
-Id : 24037, {_}: ?24612 =<= meet (join (meet ?24612 ?24613) ?24612) ?24612 [24613, 24612] by Super 4586 with 23892 at 1,3
-Id : 23902, {_}: join (meet (join (meet ?24420 ?24421) ?24420) ?24420) (meet (join (meet ?24420 ?24421) ?24420) ?24420) =>= join (meet ?24420 ?24421) ?24420 [24421, 24420] by Super 1492 with 23793 at 2,2,2
-Id : 23961, {_}: meet (join (meet ?24420 ?24421) ?24420) ?24420 =>= join (meet ?24420 ?24421) ?24420 [24421, 24420] by Demod 23902 with 23235 at 2
-Id : 24344, {_}: ?24612 =<= join (meet ?24612 ?24613) ?24612 [24613, 24612] by Demod 24037 with 23961 at 3
-Id : 24361, {_}: join (meet (meet ?24861 ?24862) ?24861) (meet (meet ?24861 ?24862) ?24861) =>= meet ?24861 ?24862 [24862, 24861] by Super 1492 with 24344 at 2,2,2
-Id : 24421, {_}: meet (meet ?24861 ?24862) ?24861 =>= meet ?24861 ?24862 [24862, 24861] by Demod 24361 with 23235 at 2
-Id : 4078, {_}: meet ?5865 ?5866 =<= meet (meet ?5866 (join ?5867 (meet ?5865 ?5866))) (meet ?5865 ?5866) [5867, 5866, 5865] by Super 4066 with 3629 at 1,1,3
-Id : 24583, {_}: ?25104 =<= join ?25104 (meet ?25104 ?25105) [25105, 25104] by Super 23478 with 24421 at 2,3
-Id : 24726, {_}: meet ?25313 ?25314 =<= meet (meet ?25314 ?25313) (meet ?25313 ?25314) [25314, 25313] by Super 4078 with 24583 at 2,1,3
-Id : 24889, {_}: meet (meet ?25590 ?25591) (meet ?25591 ?25590) =?= meet (meet ?25591 ?25590) (meet ?25590 ?25591) [25591, 25590] by Super 24421 with 24726 at 1,2
-Id : 24922, {_}: meet ?25591 ?25590 =<= meet (meet ?25591 ?25590) (meet ?25590 ?25591) [25590, 25591] by Demod 24889 with 24726 at 2
-Id : 24923, {_}: meet ?25591 ?25590 =?= meet ?25590 ?25591 [25590, 25591] by Demod 24922 with 24726 at 3
-Id : 25184, {_}: meet a b === meet a b [] by Demod 2 with 24923 at 2
-Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-% SZS output end CNFRefutation for LAT093-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H7 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246076965.33
-Last chance: all is indexed 1246077716.
-Last chance: failed over 100 goal 1246077716.
-FAILURE in 0 iterations
-% SZS status Timeout for LAT138-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H2 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-Last chance: 1246078016.26
-Last chance: all is indexed 1246078786.2
-Last chance: failed over 100 goal 1246078786.2
-FAILURE in 0 iterations
-% SZS status Timeout for LAT140-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H34 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H28 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-Last chance: 1246079087.04
-Last chance: all is indexed 1246079747.64
-Last chance: failed over 100 goal 1246079747.65
-FAILURE in 0 iterations
-% SZS status Timeout for LAT146-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H34 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Last chance: 1246080050.64
-Last chance: all is indexed 1246080823.29
-Last chance: failed over 100 goal 1246080823.29
-FAILURE in 0 iterations
-% SZS status Timeout for LAT148-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H40 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246081123.41
-Last chance: all is indexed 1246081806.12
-Last chance: failed over 100 goal 1246081806.12
-FAILURE in 0 iterations
-% SZS status Timeout for LAT152-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246082106.73
-Last chance: all is indexed 1246082875.19
-Last chance: failed over 100 goal 1246082875.19
-FAILURE in 0 iterations
-% SZS status Timeout for LAT156-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H50 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Last chance: 1246083177.41
-Last chance: all is indexed 1246083936.64
-Last chance: failed over 100 goal 1246083936.64
-FAILURE in 0 iterations
-% SZS status Timeout for LAT159-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H76 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246084236.73
-Last chance: all is indexed 1246084965.23
-Last chance: failed over 100 goal 1246084965.24
-FAILURE in 0 iterations
-% SZS status Timeout for LAT164-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H77 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-Last chance: 1246085265.76
-Last chance: all is indexed 1246086029.27
-Last chance: failed over 100 goal 1246086029.27
-FAILURE in 0 iterations
-% SZS status Timeout for LAT165-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H77 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H78 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-Last chance: 1246086331.52
-Last chance: all is indexed 1246087040.97
-Last chance: failed over 100 goal 1246087040.97
-FAILURE in 0 iterations
-% SZS status Timeout for LAT166-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Last chance: 1246087341.15
-Last chance: all is indexed 1246088084.75
-Last chance: failed over 100 goal 1246088084.75
-FAILURE in 0 iterations
-% SZS status Timeout for LAT169-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Last chance: 1246088386.61
-Last chance: all is indexed 1246089088.1
-Last chance: failed over 100 goal 1246089088.1
-FAILURE in 0 iterations
-% SZS status Timeout for LAT170-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H40 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-Last chance: 1246089390.3
-Last chance: all is indexed 1246090126.61
-Last chance: failed over 100 goal 1246090126.62
-FAILURE in 0 iterations
-% SZS status Timeout for LAT173-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H79_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H32 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-Last chance: 1246090428.09
-Last chance: all is indexed 1246091152.16
-Last chance: failed over 100 goal 1246091152.16
-FAILURE in 0 iterations
-% SZS status Timeout for LAT175-1.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_cubed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Last chance: 1246091452.34
-Last chance: all is indexed 1246092379.97
-Last chance: failed over 100 goal 1246092379.97
-FAILURE in 0 iterations
-% SZS status Timeout for RNG009-7.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Last chance: 1246092681.04
-Last chance: all is indexed 1246093632.21
-Last chance: failed over 100 goal 1246093632.21
-FAILURE in 0 iterations
-% SZS status Timeout for RNG019-6.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- distributivity_of_difference1 is 71
- distributivity_of_difference2 is 70
- distributivity_of_difference3 is 69
- distributivity_of_difference4 is 68
- inverse_product1 is 73
- inverse_product2 is 72
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- product_of_inverses is 74
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Last chance: 1246093932.41
-Last chance: all is indexed 1246095402.48
-Last chance: failed over 100 goal 1246095402.49
-FAILURE in 0 iterations
-% SZS status Timeout for RNG019-7.p
-Order
- == is 100
- _ is 99
- add is 95
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form2 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 97
- v is 96
- x is 98
- y is 94
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-Last chance: 1246095704.23
-Last chance: all is indexed 1246096665.27
-Last chance: failed over 100 goal 1246096665.27
-FAILURE in 0 iterations
-% SZS status Timeout for RNG020-6.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 92
- additive_identity is 90
- additive_inverse is 91
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- b is 97
- c is 95
- commutativity_for_addition is 79
- commutator is 75
- d is 94
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 88
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 86
- multiply is 96
- prove_teichmuller_identity is 89
- right_additive_identity is 87
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 85
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-Last chance: 1246096966.68
-Last chance: all is indexed 1246097932.32
-Last chance: failed over 100 goal 1246097932.59
-FAILURE in 0 iterations
-% SZS status Timeout for RNG026-6.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- cx is 97
- cy is 96
- cz is 98
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 95
- product_of_inverses is 75
- prove_right_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-Last chance: 1246098233.93
-Last chance: all is indexed 1246099724.05
-Last chance: failed over 100 goal 1246099724.05
-FAILURE in 0 iterations
-% SZS status Timeout for RNG027-7.p
-Order
- == is 100
- _ is 99
- add is 91
- additive_identity is 92
- additive_inverse is 86
- additive_inverse_additive_inverse is 83
- associativity_for_addition is 79
- associator is 94
- commutativity_for_addition is 80
- commutator is 76
- distribute1 is 82
- distribute2 is 81
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 90
- left_additive_inverse is 85
- left_alternative is 77
- left_multiplicative_zero is 88
- multiply is 96
- product_of_inverses is 75
- prove_left_moufang is 93
- right_additive_identity is 89
- right_additive_inverse is 84
- right_alternative is 78
- right_multiplicative_zero is 87
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-Last chance: 1246100026.03
-Last chance: all is indexed 1246101492.29
-Last chance: failed over 100 goal 1246101492.29
-FAILURE in 0 iterations
-% SZS status Timeout for RNG028-9.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 96
- product_of_inverses is 75
- prove_middle_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-Last chance: 1246101794.55
-Last chance: all is indexed 1246103287.97
-Last chance: failed over 100 goal 1246103287.97
-FAILURE in 0 iterations
-% SZS status Timeout for RNG029-7.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_fourthed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Last chance: 1246103588.12
-Last chance: all is indexed 1246104654.48
-Last chance: failed over 100 goal 1246104654.5
-FAILURE in 0 iterations
-% SZS status Timeout for RNG035-7.p
-Order
- == is 100
- _ is 99
- a is 98
- absorbtion is 88
- add is 95
- associativity_of_add is 92
- b is 97
- c is 90
- commutativity_of_add is 93
- d is 89
- negate is 96
- prove_huntingtons_axiom is 94
- robbins_axiom is 91
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
- Id : 8, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-Last chance: 1246104961.92
-Last chance: all is indexed 1246105219.5
-Last chance: failed over 100 goal 1246105219.5
-FAILURE in 0 iterations
-% SZS status Timeout for ROB006-1.p
-Order
- == is 100
- _ is 99
- absorbtion is 90
- add is 98
- associativity_of_add is 95
- c is 92
- commutativity_of_add is 96
- d is 91
- negate is 94
- prove_idempotence is 97
- robbins_axiom is 93
-Facts
- Id : 4, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
- Id : 6, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
- Id : 8, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-Last chance: 1246105523.
-Last chance: all is indexed 1246105812.88
-Last chance: failed over 100 goal 1246105960.3
-FAILURE in 0 iterations
-% SZS status Timeout for ROB006-2.p
+++ /dev/null
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 77
- additive_id2 is 76
- additive_identity is 82
- additive_inverse1 is 84
- additive_inverse2 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- distributivity3 is 88
- distributivity4 is 87
- inverse is 86
- multiplicative_id1 is 79
- multiplicative_id2 is 78
- multiplicative_identity is 85
- multiplicative_inverse1 is 81
- multiplicative_inverse2 is 80
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
- Id : 14, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
- Id : 16, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
- Id : 18, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
- Id : 20, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
- Id : 22, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
- Id : 24, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
- Id : 26, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
- Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
- Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 49.803119s
-% SZS status Unsatisfiable for BOO007-2.p
-% SZS output start CNFRefutation for BOO007-2.p
-Id : 22, {_}: multiply (inverse ?30) ?30 =>= additive_identity [30] by multiplicative_inverse2 ?30
-Id : 24, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
-Id : 69, {_}: multiply (add ?160 ?161) ?162 =<= add (multiply ?160 ?162) (multiply ?161 ?162) [162, 161, 160] by distributivity3 ?160 ?161 ?162
-Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-Id : 16, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
-Id : 10, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 26, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
-Id : 18, {_}: add (inverse ?26) ?26 =>= multiplicative_identity [26] by additive_inverse2 ?26
-Id : 8, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 20, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
-Id : 14, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
-Id : 12, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
-Id : 6, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 151, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= add (multiply ?356 ?357) additive_identity [357, 356] by Super 14 with 20 at 2,3
-Id : 157, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= add additive_identity (multiply ?356 ?357) [357, 356] by Demod 151 with 4 at 3
-Id : 3270, {_}: multiply ?3107 (add ?3108 (inverse ?3107)) =>= multiply ?3107 ?3108 [3108, 3107] by Demod 157 with 30 at 3
-Id : 136, {_}: add (multiply (inverse ?335) ?336) ?335 =>= multiply multiplicative_identity (add ?336 ?335) [336, 335] by Super 8 with 18 at 1,3
-Id : 2697, {_}: add (multiply (inverse ?335) ?336) ?335 =>= add ?336 ?335 [336, 335] by Demod 136 with 26 at 3
-Id : 3279, {_}: multiply ?3129 (add ?3128 (inverse ?3129)) =<= multiply ?3129 (multiply (inverse (inverse ?3129)) ?3128) [3128, 3129] by Super 3270 with 2697 at 2,2
-Id : 3256, {_}: multiply ?356 (add ?357 (inverse ?356)) =>= multiply ?356 ?357 [357, 356] by Demod 157 with 30 at 3
-Id : 3316, {_}: multiply ?3129 ?3128 =<= multiply ?3129 (multiply (inverse (inverse ?3129)) ?3128) [3128, 3129] by Demod 3279 with 3256 at 2
-Id : 135, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= multiply (add ?333 ?332) multiplicative_identity [332, 333] by Super 8 with 18 at 2,3
-Id : 141, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= multiply multiplicative_identity (add ?333 ?332) [332, 333] by Demod 135 with 6 at 3
-Id : 2790, {_}: add (multiply ?333 (inverse ?332)) ?332 =>= add ?333 ?332 [332, 333] by Demod 141 with 26 at 3
-Id : 152, {_}: multiply ?359 (add (inverse ?359) ?360) =>= add additive_identity (multiply ?359 ?360) [360, 359] by Super 14 with 20 at 1,3
-Id : 2899, {_}: multiply ?2812 (add (inverse ?2812) ?2813) =>= multiply ?2812 ?2813 [2813, 2812] by Demod 152 with 30 at 3
-Id : 122, {_}: add ?311 (multiply (inverse ?311) ?312) =>= multiply multiplicative_identity (add ?311 ?312) [312, 311] by Super 10 with 16 at 1,3
-Id : 1484, {_}: add ?1608 (multiply (inverse ?1608) ?1609) =>= add ?1608 ?1609 [1609, 1608] by Demod 122 with 26 at 3
-Id : 1488, {_}: add ?1618 additive_identity =<= add ?1618 (inverse (inverse ?1618)) [1618] by Super 1484 with 20 at 2,2
-Id : 1524, {_}: ?1618 =<= add ?1618 (inverse (inverse ?1618)) [1618] by Demod 1488 with 28 at 2
-Id : 2914, {_}: multiply ?2849 (inverse ?2849) =<= multiply ?2849 (inverse (inverse (inverse ?2849))) [2849] by Super 2899 with 1524 at 2,2
-Id : 2987, {_}: additive_identity =<= multiply ?2849 (inverse (inverse (inverse ?2849))) [2849] by Demod 2914 with 20 at 2
-Id : 3172, {_}: add additive_identity (inverse (inverse ?3022)) =?= add ?3022 (inverse (inverse ?3022)) [3022] by Super 2790 with 2987 at 1,2
-Id : 3182, {_}: inverse (inverse ?3022) =<= add ?3022 (inverse (inverse ?3022)) [3022] by Demod 3172 with 30 at 2
-Id : 3183, {_}: inverse (inverse ?3022) =>= ?3022 [3022] by Demod 3182 with 1524 at 3
-Id : 3317, {_}: multiply ?3129 ?3128 =<= multiply ?3129 (multiply ?3129 ?3128) [3128, 3129] by Demod 3316 with 3183 at 1,2,3
-Id : 3479, {_}: multiply (multiply ?3373 ?3374) ?3373 =>= multiply ?3373 ?3374 [3374, 3373] by Super 6 with 3317 at 3
-Id : 3807, {_}: multiply (add ?3814 (multiply ?3812 ?3813)) ?3812 =>= add (multiply ?3814 ?3812) (multiply ?3812 ?3813) [3813, 3812, 3814] by Super 12 with 3479 at 2,3
-Id : 70, {_}: multiply (add ?164 ?165) ?166 =<= add (multiply ?164 ?166) (multiply ?166 ?165) [166, 165, 164] by Super 69 with 6 at 2,3
-Id : 27040, {_}: multiply (add ?32987 (multiply ?32988 ?32989)) ?32988 =>= multiply (add ?32987 ?32989) ?32988 [32989, 32988, 32987] by Demod 3807 with 70 at 3
-Id : 27129, {_}: multiply (multiply (add ?33340 ?33341) ?33342) ?33341 =?= multiply (add (multiply ?33340 ?33342) ?33342) ?33341 [33342, 33341, 33340] by Super 27040 with 12 at 1,2
-Id : 1722, {_}: add (multiply ?1843 ?1842) (inverse (inverse ?1842)) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1842, 1843] by Super 8 with 1524 at 2,3
-Id : 1739, {_}: add (inverse (inverse ?1842)) (multiply ?1843 ?1842) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1843, 1842] by Demod 1722 with 4 at 2
-Id : 6934, {_}: add ?1842 (multiply ?1843 ?1842) =<= multiply (add ?1843 (inverse (inverse ?1842))) ?1842 [1843, 1842] by Demod 1739 with 3183 at 1,2
-Id : 6935, {_}: add ?1842 (multiply ?1843 ?1842) =<= multiply (add ?1843 ?1842) ?1842 [1843, 1842] by Demod 6934 with 3183 at 2,1,3
-Id : 235, {_}: add (multiply ?485 additive_identity) ?484 =<= multiply (add ?485 ?484) ?484 [484, 485] by Super 8 with 30 at 2,3
-Id : 498, {_}: multiply ?740 (add ?739 ?740) =>= add (multiply ?739 additive_identity) ?740 [739, 740] by Super 6 with 235 at 3
-Id : 236, {_}: add (multiply additive_identity ?488) ?487 =<= multiply ?487 (add ?488 ?487) [487, 488] by Super 8 with 30 at 1,3
-Id : 968, {_}: add (multiply additive_identity ?739) ?740 =?= add (multiply ?739 additive_identity) ?740 [740, 739] by Demod 498 with 236 at 2
-Id : 450, {_}: add ?682 (multiply additive_identity ?683) =<= multiply ?682 (add ?682 ?683) [683, 682] by Super 10 with 28 at 1,3
-Id : 453, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= multiply (inverse ?690) multiplicative_identity [690] by Super 450 with 18 at 2,3
-Id : 478, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= multiply multiplicative_identity (inverse ?690) [690] by Demod 453 with 6 at 3
-Id : 479, {_}: add (inverse ?690) (multiply additive_identity ?690) =>= inverse ?690 [690] by Demod 478 with 26 at 3
-Id : 2879, {_}: multiply ?359 (add (inverse ?359) ?360) =>= multiply ?359 ?360 [360, 359] by Demod 152 with 30 at 3
-Id : 2886, {_}: add (inverse (add (inverse additive_identity) ?2774)) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Super 479 with 2879 at 2,2
-Id : 221, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 18 with 28 at 2
-Id : 2945, {_}: add (inverse (add multiplicative_identity ?2774)) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2886 with 221 at 1,1,1,2
-Id : 1490, {_}: add ?1622 (inverse ?1622) =>= add ?1622 multiplicative_identity [1622] by Super 1484 with 24 at 2,2
-Id : 1526, {_}: multiplicative_identity =<= add ?1622 multiplicative_identity [1622] by Demod 1490 with 16 at 2
-Id : 1546, {_}: add multiplicative_identity ?1675 =>= multiplicative_identity [1675] by Super 4 with 1526 at 3
-Id : 2946, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2945 with 1546 at 1,1,2
-Id : 183, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 22 with 24 at 2
-Id : 2947, {_}: add additive_identity (multiply additive_identity ?2774) =>= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2946 with 183 at 1,2
-Id : 2948, {_}: multiply additive_identity ?2774 =<= inverse (add (inverse additive_identity) ?2774) [2774] by Demod 2947 with 30 at 2
-Id : 2949, {_}: multiply additive_identity ?2774 =<= inverse (add multiplicative_identity ?2774) [2774] by Demod 2948 with 221 at 1,1,3
-Id : 2950, {_}: multiply additive_identity ?2774 =>= inverse multiplicative_identity [2774] by Demod 2949 with 1546 at 1,3
-Id : 2951, {_}: multiply additive_identity ?2774 =>= additive_identity [2774] by Demod 2950 with 183 at 3
-Id : 3009, {_}: add additive_identity ?740 =<= add (multiply ?739 additive_identity) ?740 [739, 740] by Demod 968 with 2951 at 1,2
-Id : 3029, {_}: ?740 =<= add (multiply ?739 additive_identity) ?740 [739, 740] by Demod 3009 with 30 at 2
-Id : 3031, {_}: ?484 =<= multiply (add ?485 ?484) ?484 [485, 484] by Demod 235 with 3029 at 2
-Id : 6936, {_}: add ?1842 (multiply ?1843 ?1842) =>= ?1842 [1843, 1842] by Demod 6935 with 3031 at 3
-Id : 6956, {_}: add (multiply ?7059 ?7058) ?7058 =>= ?7058 [7058, 7059] by Super 4 with 6936 at 3
-Id : 52241, {_}: multiply (multiply (add ?83798 ?83799) ?83800) ?83799 =>= multiply ?83800 ?83799 [83800, 83799, 83798] by Demod 27129 with 6956 at 1,3
-Id : 52270, {_}: multiply (multiply ?83922 ?83923) (multiply ?83921 ?83922) =>= multiply ?83923 (multiply ?83921 ?83922) [83921, 83923, 83922] by Super 52241 with 6936 at 1,1,2
-Id : 3280, {_}: multiply ?3132 (add ?3131 (inverse ?3132)) =<= multiply ?3132 (multiply ?3131 (inverse (inverse ?3132))) [3131, 3132] by Super 3270 with 2790 at 2,2
-Id : 3318, {_}: multiply ?3132 ?3131 =<= multiply ?3132 (multiply ?3131 (inverse (inverse ?3132))) [3131, 3132] by Demod 3280 with 3256 at 2
-Id : 3319, {_}: multiply ?3132 ?3131 =<= multiply ?3132 (multiply ?3131 ?3132) [3131, 3132] by Demod 3318 with 3183 at 2,2,3
-Id : 3542, {_}: multiply ?3472 (add ?3474 (multiply ?3473 ?3472)) =>= add (multiply ?3472 ?3474) (multiply ?3472 ?3473) [3473, 3474, 3472] by Super 14 with 3319 at 2,3
-Id : 23927, {_}: multiply ?27205 (add ?27206 (multiply ?27207 ?27205)) =>= multiply ?27205 (add ?27206 ?27207) [27207, 27206, 27205] by Demod 3542 with 14 at 3
-Id : 24009, {_}: multiply ?27527 (multiply ?27528 (add ?27526 ?27527)) =?= multiply ?27527 (add (multiply ?27528 ?27526) ?27528) [27526, 27528, 27527] by Super 23927 with 14 at 2,2
-Id : 7091, {_}: add (multiply ?7292 ?7293) ?7293 =>= ?7293 [7293, 7292] by Super 4 with 6936 at 3
-Id : 7092, {_}: add (multiply ?7296 ?7295) ?7296 =>= ?7296 [7295, 7296] by Super 7091 with 6 at 1,2
-Id : 49144, {_}: multiply ?77879 (multiply ?77880 (add ?77881 ?77879)) =>= multiply ?77879 ?77880 [77881, 77880, 77879] by Demod 24009 with 7092 at 2,3
-Id : 6968, {_}: add ?7096 (multiply ?7097 ?7096) =>= ?7096 [7097, 7096] by Demod 6935 with 3031 at 3
-Id : 6969, {_}: add ?7099 (multiply ?7099 ?7100) =>= ?7099 [7100, 7099] by Super 6968 with 6 at 2,2
-Id : 49175, {_}: multiply (multiply ?78012 ?78010) (multiply ?78011 ?78012) =>= multiply (multiply ?78012 ?78010) ?78011 [78011, 78010, 78012] by Super 49144 with 6969 at 2,2,2
-Id : 77462, {_}: multiply (multiply ?134082 ?134083) ?134084 =?= multiply ?134083 (multiply ?134084 ?134082) [134084, 134083, 134082] by Demod 52270 with 49175 at 2
-Id : 77468, {_}: multiply (multiply (add (inverse ?134104) ?134102) ?134103) ?134104 =>= multiply ?134103 (multiply ?134104 ?134102) [134103, 134102, 134104] by Super 77462 with 2879 at 2,3
-Id : 3544, {_}: multiply (multiply ?3481 ?3480) ?3480 =>= multiply ?3480 ?3481 [3480, 3481] by Super 6 with 3319 at 3
-Id : 3902, {_}: multiply (add ?3943 (multiply ?3941 ?3942)) ?3942 =>= add (multiply ?3943 ?3942) (multiply ?3942 ?3941) [3942, 3941, 3943] by Super 12 with 3544 at 2,3
-Id : 27853, {_}: multiply (add ?34448 (multiply ?34449 ?34450)) ?34450 =>= multiply (add ?34448 ?34449) ?34450 [34450, 34449, 34448] by Demod 3902 with 70 at 3
-Id : 27945, {_}: multiply (multiply ?34816 (add ?34815 ?34817)) ?34817 =?= multiply (add (multiply ?34816 ?34815) ?34816) ?34817 [34817, 34815, 34816] by Super 27853 with 14 at 1,2
-Id : 53412, {_}: multiply (multiply ?86132 (add ?86133 ?86134)) ?86134 =>= multiply ?86132 ?86134 [86134, 86133, 86132] by Demod 27945 with 7092 at 1,3
-Id : 53441, {_}: multiply (multiply ?86256 ?86257) (multiply ?86255 ?86257) =>= multiply ?86256 (multiply ?86255 ?86257) [86255, 86257, 86256] by Super 53412 with 6936 at 2,1,2
-Id : 49173, {_}: multiply (multiply ?78002 ?78004) (multiply ?78003 ?78004) =>= multiply (multiply ?78002 ?78004) ?78003 [78003, 78004, 78002] by Super 49144 with 6936 at 2,2,2
-Id : 79216, {_}: multiply (multiply ?86256 ?86257) ?86255 =?= multiply ?86256 (multiply ?86255 ?86257) [86255, 86257, 86256] by Demod 53441 with 49173 at 2
-Id : 290220, {_}: multiply (add (inverse ?134104) ?134102) (multiply ?134104 ?134103) =>= multiply ?134103 (multiply ?134104 ?134102) [134103, 134102, 134104] by Demod 77468 with 79216 at 2
-Id : 148, {_}: multiply (add ?349 ?350) (inverse ?349) =>= add additive_identity (multiply ?350 (inverse ?349)) [350, 349] by Super 12 with 20 at 1,3
-Id : 160, {_}: multiply (inverse ?349) (add ?349 ?350) =>= add additive_identity (multiply ?350 (inverse ?349)) [350, 349] by Demod 148 with 6 at 2
-Id : 4141, {_}: multiply (inverse ?4194) (add ?4194 ?4195) =>= multiply ?4195 (inverse ?4194) [4195, 4194] by Demod 160 with 30 at 3
-Id : 3259, {_}: add (multiply (inverse ?3073) ?3072) ?3073 =<= add (add ?3072 (inverse (inverse ?3073))) ?3073 [3072, 3073] by Super 2697 with 3256 at 1,2
-Id : 3300, {_}: add ?3072 ?3073 =<= add (add ?3072 (inverse (inverse ?3073))) ?3073 [3073, 3072] by Demod 3259 with 2697 at 2
-Id : 3301, {_}: add ?3072 ?3073 =<= add (add ?3072 ?3073) ?3073 [3073, 3072] by Demod 3300 with 3183 at 2,1,3
-Id : 4158, {_}: multiply (inverse (add ?4240 ?4241)) (add ?4240 ?4241) =>= multiply ?4241 (inverse (add ?4240 ?4241)) [4241, 4240] by Super 4141 with 3301 at 2,2
-Id : 4229, {_}: additive_identity =<= multiply ?4241 (inverse (add ?4240 ?4241)) [4240, 4241] by Demod 4158 with 22 at 2
-Id : 5045, {_}: multiply (inverse (add ?4937 ?4936)) ?4936 =>= additive_identity [4936, 4937] by Super 6 with 4229 at 3
-Id : 7219, {_}: multiply (inverse ?7487) (multiply ?7487 ?7488) =>= additive_identity [7488, 7487] by Super 5045 with 6969 at 1,1,2
-Id : 7871, {_}: multiply (add (inverse ?8300) ?8302) (multiply ?8300 ?8301) =>= add additive_identity (multiply ?8302 (multiply ?8300 ?8301)) [8301, 8302, 8300] by Super 12 with 7219 at 1,3
-Id : 7967, {_}: multiply (add (inverse ?8300) ?8302) (multiply ?8300 ?8301) =>= multiply ?8302 (multiply ?8300 ?8301) [8301, 8302, 8300] by Demod 7871 with 30 at 3
-Id : 290221, {_}: multiply ?134102 (multiply ?134104 ?134103) =?= multiply ?134103 (multiply ?134104 ?134102) [134103, 134104, 134102] by Demod 290220 with 7967 at 2
-Id : 166, {_}: multiply (add (inverse ?383) ?384) ?383 =>= add additive_identity (multiply ?384 ?383) [384, 383] by Super 12 with 22 at 1,3
-Id : 4249, {_}: multiply (add (inverse ?383) ?384) ?383 =>= multiply ?384 ?383 [384, 383] by Demod 166 with 30 at 3
-Id : 77480, {_}: multiply (multiply ?134153 ?134154) (add (inverse ?134153) ?134152) =>= multiply ?134154 (multiply ?134152 ?134153) [134152, 134154, 134153] by Super 77462 with 4249 at 2,3
-Id : 77935, {_}: multiply (add (inverse ?134153) ?134152) (multiply ?134153 ?134154) =>= multiply ?134154 (multiply ?134152 ?134153) [134154, 134152, 134153] by Demod 77480 with 6 at 2
-Id : 295050, {_}: multiply ?134152 (multiply ?134153 ?134154) =?= multiply ?134154 (multiply ?134152 ?134153) [134154, 134153, 134152] by Demod 77935 with 7967 at 2
-Id : 3012, {_}: add additive_identity ?487 =<= multiply ?487 (add ?488 ?487) [488, 487] by Demod 236 with 2951 at 1,2
-Id : 3025, {_}: ?487 =<= multiply ?487 (add ?488 ?487) [488, 487] by Demod 3012 with 30 at 2
-Id : 6954, {_}: add ?7050 (multiply ?7052 (multiply ?7051 ?7050)) =>= multiply (add ?7050 ?7052) ?7050 [7051, 7052, 7050] by Super 10 with 6936 at 2,3
-Id : 219, {_}: add ?458 (multiply ?459 additive_identity) =<= multiply (add ?458 ?459) ?458 [459, 458] by Super 10 with 28 at 2,3
-Id : 310, {_}: multiply ?527 (add ?527 ?528) =>= add ?527 (multiply ?528 additive_identity) [528, 527] by Super 6 with 219 at 3
-Id : 220, {_}: add ?461 (multiply additive_identity ?462) =<= multiply ?461 (add ?461 ?462) [462, 461] by Super 10 with 28 at 1,3
-Id : 632, {_}: add ?527 (multiply additive_identity ?528) =?= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 310 with 220 at 2
-Id : 3013, {_}: add ?527 additive_identity =<= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 632 with 2951 at 2,2
-Id : 3021, {_}: ?527 =<= add ?527 (multiply ?528 additive_identity) [528, 527] by Demod 3013 with 28 at 2
-Id : 3024, {_}: ?458 =<= multiply (add ?458 ?459) ?458 [459, 458] by Demod 219 with 3021 at 2
-Id : 7015, {_}: add ?7050 (multiply ?7052 (multiply ?7051 ?7050)) =>= ?7050 [7051, 7052, 7050] by Demod 6954 with 3024 at 3
-Id : 54601, {_}: multiply ?88480 (multiply ?88481 ?88482) =<= multiply (multiply ?88480 (multiply ?88481 ?88482)) ?88482 [88482, 88481, 88480] by Super 3025 with 7015 at 2,3
-Id : 54602, {_}: multiply ?88484 (multiply ?88485 ?88486) =<= multiply (multiply ?88484 (multiply ?88486 ?88485)) ?88486 [88486, 88485, 88484] by Super 54601 with 6 at 2,1,3
-Id : 7204, {_}: add ?7439 (multiply ?7441 (multiply ?7439 ?7440)) =>= multiply (add ?7439 ?7441) ?7439 [7440, 7441, 7439] by Super 10 with 6969 at 2,3
-Id : 7269, {_}: add ?7439 (multiply ?7441 (multiply ?7439 ?7440)) =>= ?7439 [7440, 7441, 7439] by Demod 7204 with 3024 at 3
-Id : 30112, {_}: multiply ?38749 (multiply ?38748 ?38750) =<= multiply (multiply ?38749 (multiply ?38748 ?38750)) ?38748 [38750, 38748, 38749] by Super 3025 with 7269 at 2,3
-Id : 81336, {_}: multiply ?88484 (multiply ?88485 ?88486) =?= multiply ?88484 (multiply ?88486 ?88485) [88486, 88485, 88484] by Demod 54602 with 30112 at 3
-Id : 297313, {_}: multiply c (multiply b a) === multiply c (multiply b a) [] by Demod 297312 with 81336 at 2
-Id : 297312, {_}: multiply c (multiply a b) =>= multiply c (multiply b a) [] by Demod 292477 with 295050 at 2
-Id : 292477, {_}: multiply b (multiply c a) =>= multiply c (multiply b a) [] by Demod 255 with 290221 at 2
-Id : 255, {_}: multiply a (multiply c b) =>= multiply c (multiply b a) [] by Demod 254 with 6 at 2,3
-Id : 254, {_}: multiply a (multiply c b) =>= multiply c (multiply a b) [] by Demod 253 with 6 at 3
-Id : 253, {_}: multiply a (multiply c b) =<= multiply (multiply a b) c [] by Demod 2 with 6 at 2,2
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-2.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 87
- additive_identity is 88
- additive_inverse1 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- inverse is 84
- multiplicative_id1 is 85
- multiplicative_identity is 86
- multiplicative_inverse1 is 82
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
- Id : 14, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
- Id : 16, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
- Id : 18, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 75.486209s
-% SZS status Unsatisfiable for BOO007-4.p
-% SZS output start CNFRefutation for BOO007-4.p
-Id : 14, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
-Id : 16, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
-Id : 8, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 18, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
-Id : 10, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 6, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 81, {_}: multiply ?187 (add (inverse ?187) ?188) =>= add additive_identity (multiply ?187 ?188) [188, 187] by Super 10 with 18 at 1,3
-Id : 57, {_}: add additive_identity ?136 =>= ?136 [136] by Super 4 with 12 at 3
-Id : 2041, {_}: multiply ?187 (add (inverse ?187) ?188) =>= multiply ?187 ?188 [188, 187] by Demod 81 with 57 at 3
-Id : 2049, {_}: multiply (add (inverse ?1798) ?1799) ?1798 =>= multiply ?1798 ?1799 [1799, 1798] by Super 6 with 2041 at 3
-Id : 72, {_}: add ?169 (multiply (inverse ?169) ?170) =>= multiply multiplicative_identity (add ?169 ?170) [170, 169] by Super 8 with 16 at 1,3
-Id : 65, {_}: multiply multiplicative_identity ?154 =>= ?154 [154] by Super 6 with 14 at 3
-Id : 1065, {_}: add ?169 (multiply (inverse ?169) ?170) =>= add ?169 ?170 [170, 169] by Demod 72 with 65 at 3
-Id : 80, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= add (multiply ?184 ?185) additive_identity [185, 184] by Super 10 with 18 at 2,3
-Id : 88, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= add additive_identity (multiply ?184 ?185) [185, 184] by Demod 80 with 4 at 3
-Id : 2371, {_}: multiply ?184 (add ?185 (inverse ?184)) =>= multiply ?184 ?185 [185, 184] by Demod 88 with 57 at 3
-Id : 2380, {_}: add ?2048 (multiply (inverse ?2048) ?2047) =<= add ?2048 (add ?2047 (inverse (inverse ?2048))) [2047, 2048] by Super 1065 with 2371 at 2,2
-Id : 2402, {_}: add ?2048 ?2047 =<= add ?2048 (add ?2047 (inverse (inverse ?2048))) [2047, 2048] by Demod 2380 with 1065 at 2
-Id : 71, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= multiply (add ?166 ?167) multiplicative_identity [167, 166] by Super 8 with 16 at 2,3
-Id : 79, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= multiply multiplicative_identity (add ?166 ?167) [167, 166] by Demod 71 with 6 at 3
-Id : 1969, {_}: add ?166 (multiply ?167 (inverse ?166)) =>= add ?166 ?167 [167, 166] by Demod 79 with 65 at 3
-Id : 2056, {_}: multiply ?1815 (add (inverse ?1815) ?1816) =>= multiply ?1815 ?1816 [1816, 1815] by Demod 81 with 57 at 3
-Id : 1077, {_}: add ?1042 (multiply (inverse ?1042) ?1043) =>= add ?1042 ?1043 [1043, 1042] by Demod 72 with 65 at 3
-Id : 1082, {_}: add ?1054 additive_identity =<= add ?1054 (inverse (inverse ?1054)) [1054] by Super 1077 with 18 at 2,2
-Id : 1115, {_}: ?1054 =<= add ?1054 (inverse (inverse ?1054)) [1054] by Demod 1082 with 12 at 2
-Id : 2072, {_}: multiply ?1854 (inverse ?1854) =<= multiply ?1854 (inverse (inverse (inverse ?1854))) [1854] by Super 2056 with 1115 at 2,2
-Id : 2140, {_}: additive_identity =<= multiply ?1854 (inverse (inverse (inverse ?1854))) [1854] by Demod 2072 with 18 at 2
-Id : 2304, {_}: add (inverse (inverse ?1984)) additive_identity =?= add (inverse (inverse ?1984)) ?1984 [1984] by Super 1969 with 2140 at 2,2
-Id : 2314, {_}: add additive_identity (inverse (inverse ?1984)) =<= add (inverse (inverse ?1984)) ?1984 [1984] by Demod 2304 with 4 at 2
-Id : 2315, {_}: inverse (inverse ?1984) =<= add (inverse (inverse ?1984)) ?1984 [1984] by Demod 2314 with 57 at 2
-Id : 1260, {_}: add (inverse (inverse ?1219)) ?1219 =>= ?1219 [1219] by Super 4 with 1115 at 3
-Id : 2316, {_}: inverse (inverse ?1984) =>= ?1984 [1984] by Demod 2315 with 1260 at 3
-Id : 2403, {_}: add ?2048 ?2047 =<= add ?2048 (add ?2047 ?2048) [2047, 2048] by Demod 2402 with 2316 at 2,2,3
-Id : 2435, {_}: add ?2108 (multiply ?2110 (add ?2109 ?2108)) =<= multiply (add ?2108 ?2110) (add ?2108 ?2109) [2109, 2110, 2108] by Super 8 with 2403 at 2,3
-Id : 2463, {_}: add ?2108 (multiply ?2110 (add ?2109 ?2108)) =>= add ?2108 (multiply ?2110 ?2109) [2109, 2110, 2108] by Demod 2435 with 8 at 3
-Id : 18875, {_}: multiply (add (inverse ?19839) (multiply ?19837 ?19838)) ?19839 =?= multiply ?19839 (multiply ?19837 (add ?19838 (inverse ?19839))) [19838, 19837, 19839] by Super 2049 with 2463 at 1,2
-Id : 151787, {_}: multiply ?278411 (multiply ?278412 ?278413) =<= multiply ?278411 (multiply ?278412 (add ?278413 (inverse ?278411))) [278413, 278412, 278411] by Demod 18875 with 2049 at 2
-Id : 1071, {_}: add (multiply (inverse ?1025) ?1026) ?1025 =>= add ?1025 ?1026 [1026, 1025] by Super 4 with 1065 at 3
-Id : 151803, {_}: multiply ?278483 (multiply ?278484 (multiply (inverse (inverse ?278483)) ?278482)) =>= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278484, 278483] by Super 151787 with 1071 at 2,2,3
-Id : 152295, {_}: multiply ?278483 (multiply ?278484 (multiply ?278483 ?278482)) =<= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278484, 278483] by Demod 151803 with 2316 at 1,2,2,2
-Id : 228, {_}: add ?322 (multiply ?323 additive_identity) =<= multiply (add ?322 ?323) ?322 [323, 322] by Super 8 with 12 at 2,3
-Id : 229, {_}: add ?325 (multiply ?326 additive_identity) =<= multiply (add ?326 ?325) ?325 [326, 325] by Super 228 with 4 at 1,3
-Id : 331, {_}: add ?429 (multiply additive_identity ?430) =<= multiply ?429 (add ?429 ?430) [430, 429] by Super 8 with 12 at 1,3
-Id : 332, {_}: add ?432 (multiply additive_identity ?433) =<= multiply ?432 (add ?433 ?432) [433, 432] by Super 331 with 4 at 2,3
-Id : 73, {_}: add (inverse ?172) ?172 =>= multiplicative_identity [172] by Super 4 with 16 at 3
-Id : 336, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= multiply (inverse ?441) multiplicative_identity [441] by Super 331 with 73 at 2,3
-Id : 355, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= multiply multiplicative_identity (inverse ?441) [441] by Demod 336 with 6 at 3
-Id : 356, {_}: add (inverse ?441) (multiply additive_identity ?441) =>= inverse ?441 [441] by Demod 355 with 65 at 3
-Id : 713, {_}: add (multiply additive_identity ?819) (multiply additive_identity (inverse ?819)) =>= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Super 332 with 356 at 2,3
-Id : 726, {_}: multiply additive_identity (add ?819 (inverse ?819)) =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 713 with 10 at 2
-Id : 727, {_}: multiply additive_identity multiplicative_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 726 with 16 at 2,2
-Id : 728, {_}: multiply multiplicative_identity additive_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 727 with 6 at 2
-Id : 729, {_}: additive_identity =<= multiply (multiply additive_identity ?819) (inverse ?819) [819] by Demod 728 with 65 at 2
-Id : 730, {_}: additive_identity =<= multiply (inverse ?819) (multiply additive_identity ?819) [819] by Demod 729 with 6 at 3
-Id : 1088, {_}: add ?1069 additive_identity =<= add ?1069 (multiply additive_identity ?1069) [1069] by Super 1077 with 730 at 2,2
-Id : 1118, {_}: ?1069 =<= add ?1069 (multiply additive_identity ?1069) [1069] by Demod 1088 with 12 at 2
-Id : 1283, {_}: add (multiply additive_identity ?1241) (multiply additive_identity ?1241) =>= multiply (multiply additive_identity ?1241) ?1241 [1241] by Super 332 with 1118 at 2,3
-Id : 1319, {_}: multiply additive_identity (add ?1241 ?1241) =<= multiply (multiply additive_identity ?1241) ?1241 [1241] by Demod 1283 with 10 at 2
-Id : 82, {_}: multiply (inverse ?190) ?190 =>= additive_identity [190] by Super 6 with 18 at 3
-Id : 1083, {_}: add ?1056 additive_identity =?= add ?1056 ?1056 [1056] by Super 1077 with 82 at 2,2
-Id : 1116, {_}: ?1056 =<= add ?1056 ?1056 [1056] by Demod 1083 with 12 at 2
-Id : 1320, {_}: multiply additive_identity ?1241 =<= multiply (multiply additive_identity ?1241) ?1241 [1241] by Demod 1319 with 1116 at 2,2
-Id : 1567, {_}: multiply ?1480 (multiply additive_identity ?1480) =>= multiply additive_identity ?1480 [1480] by Super 6 with 1320 at 3
-Id : 2051, {_}: add (inverse (add (inverse additive_identity) ?1804)) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Super 356 with 2041 at 2,2
-Id : 92, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 16 with 57 at 2
-Id : 2095, {_}: add (inverse (add multiplicative_identity ?1804)) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2051 with 92 at 1,1,1,2
-Id : 1081, {_}: add ?1052 (inverse ?1052) =>= add ?1052 multiplicative_identity [1052] by Super 1077 with 14 at 2,2
-Id : 1114, {_}: multiplicative_identity =<= add ?1052 multiplicative_identity [1052] by Demod 1081 with 16 at 2
-Id : 1133, {_}: add multiplicative_identity ?1095 =>= multiplicative_identity [1095] by Super 4 with 1114 at 3
-Id : 2096, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2095 with 1133 at 1,1,2
-Id : 139, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 18 with 65 at 2
-Id : 2097, {_}: add additive_identity (multiply additive_identity ?1804) =>= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2096 with 139 at 1,2
-Id : 2098, {_}: multiply additive_identity ?1804 =<= inverse (add (inverse additive_identity) ?1804) [1804] by Demod 2097 with 57 at 2
-Id : 2099, {_}: multiply additive_identity ?1804 =<= inverse (add multiplicative_identity ?1804) [1804] by Demod 2098 with 92 at 1,1,3
-Id : 2100, {_}: multiply additive_identity ?1804 =>= inverse multiplicative_identity [1804] by Demod 2099 with 1133 at 1,3
-Id : 2101, {_}: multiply additive_identity ?1804 =>= additive_identity [1804] by Demod 2100 with 139 at 3
-Id : 2167, {_}: multiply ?1480 additive_identity =?= multiply additive_identity ?1480 [1480] by Demod 1567 with 2101 at 2,2
-Id : 2168, {_}: multiply ?1480 additive_identity =>= additive_identity [1480] by Demod 2167 with 2101 at 3
-Id : 2174, {_}: add ?325 additive_identity =<= multiply (add ?326 ?325) ?325 [326, 325] by Demod 229 with 2168 at 2,2
-Id : 2180, {_}: ?325 =<= multiply (add ?326 ?325) ?325 [326, 325] by Demod 2174 with 12 at 2
-Id : 1258, {_}: add ?1213 (multiply ?1214 (inverse (inverse ?1213))) =>= multiply (add ?1213 ?1214) ?1213 [1214, 1213] by Super 8 with 1115 at 2,3
-Id : 55, {_}: add ?130 (multiply ?131 additive_identity) =<= multiply (add ?130 ?131) ?130 [131, 130] by Super 8 with 12 at 2,3
-Id : 1274, {_}: add ?1213 (multiply ?1214 (inverse (inverse ?1213))) =>= add ?1213 (multiply ?1214 additive_identity) [1214, 1213] by Demod 1258 with 55 at 3
-Id : 5845, {_}: add ?1213 (multiply ?1214 ?1213) =?= add ?1213 (multiply ?1214 additive_identity) [1214, 1213] by Demod 1274 with 2316 at 2,2,2
-Id : 5846, {_}: add ?1213 (multiply ?1214 ?1213) =>= add ?1213 additive_identity [1214, 1213] by Demod 5845 with 2168 at 2,3
-Id : 5877, {_}: add ?5881 (multiply ?5882 ?5881) =>= ?5881 [5882, 5881] by Demod 5846 with 12 at 3
-Id : 5878, {_}: add ?5884 (multiply ?5884 ?5885) =>= ?5884 [5885, 5884] by Super 5877 with 6 at 2,2
-Id : 6099, {_}: add ?6204 (multiply ?6206 (multiply ?6204 ?6205)) =>= multiply (add ?6204 ?6206) ?6204 [6205, 6206, 6204] by Super 8 with 5878 at 2,3
-Id : 2175, {_}: add ?130 additive_identity =<= multiply (add ?130 ?131) ?130 [131, 130] by Demod 55 with 2168 at 2,2
-Id : 2179, {_}: ?130 =<= multiply (add ?130 ?131) ?130 [131, 130] by Demod 2175 with 12 at 2
-Id : 6162, {_}: add ?6204 (multiply ?6206 (multiply ?6204 ?6205)) =>= ?6204 [6205, 6206, 6204] by Demod 6099 with 2179 at 3
-Id : 23650, {_}: multiply ?28445 (multiply ?28444 ?28446) =<= multiply ?28444 (multiply ?28445 (multiply ?28444 ?28446)) [28446, 28444, 28445] by Super 2180 with 6162 at 1,3
-Id : 152296, {_}: multiply ?278484 (multiply ?278483 ?278482) =<= multiply ?278483 (multiply ?278484 (add (inverse ?278483) ?278482)) [278482, 278483, 278484] by Demod 152295 with 23650 at 2
-Id : 2442, {_}: add ?2131 ?2132 =<= add ?2131 (add ?2132 ?2131) [2132, 2131] by Demod 2402 with 2316 at 2,2,3
-Id : 2443, {_}: add ?2134 ?2135 =<= add ?2134 (add ?2134 ?2135) [2135, 2134] by Super 2442 with 4 at 2,3
-Id : 2558, {_}: add ?2283 (multiply ?2285 (add ?2283 ?2284)) =<= multiply (add ?2283 ?2285) (add ?2283 ?2284) [2284, 2285, 2283] by Super 8 with 2443 at 2,3
-Id : 2593, {_}: add ?2283 (multiply ?2285 (add ?2283 ?2284)) =>= add ?2283 (multiply ?2285 ?2284) [2284, 2285, 2283] by Demod 2558 with 8 at 3
-Id : 19422, {_}: multiply (add (inverse ?20977) (multiply ?20975 ?20976)) ?20977 =?= multiply ?20977 (multiply ?20975 (add (inverse ?20977) ?20976)) [20976, 20975, 20977] by Super 2049 with 2593 at 1,2
-Id : 19552, {_}: multiply ?20977 (multiply ?20975 ?20976) =<= multiply ?20977 (multiply ?20975 (add (inverse ?20977) ?20976)) [20976, 20975, 20977] by Demod 19422 with 2049 at 2
-Id : 352787, {_}: multiply ?278484 (multiply ?278483 ?278482) =?= multiply ?278483 (multiply ?278484 ?278482) [278482, 278483, 278484] by Demod 152296 with 19552 at 3
-Id : 2159, {_}: add ?432 additive_identity =<= multiply ?432 (add ?433 ?432) [433, 432] by Demod 332 with 2101 at 2,2
-Id : 2194, {_}: ?432 =<= multiply ?432 (add ?433 ?432) [433, 432] by Demod 2159 with 12 at 2
-Id : 5847, {_}: add ?1213 (multiply ?1214 ?1213) =>= ?1213 [1214, 1213] by Demod 5846 with 12 at 3
-Id : 5862, {_}: add ?5837 (multiply ?5839 (multiply ?5838 ?5837)) =>= multiply (add ?5837 ?5839) ?5837 [5838, 5839, 5837] by Super 8 with 5847 at 2,3
-Id : 5925, {_}: add ?5837 (multiply ?5839 (multiply ?5838 ?5837)) =>= ?5837 [5838, 5839, 5837] by Demod 5862 with 2179 at 3
-Id : 36958, {_}: multiply ?53806 (multiply ?53807 ?53808) =<= multiply (multiply ?53806 (multiply ?53807 ?53808)) ?53808 [53808, 53807, 53806] by Super 2194 with 5925 at 2,3
-Id : 36959, {_}: multiply ?53810 (multiply ?53811 ?53812) =<= multiply (multiply ?53810 (multiply ?53812 ?53811)) ?53812 [53812, 53811, 53810] by Super 36958 with 6 at 2,1,3
-Id : 23651, {_}: multiply ?28449 (multiply ?28448 ?28450) =<= multiply (multiply ?28449 (multiply ?28448 ?28450)) ?28448 [28450, 28448, 28449] by Super 2194 with 6162 at 2,3
-Id : 58893, {_}: multiply ?53810 (multiply ?53811 ?53812) =?= multiply ?53810 (multiply ?53812 ?53811) [53812, 53811, 53810] by Demod 36959 with 23651 at 3
-Id : 355225, {_}: multiply c (multiply b a) === multiply c (multiply b a) [] by Demod 355224 with 58893 at 2
-Id : 355224, {_}: multiply c (multiply a b) =>= multiply c (multiply b a) [] by Demod 91 with 352787 at 2
-Id : 91, {_}: multiply a (multiply c b) =>= multiply c (multiply b a) [] by Demod 90 with 6 at 2,3
-Id : 90, {_}: multiply a (multiply c b) =>= multiply c (multiply a b) [] by Demod 89 with 6 at 3
-Id : 89, {_}: multiply a (multiply c b) =<= multiply (multiply a b) c [] by Demod 2 with 6 at 2,2
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-4.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 95
- additive_inverse is 83
- associativity_of_add is 80
- associativity_of_multiply is 79
- b is 97
- c is 96
- distributivity is 92
- inverse is 89
- l1 is 91
- l2 is 87
- l3 is 90
- l4 is 86
- multiplicative_inverse is 81
- multiply is 94
- n0 is 82
- n1 is 84
- property3 is 88
- property3_dual is 85
- prove_multiply_add_property is 93
-Facts
- Id : 4, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
- Id : 6, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
- Id : 8, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
- Id : 10, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
- Id : 12, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
- Id : 14, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
- Id : 16, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
- Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
- Id : 20, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
- Id : 22, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
- Id : 24, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Goal
- Id : 2, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-Found proof, 19.854450s
-% SZS status Unsatisfiable for BOO031-1.p
-% SZS output start CNFRefutation for BOO031-1.p
-Id : 16, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
-Id : 20, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
-Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-Id : 14, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
-Id : 10, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
-Id : 64, {_}: multiply (multiply (add ?211 ?212) (add ?212 ?213)) ?212 =>= ?212 [213, 212, 211] by l4 ?211 ?212 ?213
-Id : 24, {_}: multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Id : 4, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
-Id : 8, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
-Id : 12, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
-Id : 49, {_}: multiply ?140 (add ?141 (add ?140 ?142)) =>= ?140 [142, 141, 140] by l2 ?140 ?141 ?142
-Id : 6, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
-Id : 30, {_}: add (add (multiply ?60 ?61) (multiply ?61 ?62)) ?61 =>= ?61 [62, 61, 60] by l3 ?60 ?61 ?62
-Id : 22, {_}: add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-Id : 31, {_}: add (multiply ?65 ?66) ?66 =>= ?66 [66, 65] by Super 30 with 6 at 1,2
-Id : 51, {_}: multiply ?151 (add ?152 ?151) =>= ?151 [152, 151] by Super 49 with 6 at 2,2,2
-Id : 568, {_}: add ?1169 (add ?1170 ?1169) =>= add ?1170 ?1169 [1170, 1169] by Super 31 with 51 at 1,2
-Id : 1034, {_}: add (add ?2011 ?2012) ?2011 =>= add ?2012 ?2011 [2012, 2011] by Super 22 with 568 at 3
-Id : 47, {_}: add ?131 (multiply ?134 ?131) =>= ?131 [134, 131] by Super 6 with 12 at 2,2,2
-Id : 54, {_}: multiply ?165 (add ?165 ?166) =>= ?165 [166, 165] by Super 49 with 8 at 2,2
-Id : 673, {_}: add (add ?1383 ?1384) ?1383 =>= add ?1383 ?1384 [1384, 1383] by Super 47 with 54 at 2,2
-Id : 1524, {_}: add ?2011 ?2012 =?= add ?2012 ?2011 [2012, 2011] by Demod 1034 with 673 at 2
-Id : 161, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (multiply (add ?2 ?3) (add ?3 ?4)) (add ?4 ?2) [4, 3, 2] by Demod 4 with 24 at 3
-Id : 727, {_}: multiply (add ?1499 ?1500) ?1500 =>= ?1500 [1500, 1499] by Super 64 with 12 at 1,2
-Id : 733, {_}: multiply ?1519 (multiply ?1518 ?1519) =>= multiply ?1518 ?1519 [1518, 1519] by Super 727 with 47 at 1,2
-Id : 1435, {_}: add (multiply ?2622 ?2620) (add (multiply ?2621 ?2620) (multiply (multiply ?2621 ?2620) ?2622)) =<= multiply (multiply (add ?2622 ?2620) (add ?2620 (multiply ?2621 ?2620))) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Super 161 with 733 at 1,2,2
-Id : 34, {_}: add ?77 (multiply ?77 ?78) =>= ?77 [78, 77] by Super 6 with 10 at 2,2
-Id : 1478, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =<= multiply (multiply (add ?2622 ?2620) (add ?2620 (multiply ?2621 ?2620))) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1435 with 34 at 2,2
-Id : 1479, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =<= multiply (multiply (add ?2622 ?2620) ?2620) (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1478 with 47 at 2,1,3
-Id : 72, {_}: multiply (add ?249 ?250) ?250 =>= ?250 [250, 249] by Super 64 with 12 at 1,2
-Id : 1480, {_}: add (multiply ?2622 ?2620) (multiply ?2621 ?2620) =>= multiply ?2620 (add (multiply ?2621 ?2620) ?2622) [2621, 2620, 2622] by Demod 1479 with 72 at 1,3
-Id : 7843, {_}: multiply ?13007 ?13008 =<= multiply ?13007 (multiply (add ?13009 ?13007) ?13008) [13009, 13008, 13007] by Super 24 with 51 at 1,2
-Id : 582, {_}: multiply ?1218 (add ?1219 ?1218) =>= ?1218 [1219, 1218] by Super 49 with 6 at 2,2,2
-Id : 587, {_}: multiply (multiply ?1235 ?1234) ?1235 =>= multiply ?1235 ?1234 [1234, 1235] by Super 582 with 34 at 2,2
-Id : 1123, {_}: multiply ?2124 ?2125 =<= multiply ?2124 (multiply ?2125 ?2124) [2125, 2124] by Super 24 with 587 at 2
-Id : 1768, {_}: multiply ?2124 ?2125 =?= multiply ?2125 ?2124 [2125, 2124] by Demod 1123 with 733 at 3
-Id : 7897, {_}: multiply ?13228 ?13229 =<= multiply ?13228 (multiply ?13229 (add ?13230 ?13228)) [13230, 13229, 13228] by Super 7843 with 1768 at 2,3
-Id : 586, {_}: multiply ?1232 ?1232 =>= ?1232 [1232] by Super 582 with 31 at 2,2
-Id : 618, {_}: multiply ?1282 ?1283 =<= multiply ?1282 (multiply ?1282 ?1283) [1283, 1282] by Super 24 with 586 at 1,2
-Id : 1266, {_}: add (multiply ?2366 ?2364) (add (multiply ?2364 ?2365) (multiply (multiply ?2364 ?2365) ?2366)) =<= multiply (multiply (add ?2366 ?2364) (add ?2364 (multiply ?2364 ?2365))) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Super 161 with 618 at 1,2,2
-Id : 1308, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =<= multiply (multiply (add ?2366 ?2364) (add ?2364 (multiply ?2364 ?2365))) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1266 with 34 at 2,2
-Id : 1309, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =<= multiply (multiply (add ?2366 ?2364) ?2364) (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1308 with 34 at 2,1,3
-Id : 16375, {_}: add (multiply ?29661 ?29662) (multiply ?29662 ?29663) =>= multiply ?29662 (add (multiply ?29662 ?29663) ?29661) [29663, 29662, 29661] by Demod 1309 with 72 at 1,3
-Id : 16381, {_}: add (multiply ?29687 (add ?29686 ?29688)) ?29688 =<= multiply (add ?29686 ?29688) (add (multiply (add ?29686 ?29688) ?29688) ?29687) [29688, 29686, 29687] by Super 16375 with 72 at 2,2
-Id : 16548, {_}: add (multiply ?29687 (add ?29686 ?29688)) ?29688 =>= multiply (add ?29686 ?29688) (add ?29688 ?29687) [29688, 29686, 29687] by Demod 16381 with 72 at 1,2,3
-Id : 91, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 10 with 18 at 1,2
-Id : 101, {_}: n0 =<= inverse n1 [] by Super 91 with 20 at 2
-Id : 206, {_}: add n1 n0 =>= n1 [] by Super 18 with 101 at 2,2
-Id : 214, {_}: multiply n1 (add ?663 n1) =>= n1 [663] by Super 12 with 206 at 2,2,2
-Id : 222, {_}: add ?663 n1 =>= n1 [663] by Demod 214 with 91 at 2
-Id : 259, {_}: multiply ?726 (add ?727 n1) =>= ?726 [727, 726] by Super 12 with 222 at 2,2,2
-Id : 268, {_}: multiply ?726 n1 =>= ?726 [726] by Demod 259 with 222 at 2,2
-Id : 306, {_}: multiply (add ?801 n1) (add n1 ?802) =>= n1 [802, 801] by Super 14 with 268 at 2
-Id : 312, {_}: multiply n1 (add n1 ?802) =>= n1 [802] by Demod 306 with 222 at 1,2
-Id : 313, {_}: add n1 ?802 =>= n1 [802] by Demod 312 with 91 at 2
-Id : 390, {_}: multiply (multiply n1 (add ?884 ?885)) ?884 =>= ?884 [885, 884] by Super 14 with 313 at 1,1,2
-Id : 401, {_}: multiply n1 (multiply (add ?884 ?885) ?884) =>= ?884 [885, 884] by Demod 390 with 24 at 2
-Id : 402, {_}: multiply (add ?884 ?885) ?884 =>= ?884 [885, 884] by Demod 401 with 91 at 2
-Id : 827, {_}: multiply (multiply ?1658 (add ?1656 ?1657)) ?1656 =>= multiply ?1658 ?1656 [1657, 1656, 1658] by Super 24 with 402 at 2,3
-Id : 77, {_}: add (multiply ?268 ?267) (multiply (inverse ?267) ?268) =<= multiply (add ?268 ?267) (multiply (add ?267 (inverse ?267)) (add (inverse ?267) ?268)) [267, 268] by Super 4 with 16 at 2,2
-Id : 88, {_}: add (multiply ?268 ?267) (multiply (inverse ?267) ?268) =>= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 77 with 10 at 2,3
-Id : 1310, {_}: add (multiply ?2366 ?2364) (multiply ?2364 ?2365) =>= multiply ?2364 (add (multiply ?2364 ?2365) ?2366) [2365, 2364, 2366] by Demod 1309 with 72 at 1,3
-Id : 16342, {_}: add (multiply ?29521 ?29522) (multiply ?29520 ?29521) =>= multiply ?29521 (add (multiply ?29521 ?29522) ?29520) [29520, 29522, 29521] by Super 1524 with 1310 at 3
-Id : 51988, {_}: multiply ?268 (add (multiply ?268 ?267) (inverse ?267)) =?= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 88 with 16342 at 2
-Id : 51989, {_}: multiply ?268 (add (inverse ?267) (multiply ?268 ?267)) =?= multiply (add ?268 ?267) (add (inverse ?267) ?268) [267, 268] by Demod 51988 with 1524 at 2,2
-Id : 52070, {_}: multiply (multiply (add ?105798 ?105797) (add (inverse ?105797) ?105798)) (inverse ?105797) =>= multiply ?105798 (inverse ?105797) [105797, 105798] by Super 827 with 51989 at 1,2
-Id : 52559, {_}: multiply (add ?105798 ?105797) (inverse ?105797) =>= multiply ?105798 (inverse ?105797) [105797, 105798] by Demod 52070 with 827 at 2
-Id : 52560, {_}: multiply (inverse ?105797) (add ?105798 ?105797) =>= multiply ?105798 (inverse ?105797) [105798, 105797] by Demod 52559 with 1768 at 2
-Id : 54336, {_}: add (multiply ?108230 (inverse ?108229)) ?108229 =<= multiply (add ?108230 ?108229) (add ?108229 (inverse ?108229)) [108229, 108230] by Super 16548 with 52560 at 1,2
-Id : 54743, {_}: add (multiply ?108230 (inverse ?108229)) ?108229 =>= multiply (add ?108230 ?108229) n1 [108229, 108230] by Demod 54336 with 18 at 2,3
-Id : 55540, {_}: add (multiply ?110128 (inverse ?110129)) ?110129 =>= add ?110128 ?110129 [110129, 110128] by Demod 54743 with 268 at 3
-Id : 57387, {_}: add (multiply (inverse ?112946) ?112947) ?112946 =>= add ?112947 ?112946 [112947, 112946] by Super 55540 with 1768 at 1,2
-Id : 119, {_}: add (multiply ?10 ?11) (add (multiply ?11 ?12) ?11) =>= ?11 [12, 11, 10] by Demod 8 with 22 at 2
-Id : 216, {_}: multiply (multiply n1 (add n0 ?667)) n0 =>= n0 [667] by Super 14 with 206 at 1,1,2
-Id : 219, {_}: multiply n1 (multiply (add n0 ?667) n0) =>= n0 [667] by Demod 216 with 24 at 2
-Id : 220, {_}: multiply (add n0 ?667) n0 =>= n0 [667] by Demod 219 with 91 at 2
-Id : 100, {_}: add n0 ?26 =>= ?26 [26] by Demod 16 with 20 at 1,2
-Id : 221, {_}: multiply ?667 n0 =>= n0 [667] by Demod 220 with 100 at 1,2
-Id : 225, {_}: add ?674 (multiply ?675 n0) =>= ?674 [675, 674] by Super 6 with 221 at 2,2,2
-Id : 251, {_}: add ?674 n0 =>= ?674 [674] by Demod 225 with 221 at 2,2
-Id : 281, {_}: add (multiply ?753 n0) (multiply n0 ?754) =>= n0 [754, 753] by Super 119 with 251 at 2,2
-Id : 292, {_}: add n0 (multiply n0 ?754) =>= n0 [754] by Demod 281 with 221 at 1,2
-Id : 293, {_}: multiply n0 ?754 =>= n0 [754] by Demod 292 with 100 at 2
-Id : 338, {_}: add n0 (add (multiply ?829 ?830) ?829) =>= ?829 [830, 829] by Super 119 with 293 at 1,2
-Id : 377, {_}: add (multiply ?829 ?830) ?829 =>= ?829 [830, 829] by Demod 338 with 100 at 2
-Id : 38238, {_}: add (multiply ?76482 ?76483) (multiply ?76484 ?76482) =>= multiply ?76482 (add (multiply ?76482 ?76483) ?76484) [76484, 76483, 76482] by Super 1524 with 1310 at 3
-Id : 38322, {_}: add ?76856 (multiply ?76857 (add ?76856 ?76855)) =<= multiply (add ?76856 ?76855) (add (multiply (add ?76856 ?76855) ?76856) ?76857) [76855, 76857, 76856] by Super 38238 with 402 at 1,2
-Id : 47380, {_}: add ?97201 (multiply ?97202 (add ?97201 ?97203)) =>= multiply (add ?97201 ?97203) (add ?97201 ?97202) [97203, 97202, 97201] by Demod 38322 with 402 at 1,2,3
-Id : 47486, {_}: add ?97677 (multiply (add ?97677 ?97679) ?97678) =>= multiply (add ?97677 ?97679) (add ?97677 ?97678) [97678, 97679, 97677] by Super 47380 with 1768 at 2,2
-Id : 52196, {_}: multiply ?106255 (add (inverse ?106256) (multiply ?106255 ?106256)) =?= multiply (add ?106255 ?106256) (add (inverse ?106256) ?106255) [106256, 106255] by Demod 51988 with 1524 at 2,2
-Id : 52239, {_}: multiply ?106398 (add (inverse (inverse ?106398)) (multiply ?106398 (inverse ?106398))) =>= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Super 52196 with 18 at 1,3
-Id : 52779, {_}: multiply ?106398 (add (inverse (inverse ?106398)) n0) =?= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Demod 52239 with 20 at 2,2,2
-Id : 52780, {_}: multiply ?106398 (inverse (inverse ?106398)) =<= multiply n1 (add (inverse (inverse ?106398)) ?106398) [106398] by Demod 52779 with 251 at 2,2
-Id : 52781, {_}: multiply ?106398 (inverse (inverse ?106398)) =<= add (inverse (inverse ?106398)) ?106398 [106398] by Demod 52780 with 91 at 3
-Id : 53322, {_}: add (inverse (inverse ?107400)) (multiply (multiply ?107400 (inverse (inverse ?107400))) ?107401) =>= multiply (add (inverse (inverse ?107400)) ?107400) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Super 47486 with 52781 at 1,2,2
-Id : 177, {_}: add ?561 (multiply (multiply ?560 ?561) ?562) =>= ?561 [562, 560, 561] by Super 6 with 24 at 2,2
-Id : 53342, {_}: inverse (inverse ?107400) =<= multiply (add (inverse (inverse ?107400)) ?107400) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Demod 53322 with 177 at 2
-Id : 53343, {_}: inverse (inverse ?107400) =<= multiply (multiply ?107400 (inverse (inverse ?107400))) (add (inverse (inverse ?107400)) ?107401) [107401, 107400] by Demod 53342 with 52781 at 1,3
-Id : 670, {_}: multiply (multiply ?1373 ?1371) (add ?1371 ?1372) =>= multiply ?1373 ?1371 [1372, 1371, 1373] by Super 24 with 54 at 2,3
-Id : 53344, {_}: inverse (inverse ?107400) =<= multiply ?107400 (inverse (inverse ?107400)) [107400] by Demod 53343 with 670 at 3
-Id : 53988, {_}: add (inverse (inverse ?107962)) ?107962 =>= ?107962 [107962] by Super 377 with 53344 at 1,2
-Id : 53931, {_}: inverse (inverse ?106398) =<= add (inverse (inverse ?106398)) ?106398 [106398] by Demod 52781 with 53344 at 2
-Id : 54117, {_}: inverse (inverse ?107962) =>= ?107962 [107962] by Demod 53988 with 53931 at 2
-Id : 57388, {_}: add (multiply ?112949 ?112950) (inverse ?112949) =>= add ?112950 (inverse ?112949) [112950, 112949] by Super 57387 with 54117 at 1,1,2
-Id : 57660, {_}: add (inverse ?112949) (multiply ?112949 ?112950) =>= add ?112950 (inverse ?112949) [112950, 112949] by Demod 57388 with 1524 at 2
-Id : 1445, {_}: multiply ?2651 (multiply ?2652 ?2651) =>= multiply ?2652 ?2651 [2652, 2651] by Super 727 with 47 at 1,2
-Id : 18543, {_}: multiply ?33695 (multiply ?33696 (multiply ?33697 ?33695)) =>= multiply (multiply ?33696 ?33697) ?33695 [33697, 33696, 33695] by Super 1445 with 24 at 2,2
-Id : 1430, {_}: multiply (multiply ?2603 ?2601) (multiply ?2602 ?2601) =>= multiply ?2603 (multiply ?2602 ?2601) [2602, 2601, 2603] by Super 24 with 733 at 2,3
-Id : 18612, {_}: multiply ?33994 (multiply ?33993 (multiply ?33995 ?33994)) =?= multiply (multiply (multiply ?33993 ?33994) ?33995) ?33994 [33995, 33993, 33994] by Super 18543 with 1430 at 2,2
-Id : 1449, {_}: multiply ?2666 (multiply ?2664 (multiply ?2665 ?2666)) =>= multiply (multiply ?2664 ?2665) ?2666 [2665, 2664, 2666] by Super 1445 with 24 at 2,2
-Id : 18850, {_}: multiply (multiply ?33993 ?33995) ?33994 =<= multiply (multiply (multiply ?33993 ?33994) ?33995) ?33994 [33994, 33995, 33993] by Demod 18612 with 1449 at 2
-Id : 4399, {_}: multiply (multiply (multiply ?6795 ?6794) ?6796) ?6794 =>= multiply (multiply ?6795 ?6794) ?6796 [6796, 6794, 6795] by Super 51 with 177 at 2,2
-Id : 43487, {_}: multiply (multiply ?33993 ?33995) ?33994 =?= multiply (multiply ?33993 ?33994) ?33995 [33994, 33995, 33993] by Demod 18850 with 4399 at 3
-Id : 54429, {_}: multiply (multiply (inverse ?108571) ?108573) (add ?108572 ?108571) =>= multiply (multiply ?108572 (inverse ?108571)) ?108573 [108572, 108573, 108571] by Super 43487 with 52560 at 1,3
-Id : 54563, {_}: multiply (inverse ?108571) (multiply ?108573 (add ?108572 ?108571)) =>= multiply (multiply ?108572 (inverse ?108571)) ?108573 [108572, 108573, 108571] by Demod 54429 with 24 at 2
-Id : 728, {_}: multiply ?1504 (multiply ?1502 (multiply ?1504 ?1503)) =>= multiply ?1502 (multiply ?1504 ?1503) [1503, 1502, 1504] by Super 727 with 6 at 1,2
-Id : 9518, {_}: multiply (multiply ?16547 ?16548) (multiply ?16547 ?16549) =>= multiply ?16548 (multiply ?16547 ?16549) [16549, 16548, 16547] by Super 24 with 728 at 3
-Id : 1122, {_}: multiply (multiply ?2120 ?2121) ?2122 =<= multiply (multiply ?2120 ?2121) (multiply ?2120 ?2122) [2122, 2121, 2120] by Super 24 with 587 at 1,2
-Id : 30202, {_}: multiply (multiply ?16547 ?16548) ?16549 =?= multiply ?16548 (multiply ?16547 ?16549) [16549, 16548, 16547] by Demod 9518 with 1122 at 2
-Id : 54564, {_}: multiply (inverse ?108571) (multiply ?108573 (add ?108572 ?108571)) =>= multiply (inverse ?108571) (multiply ?108572 ?108573) [108572, 108573, 108571] by Demod 54563 with 30202 at 3
-Id : 145944, {_}: add (inverse (inverse ?250795)) (multiply (inverse ?250795) (multiply ?250797 ?250796)) =>= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Super 57660 with 54564 at 2,2
-Id : 146263, {_}: add (multiply ?250797 ?250796) (inverse (inverse ?250795)) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250795, 250796, 250797] by Demod 145944 with 57660 at 2
-Id : 146264, {_}: add (inverse (inverse ?250795)) (multiply ?250797 ?250796) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Demod 146263 with 1524 at 2
-Id : 146265, {_}: add ?250795 (multiply ?250797 ?250796) =<= add (multiply ?250796 (add ?250797 ?250795)) (inverse (inverse ?250795)) [250796, 250797, 250795] by Demod 146264 with 54117 at 1,2
-Id : 146266, {_}: add ?250795 (multiply ?250797 ?250796) =<= add (inverse (inverse ?250795)) (multiply ?250796 (add ?250797 ?250795)) [250796, 250797, 250795] by Demod 146265 with 1524 at 3
-Id : 146267, {_}: add ?250795 (multiply ?250797 ?250796) =<= add ?250795 (multiply ?250796 (add ?250797 ?250795)) [250796, 250797, 250795] by Demod 146266 with 54117 at 1,3
-Id : 38316, {_}: add ?76835 (multiply ?76836 (add ?76834 ?76835)) =<= multiply (add ?76834 ?76835) (add (multiply (add ?76834 ?76835) ?76835) ?76836) [76834, 76836, 76835] by Super 38238 with 72 at 1,2
-Id : 38565, {_}: add ?76835 (multiply ?76836 (add ?76834 ?76835)) =>= multiply (add ?76834 ?76835) (add ?76835 ?76836) [76834, 76836, 76835] by Demod 38316 with 72 at 1,2,3
-Id : 146268, {_}: add ?250795 (multiply ?250797 ?250796) =<= multiply (add ?250797 ?250795) (add ?250795 ?250796) [250796, 250797, 250795] by Demod 146267 with 38565 at 3
-Id : 147010, {_}: multiply ?252446 (add ?252445 ?252444) =<= multiply ?252446 (add ?252444 (multiply ?252445 ?252446)) [252444, 252445, 252446] by Super 7897 with 146268 at 2,3
-Id : 152622, {_}: multiply a (add c b) === multiply a (add c b) [] by Demod 152621 with 1524 at 2,3
-Id : 152621, {_}: multiply a (add c b) =<= multiply a (add b c) [] by Demod 19333 with 147010 at 3
-Id : 19333, {_}: multiply a (add c b) =<= multiply a (add c (multiply b a)) [] by Demod 19332 with 1524 at 2,3
-Id : 19332, {_}: multiply a (add c b) =<= multiply a (add (multiply b a) c) [] by Demod 1703 with 1480 at 3
-Id : 1703, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 1702 with 1524 at 3
-Id : 1702, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 2 with 1524 at 2,2
-Id : 2, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
-% SZS output end CNFRefutation for BOO031-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- b is 96
- c is 94
- d is 93
- e is 92
- f is 91
- g is 90
- inverse is 97
- left_inverse is 85
- multiply is 95
- prove_single_axiom is 89
- right_inverse is 84
- ternary_multiply_1 is 87
- ternary_multiply_2 is 86
-Facts
- Id : 4, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
- Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
- Id : 8, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
- Id : 10, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
- Id : 12, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-Goal
- Id : 2, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-Found proof, 2.683225s
-% SZS status Unsatisfiable for BOO034-1.p
-% SZS output start CNFRefutation for BOO034-1.p
-Id : 8, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
-Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-Id : 12, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
-Id : 10, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
-Id : 4, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-Id : 75, {_}: multiply ?212 ?213 ?214 =<= multiply ?212 ?213 (multiply ?215 (multiply ?212 ?213 ?214) ?214) [215, 214, 213, 212] by Super 4 with 6 at 2
-Id : 84, {_}: multiply ?257 ?258 ?259 =<= multiply ?257 ?258 (multiply ?257 ?258 ?259) [259, 258, 257] by Super 75 with 8 at 3,3
-Id : 115, {_}: multiply (multiply ?285 ?286 ?288) ?289 (multiply ?285 ?286 ?287) =?= multiply ?285 ?286 (multiply ?288 ?289 (multiply ?285 ?286 ?287)) [287, 289, 288, 286, 285] by Super 4 with 84 at 3,2
-Id : 298, {_}: multiply ?735 ?736 (multiply ?737 ?738 ?739) =<= multiply ?735 ?736 (multiply ?737 ?738 (multiply ?735 ?736 ?739)) [739, 738, 737, 736, 735] by Demod 115 with 4 at 2
-Id : 184, {_}: multiply ?446 ?447 ?448 =<= multiply ?446 ?447 (multiply ?448 (multiply ?446 ?447 ?448) ?449) [449, 448, 447, 446] by Super 4 with 8 at 2
-Id : 189, {_}: multiply ?470 ?471 (inverse ?471) =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Super 184 with 12 at 2,3,3
-Id : 225, {_}: ?470 =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Demod 189 with 12 at 2
-Id : 321, {_}: multiply (inverse ?865) ?864 (multiply ?864 ?865 ?866) =>= multiply (inverse ?865) ?864 ?864 [866, 864, 865] by Super 298 with 225 at 3,3
-Id : 387, {_}: multiply (inverse ?963) ?964 (multiply ?964 ?963 ?965) =>= ?964 [965, 964, 963] by Demod 321 with 6 at 3
-Id : 389, {_}: multiply (inverse ?974) ?973 ?974 =>= ?973 [973, 974] by Super 387 with 6 at 3,2
-Id : 437, {_}: ?1071 =<= inverse (inverse ?1071) [1071] by Super 12 with 389 at 2
-Id : 462, {_}: multiply ?1119 (inverse ?1119) ?1120 =>= ?1120 [1120, 1119] by Super 10 with 437 at 1,2
-Id : 116, {_}: multiply (multiply ?291 ?292 ?293) ?294 (multiply ?291 ?292 ?295) =?= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Super 4 with 84 at 1,2
-Id : 12671, {_}: multiply ?19232 ?19233 (multiply ?19234 ?19235 ?19236) =<= multiply ?19232 ?19233 (multiply (multiply ?19232 ?19233 ?19234) ?19235 ?19236) [19236, 19235, 19234, 19233, 19232] by Demod 116 with 4 at 2
-Id : 80, {_}: multiply ?236 ?237 (inverse ?237) =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Super 75 with 12 at 2,3,3
-Id : 105, {_}: ?236 =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Demod 80 with 12 at 2
-Id : 996, {_}: ?2202 =<= multiply ?2202 (inverse ?2203) (multiply ?2204 ?2202 ?2203) [2204, 2203, 2202] by Super 105 with 437 at 3,3,3
-Id : 1012, {_}: ?2262 =<= multiply ?2262 (inverse (multiply ?2261 ?2263 (inverse ?2262))) ?2263 [2263, 2261, 2262] by Super 996 with 105 at 3,3
-Id : 459, {_}: ?1109 =<= multiply ?1109 (inverse ?1108) (multiply ?1108 ?1109 ?1110) [1110, 1108, 1109] by Super 225 with 437 at 1,3,3
-Id : 1017, {_}: inverse ?2283 =<= multiply (inverse ?2283) (inverse (multiply ?2283 ?2285 ?2284)) ?2285 [2284, 2285, 2283] by Super 996 with 459 at 3,3
-Id : 1909, {_}: ?3987 =<= multiply ?3987 (inverse (inverse ?3985)) (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Super 1012 with 1017 at 1,2,3
-Id : 1996, {_}: ?3987 =<= multiply ?3987 ?3985 (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Demod 1909 with 437 at 2,3
-Id : 2510, {_}: ?5132 =<= multiply ?5132 (multiply ?5132 (inverse ?5131) ?5133) ?5131 [5133, 5131, 5132] by Super 105 with 1996 at 3,3
-Id : 2812, {_}: multiply ?5719 (inverse (inverse ?5721)) ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Super 105 with 2510 at 3,3
-Id : 2874, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2812 with 437 at 2,2
-Id : 2875, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 ?5721 ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2874 with 437 at 2,1,3
-Id : 12777, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =?= multiply ?19864 ?19863 (multiply ?19864 ?19863 ?19862) [19862, 19863, 19864] by Super 12671 with 2875 at 3,3
-Id : 12993, {_}: multiply ?20226 ?20227 (multiply ?20228 ?20227 ?20226) =>= multiply ?20226 ?20227 ?20228 [20228, 20227, 20226] by Demod 12777 with 84 at 3
-Id : 19, {_}: multiply ?58 ?59 ?61 =<= multiply ?58 ?59 (multiply ?60 (multiply ?58 ?59 ?61) ?61) [60, 61, 59, 58] by Super 4 with 6 at 2
-Id : 463, {_}: multiply ?1122 ?1123 (inverse ?1122) =>= ?1123 [1123, 1122] by Super 389 with 437 at 1,2
-Id : 607, {_}: multiply ?1371 ?1372 (inverse ?1371) =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1372, 1371] by Super 19 with 463 at 2,3,3
-Id : 625, {_}: ?1372 =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1371, 1372] by Demod 607 with 463 at 2
-Id : 460, {_}: ?1113 =<= multiply ?1113 (inverse ?1112) (multiply ?1114 ?1113 ?1112) [1114, 1112, 1113] by Super 105 with 437 at 3,3,3
-Id : 1018, {_}: inverse ?2287 =<= multiply (inverse ?2287) (inverse (multiply ?2288 ?2289 ?2287)) ?2289 [2289, 2288, 2287] by Super 996 with 460 at 3,3
-Id : 2078, {_}: ?4356 =<= multiply ?4356 (inverse (inverse ?4354)) (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Super 1012 with 1018 at 1,2,3
-Id : 2124, {_}: ?4356 =<= multiply ?4356 ?4354 (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Demod 2078 with 437 at 2,3
-Id : 3650, {_}: ?7215 =<= multiply ?7215 (multiply ?7216 (inverse ?7214) ?7215) ?7214 [7214, 7216, 7215] by Super 105 with 2124 at 3,3
-Id : 4032, {_}: multiply ?7968 (inverse (inverse ?7969)) ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Super 625 with 3650 at 3,3
-Id : 4103, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Demod 4032 with 437 at 2,2
-Id : 4104, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 ?7969 ?7967) ?7967 [7967, 7969, 7968] by Demod 4103 with 437 at 2,2,3
-Id : 13062, {_}: multiply ?20502 (multiply ?20501 ?20503 ?20502) (multiply ?20501 ?20503 ?20502) =>= multiply ?20502 (multiply ?20501 ?20503 ?20502) ?20503 [20503, 20501, 20502] by Super 12993 with 4104 at 3,2
-Id : 13612, {_}: multiply ?21322 ?21323 ?21324 =<= multiply ?21324 (multiply ?21322 ?21323 ?21324) ?21323 [21324, 21323, 21322] by Demod 13062 with 6 at 2
-Id : 12903, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =>= multiply ?19864 ?19863 ?19862 [19862, 19863, 19864] by Demod 12777 with 84 at 3
-Id : 13625, {_}: multiply ?21368 ?21369 (multiply ?21367 ?21369 ?21368) =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Super 13612 with 12903 at 2,3
-Id : 13783, {_}: multiply ?21368 ?21369 ?21367 =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Demod 13625 with 12903 at 2
-Id : 34256, {_}: multiply (multiply ?56219 ?56220 ?56221) ?56222 ?56219 =<= multiply ?56219 ?56220 (multiply ?56221 ?56222 (multiply ?56223 ?56219 (inverse ?56220))) [56223, 56222, 56221, 56220, 56219] by Super 4 with 105 at 3,2
-Id : 34781, {_}: multiply (multiply ?57676 ?57677 ?57678) ?57678 ?57676 =>= multiply ?57676 ?57677 ?57678 [57678, 57677, 57676] by Super 34256 with 8 at 3,3
-Id : 34858, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =?= multiply ?57993 (multiply ?57992 ?57993 ?57994) ?57994 [57994, 57993, 57992] by Super 34781 with 4104 at 1,2
-Id : 35129, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =>= multiply ?57992 ?57993 ?57994 [57994, 57993, 57992] by Demod 34858 with 4104 at 3
-Id : 36343, {_}: multiply (multiply ?60132 ?60133 ?60134) ?60134 ?60133 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Super 13783 with 35129 at 2,3
-Id : 36700, {_}: multiply ?60132 ?60133 ?60134 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Demod 36343 with 35129 at 2
-Id : 36701, {_}: multiply ?60132 ?60133 ?60134 =<= multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134) [60134, 60133, 60132] by Demod 36700 with 35129 at 3
-Id : 136, {_}: multiply ?291 ?292 (multiply ?293 ?294 ?295) =<= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Demod 116 with 4 at 2
-Id : 2796, {_}: multiply ?5648 (inverse (inverse ?5650)) ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Super 625 with 2510 at 3,3
-Id : 2887, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Demod 2796 with 437 at 2,2
-Id : 2888, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 ?5650 ?5649) ?5648 [5649, 5650, 5648] by Demod 2887 with 437 at 2,2,3
-Id : 34853, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =?= multiply ?57973 (multiply ?57974 ?57973 ?57972) ?57974 [57972, 57973, 57974] by Super 34781 with 2888 at 1,2
-Id : 35120, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =>= multiply ?57974 ?57973 ?57972 [57972, 57973, 57974] by Demod 34853 with 2888 at 3
-Id : 35775, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =?= multiply ?59268 ?59269 (multiply ?59268 ?59269 ?59270) [59270, 59269, 59268] by Super 136 with 35120 at 3,3
-Id : 36064, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =>= multiply ?59268 ?59269 ?59270 [59270, 59269, 59268] by Demod 35775 with 84 at 3
-Id : 37436, {_}: multiply ?60132 ?60133 ?60134 =?= multiply ?60133 ?60134 ?60132 [60134, 60133, 60132] by Demod 36701 with 36064 at 3
-Id : 25, {_}: multiply ?84 ?85 ?86 =<= multiply ?84 ?85 (multiply ?86 (multiply ?84 ?85 ?86) ?87) [87, 86, 85, 84] by Super 4 with 8 at 2
-Id : 317, {_}: multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?848) =?= multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?845) [848, 847, 846, 845] by Super 298 with 25 at 3,3
-Id : 24761, {_}: multiply ?36657 (multiply ?36658 ?36659 ?36657) (multiply ?36658 ?36659 ?36660) =>= multiply ?36658 ?36659 ?36657 [36660, 36659, 36658, 36657] by Demod 317 with 6 at 3
-Id : 24766, {_}: multiply ?36681 (multiply ?36682 ?36683 ?36681) ?36682 =>= multiply ?36682 ?36683 ?36681 [36683, 36682, 36681] by Super 24761 with 12 at 3,2
-Id : 37850, {_}: multiply ?63783 ?63784 (multiply ?63783 ?63785 ?63784) =>= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Super 24766 with 37436 at 2
-Id : 37801, {_}: multiply ?63587 ?63589 (multiply ?63587 ?63588 ?63589) =>= multiply ?63587 ?63589 ?63588 [63588, 63589, 63587] by Super 12903 with 37436 at 3,2
-Id : 41412, {_}: multiply ?63783 ?63784 ?63785 =?= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Demod 37850 with 37801 at 2
-Id : 42484, {_}: b === b [] by Demod 42483 with 12 at 2
-Id : 42483, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 42482 with 41412 at 3,1,3,2
-Id : 42482, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 42481 with 41412 at 1,3,2
-Id : 42481, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 42480 with 41412 at 2,2
-Id : 42480, {_}: multiply b (multiply d (multiply g f e) c) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 38492 with 41412 at 2
-Id : 38492, {_}: multiply b (inverse (multiply d (multiply g e f) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38491 with 37436 at 2,1,2,2
-Id : 38491, {_}: multiply b (inverse (multiply d (multiply f g e) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38490 with 37436 at 2,1,2,2
-Id : 38490, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 595 with 37436 at 1,2,2
-Id : 595, {_}: multiply b (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 53 with 462 at 1,2
-Id : 53, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 2 with 4 at 1,2,2
-Id : 2, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
-% SZS output end CNFRefutation for BOO034-1.p
-Order
- == is 100
- _ is 99
- a is 97
- add is 96
- b is 98
- dn1 is 93
- huntinton_1 is 95
- inverse is 94
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-Found proof, 0.407895s
-% SZS status Unsatisfiable for BOO072-1.p
-% SZS output start CNFRefutation for BOO072-1.p
-Id : 5, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
-Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
-Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
-Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
-Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
-Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
-Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
-Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
-Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
-Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
-Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
-Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
-Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
-Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
-Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
-Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
-Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
-Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
-Id : 835, {_}: add (inverse ?1599) ?1600 =<= add ?1600 (inverse (add ?1599 (inverse (add (inverse ?1599) ?1600)))) [1600, 1599] by Demod 447 with 427 at 2
-Id : 839, {_}: add (inverse (inverse ?1617)) ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Super 835 with 427 at 1,1,2,1,2,3
-Id : 866, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Demod 839 with 427 at 1,2
-Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
-Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
-Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 443, {_}: inverse (inverse ?1079) =<= add (inverse (add ?1079 (inverse ?1079))) ?1079 [1079] by Super 441 with 22 at 1,2
-Id : 476, {_}: ?1141 =<= add (inverse (add ?1141 (inverse ?1141))) ?1141 [1141] by Demod 443 with 427 at 2
-Id : 483, {_}: inverse ?1163 =<= add (inverse (add (inverse ?1163) ?1163)) (inverse ?1163) [1163] by Super 476 with 427 at 2,1,1,3
-Id : 545, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1237)) ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Super 428 with 483 at 1,1,1,1,1,1,1,2
-Id : 596, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 545 with 427 at 1,1,1,1,1,1,2
-Id : 597, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) ?1237)) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 596 with 427 at 2,1,1,1,2
-Id : 1828, {_}: inverse (add (inverse (add (inverse (add ?2824 ?2825)) ?2824)) (inverse ?2824)) =>= ?2824 [2825, 2824] by Demod 597 with 427 at 3
-Id : 1862, {_}: inverse (add ?2924 (inverse (inverse (add ?2923 ?2924)))) =>= inverse (add ?2923 ?2924) [2923, 2924] by Super 1828 with 57 at 1,1,2
-Id : 1957, {_}: inverse (add ?2924 (add ?2923 ?2924)) =>= inverse (add ?2923 ?2924) [2923, 2924] by Demod 1862 with 427 at 2,1,2
-Id : 1989, {_}: inverse (inverse (add ?3044 ?3043)) =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Super 427 with 1957 at 1,2
-Id : 2126, {_}: add ?3204 ?3205 =<= add ?3205 (add ?3204 ?3205) [3205, 3204] by Demod 1989 with 427 at 2
-Id : 733, {_}: inverse ?1452 =<= add (inverse (add ?1453 ?1452)) (inverse (add (inverse ?1453) ?1452)) [1453, 1452] by Super 441 with 141 at 1,2
-Id : 738, {_}: inverse ?1475 =<= add (inverse (add (inverse ?1474) ?1475)) (inverse (add ?1474 ?1475)) [1474, 1475] by Super 733 with 427 at 1,1,2,3
-Id : 2134, {_}: add (inverse (add (inverse ?3224) ?3223)) (inverse (add ?3224 ?3223)) =>= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3223, 3224] by Super 2126 with 738 at 2,3
-Id : 2159, {_}: inverse ?3223 =<= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3224, 3223] by Demod 2134 with 738 at 2
-Id : 2197, {_}: inverse (add (inverse (inverse ?3289)) (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Super 57 with 2159 at 1,1,1,2
-Id : 2249, {_}: inverse (add ?3289 (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Demod 2197 with 427 at 1,1,2
-Id : 2455, {_}: add (inverse ?3654) (inverse (add ?3653 (inverse (inverse ?3654)))) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Super 459 with 2249 at 2,1,2,3
-Id : 2497, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2455 with 427 at 2,1,2,2
-Id : 2498, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2497 with 427 at 2,1,1,3
-Id : 2499, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 ?3654)) [3653, 3654] by Demod 2498 with 427 at 2,1,2,3
-Id : 2500, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =?= add (inverse (add ?3653 ?3654)) (inverse ?3654) [3653, 3654] by Demod 2499 with 418 at 1,2,3
-Id : 2501, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =>= inverse ?3654 [3653, 3654] by Demod 2500 with 2159 at 3
-Id : 2761, {_}: add (inverse ?4078) (inverse (add ?4079 ?4078)) =>= inverse ?4078 [4079, 4078] by Demod 2500 with 2159 at 3
-Id : 2775, {_}: add (inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Super 2761 with 4 at 2,2
-Id : 2871, {_}: add (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Demod 2775 with 427 at 1,2
-Id : 4872, {_}: add (add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487))))) ?6486 =>= add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487)))) [6487, 6486, 6485] by Demod 2871 with 427 at 3
-Id : 4906, {_}: add (inverse (inverse (add ?6624 ?6625))) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Super 4872 with 2501 at 1,2
-Id : 5128, {_}: add (add ?6624 ?6625) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Demod 4906 with 427 at 1,2
-Id : 5129, {_}: add (add ?6624 ?6625) ?6624 =>= inverse (inverse (add ?6624 ?6625)) [6625, 6624] by Demod 5128 with 2501 at 3
-Id : 5130, {_}: add (add ?6624 ?6625) ?6624 =>= add ?6624 ?6625 [6625, 6624] by Demod 5129 with 427 at 3
-Id : 5176, {_}: add (inverse ?6745) (inverse (add ?6745 ?6746)) =>= inverse ?6745 [6746, 6745] by Super 2501 with 5130 at 1,2,2
-Id : 5963, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (inverse ?1617)) [1618, 1617] by Demod 866 with 5176 at 1,2,3
-Id : 5973, {_}: add ?1617 ?1618 =?= add ?1618 ?1617 [1618, 1617] by Demod 5963 with 427 at 2,3
-Id : 6201, {_}: add a b === add a b [] by Demod 2 with 5973 at 2
-Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-% SZS output end CNFRefutation for BOO072-1.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 96
- b is 97
- c is 95
- dn1 is 92
- huntinton_2 is 94
- inverse is 93
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-Found proof, 88.886424s
-% SZS status Unsatisfiable for BOO073-1.p
-% SZS output start CNFRefutation for BOO073-1.p
-Id : 5, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
-Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
-Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
-Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
-Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
-Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
-Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
-Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
-Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
-Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
-Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
-Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
-Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
-Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
-Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
-Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
-Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
-Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
-Id : 835, {_}: add (inverse ?1599) ?1600 =<= add ?1600 (inverse (add ?1599 (inverse (add (inverse ?1599) ?1600)))) [1600, 1599] by Demod 447 with 427 at 2
-Id : 839, {_}: add (inverse (inverse ?1617)) ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Super 835 with 427 at 1,1,2,1,2,3
-Id : 866, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (add (inverse ?1617) (inverse (add ?1617 ?1618)))) [1618, 1617] by Demod 839 with 427 at 1,2
-Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
-Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
-Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 443, {_}: inverse (inverse ?1079) =<= add (inverse (add ?1079 (inverse ?1079))) ?1079 [1079] by Super 441 with 22 at 1,2
-Id : 476, {_}: ?1141 =<= add (inverse (add ?1141 (inverse ?1141))) ?1141 [1141] by Demod 443 with 427 at 2
-Id : 483, {_}: inverse ?1163 =<= add (inverse (add (inverse ?1163) ?1163)) (inverse ?1163) [1163] by Super 476 with 427 at 2,1,1,3
-Id : 545, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1237)) ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Super 428 with 483 at 1,1,1,1,1,1,1,2
-Id : 596, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) (inverse (inverse ?1237)))) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 545 with 427 at 1,1,1,1,1,1,2
-Id : 597, {_}: inverse (add (inverse (add (inverse (add ?1237 ?1238)) ?1237)) (inverse ?1237)) =>= inverse (inverse ?1237) [1238, 1237] by Demod 596 with 427 at 2,1,1,1,2
-Id : 1828, {_}: inverse (add (inverse (add (inverse (add ?2824 ?2825)) ?2824)) (inverse ?2824)) =>= ?2824 [2825, 2824] by Demod 597 with 427 at 3
-Id : 1862, {_}: inverse (add ?2924 (inverse (inverse (add ?2923 ?2924)))) =>= inverse (add ?2923 ?2924) [2923, 2924] by Super 1828 with 57 at 1,1,2
-Id : 1957, {_}: inverse (add ?2924 (add ?2923 ?2924)) =>= inverse (add ?2923 ?2924) [2923, 2924] by Demod 1862 with 427 at 2,1,2
-Id : 1989, {_}: inverse (inverse (add ?3044 ?3043)) =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Super 427 with 1957 at 1,2
-Id : 2126, {_}: add ?3204 ?3205 =<= add ?3205 (add ?3204 ?3205) [3205, 3204] by Demod 1989 with 427 at 2
-Id : 733, {_}: inverse ?1452 =<= add (inverse (add ?1453 ?1452)) (inverse (add (inverse ?1453) ?1452)) [1453, 1452] by Super 441 with 141 at 1,2
-Id : 738, {_}: inverse ?1475 =<= add (inverse (add (inverse ?1474) ?1475)) (inverse (add ?1474 ?1475)) [1474, 1475] by Super 733 with 427 at 1,1,2,3
-Id : 2134, {_}: add (inverse (add (inverse ?3224) ?3223)) (inverse (add ?3224 ?3223)) =>= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3223, 3224] by Super 2126 with 738 at 2,3
-Id : 2159, {_}: inverse ?3223 =<= add (inverse (add ?3224 ?3223)) (inverse ?3223) [3224, 3223] by Demod 2134 with 738 at 2
-Id : 2197, {_}: inverse (add (inverse (inverse ?3289)) (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Super 57 with 2159 at 1,1,1,2
-Id : 2249, {_}: inverse (add ?3289 (inverse (add ?3290 (inverse ?3289)))) =>= inverse ?3289 [3290, 3289] by Demod 2197 with 427 at 1,1,2
-Id : 2455, {_}: add (inverse ?3654) (inverse (add ?3653 (inverse (inverse ?3654)))) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Super 459 with 2249 at 2,1,2,3
-Id : 2497, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 (inverse (inverse ?3654)))) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2455 with 427 at 2,1,2,2
-Id : 2498, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 (inverse (inverse ?3654)))) [3653, 3654] by Demod 2497 with 427 at 2,1,1,3
-Id : 2499, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =<= add (inverse (add ?3653 ?3654)) (inverse (add ?3654 ?3654)) [3653, 3654] by Demod 2498 with 427 at 2,1,2,3
-Id : 2500, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =?= add (inverse (add ?3653 ?3654)) (inverse ?3654) [3653, 3654] by Demod 2499 with 418 at 1,2,3
-Id : 2501, {_}: add (inverse ?3654) (inverse (add ?3653 ?3654)) =>= inverse ?3654 [3653, 3654] by Demod 2500 with 2159 at 3
-Id : 2761, {_}: add (inverse ?4078) (inverse (add ?4079 ?4078)) =>= inverse ?4078 [4079, 4078] by Demod 2500 with 2159 at 3
-Id : 2775, {_}: add (inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Super 2761 with 4 at 2,2
-Id : 2871, {_}: add (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119))))) ?4118 =>= inverse (inverse (add ?4116 (inverse (add (inverse ?4118) (inverse (add ?4118 ?4119)))))) [4119, 4118, 4116] by Demod 2775 with 427 at 1,2
-Id : 4872, {_}: add (add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487))))) ?6486 =>= add ?6485 (inverse (add (inverse ?6486) (inverse (add ?6486 ?6487)))) [6487, 6486, 6485] by Demod 2871 with 427 at 3
-Id : 4906, {_}: add (inverse (inverse (add ?6624 ?6625))) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Super 4872 with 2501 at 1,2
-Id : 5128, {_}: add (add ?6624 ?6625) ?6624 =<= add (inverse (inverse (add ?6624 ?6625))) (inverse (add (inverse ?6624) (inverse (add ?6624 ?6625)))) [6625, 6624] by Demod 4906 with 427 at 1,2
-Id : 5129, {_}: add (add ?6624 ?6625) ?6624 =>= inverse (inverse (add ?6624 ?6625)) [6625, 6624] by Demod 5128 with 2501 at 3
-Id : 5130, {_}: add (add ?6624 ?6625) ?6624 =>= add ?6624 ?6625 [6625, 6624] by Demod 5129 with 427 at 3
-Id : 5176, {_}: add (inverse ?6745) (inverse (add ?6745 ?6746)) =>= inverse ?6745 [6746, 6745] by Super 2501 with 5130 at 1,2,2
-Id : 5963, {_}: add ?1617 ?1618 =<= add ?1618 (inverse (inverse ?1617)) [1618, 1617] by Demod 866 with 5176 at 1,2,3
-Id : 5973, {_}: add ?1617 ?1618 =?= add ?1618 ?1617 [1618, 1617] by Demod 5963 with 427 at 2,3
-Id : 445, {_}: inverse ?1086 =<= add (inverse (add (inverse (add ?1084 ?1085)) ?1086)) (inverse (add ?1084 ?1086)) [1085, 1084, 1086] by Super 441 with 57 at 1,2
-Id : 3282, {_}: inverse ?4640 =<= add (inverse (add (inverse (add ?4641 ?4642)) ?4640)) (inverse (add ?4641 ?4640)) [4642, 4641, 4640] by Super 441 with 57 at 1,2
-Id : 3306, {_}: inverse ?4739 =<= add (inverse (add (inverse (add ?4738 ?4740)) ?4739)) (inverse (add ?4740 ?4739)) [4740, 4738, 4739] by Super 3282 with 866 at 1,1,1,1,3
-Id : 9402, {_}: inverse (inverse (add ?10628 ?10626)) =<= add (inverse (inverse ?10626)) (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Super 445 with 3306 at 1,1,3
-Id : 9643, {_}: add ?10628 ?10626 =<= add (inverse (inverse ?10626)) (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Demod 9402 with 427 at 2
-Id : 9644, {_}: add ?10628 ?10626 =<= add ?10626 (inverse (add (inverse (add ?10627 ?10628)) (inverse (add ?10628 ?10626)))) [10627, 10626, 10628] by Demod 9643 with 427 at 1,3
-Id : 3277, {_}: add (inverse (add (inverse (add ?4621 ?4622)) ?4620)) (inverse (add ?4621 ?4620)) =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (inverse (add (inverse (add ?4621 ?4622)) ?4620))) (inverse (inverse ?4620)))) [4620, 4622, 4621] by Super 866 with 445 at 1,2,1,2,3
-Id : 3341, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (inverse (add (inverse (add ?4621 ?4622)) ?4620))) (inverse (inverse ?4620)))) [4622, 4621, 4620] by Demod 3277 with 445 at 2
-Id : 3342, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (add (inverse (add ?4621 ?4622)) ?4620) (inverse (inverse ?4620)))) [4622, 4621, 4620] by Demod 3341 with 427 at 1,1,2,3
-Id : 3343, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (add (inverse (add ?4621 ?4622)) ?4620) ?4620)) [4622, 4621, 4620] by Demod 3342 with 427 at 2,1,2,3
-Id : 2463, {_}: inverse (add ?3677 (inverse (add ?3678 (inverse ?3677)))) =>= inverse ?3677 [3678, 3677] by Demod 2197 with 427 at 1,1,2
-Id : 2485, {_}: inverse (add (add ?3744 ?3746) ?3746) =>= inverse (add ?3744 ?3746) [3746, 3744] by Super 2463 with 57 at 2,1,2
-Id : 2605, {_}: add (add ?3852 ?3853) ?3853 =<= add ?3853 (inverse (add (inverse (add ?3852 ?3853)) (inverse (add ?3852 ?3853)))) [3853, 3852] by Super 866 with 2485 at 2,1,2,3
-Id : 2630, {_}: add (add ?3852 ?3853) ?3853 =<= add ?3853 (inverse (inverse (add ?3852 ?3853))) [3853, 3852] by Demod 2605 with 418 at 1,2,3
-Id : 2631, {_}: add (add ?3852 ?3853) ?3853 =?= add ?3853 (add ?3852 ?3853) [3853, 3852] by Demod 2630 with 427 at 2,3
-Id : 2044, {_}: add ?3044 ?3043 =<= add ?3043 (add ?3044 ?3043) [3043, 3044] by Demod 1989 with 427 at 2
-Id : 2632, {_}: add (add ?3852 ?3853) ?3853 =>= add ?3852 ?3853 [3853, 3852] by Demod 2631 with 2044 at 3
-Id : 3344, {_}: inverse ?4620 =<= add (inverse (add ?4621 ?4620)) (inverse (add (inverse (add ?4621 ?4622)) ?4620)) [4622, 4621, 4620] by Demod 3343 with 2632 at 1,2,3
-Id : 9856, {_}: inverse (inverse (add (inverse (add ?11316 ?11317)) ?11315)) =<= add (inverse (inverse ?11315)) (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Super 445 with 3344 at 1,1,3
-Id : 10050, {_}: add (inverse (add ?11316 ?11317)) ?11315 =<= add (inverse (inverse ?11315)) (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Demod 9856 with 427 at 2
-Id : 10051, {_}: add (inverse (add ?11316 ?11317)) ?11315 =<= add ?11315 (inverse (add ?11316 (inverse (add (inverse (add ?11316 ?11317)) ?11315)))) [11315, 11317, 11316] by Demod 10050 with 427 at 1,3
-Id : 27274, {_}: add (inverse (add ?27240 ?27241)) ?27242 =<= add ?27242 (inverse (add ?27240 (inverse (add (inverse (add ?27240 ?27241)) ?27242)))) [27242, 27241, 27240] by Demod 10050 with 427 at 1,3
-Id : 446, {_}: inverse ?1089 =<= add (inverse (add ?1088 ?1089)) (inverse (add (inverse ?1088) ?1089)) [1088, 1089] by Super 441 with 141 at 1,2
-Id : 3303, {_}: inverse ?4728 =<= add (inverse (add (inverse (inverse ?4726)) ?4728)) (inverse (add (inverse (add ?4727 ?4726)) ?4728)) [4727, 4726, 4728] by Super 3282 with 446 at 1,1,1,1,3
-Id : 3407, {_}: inverse ?4728 =<= add (inverse (add ?4726 ?4728)) (inverse (add (inverse (add ?4727 ?4726)) ?4728)) [4727, 4726, 4728] by Demod 3303 with 427 at 1,1,1,3
-Id : 27388, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= add ?27679 (inverse (inverse ?27679)) [27679, 27678] by Super 27274 with 3407 at 1,2,3
-Id : 27835, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= add ?27679 ?27679 [27679, 27678] by Demod 27388 with 427 at 2,3
-Id : 27836, {_}: add (inverse (add (inverse (add ?27678 ?27679)) ?27678)) ?27679 =>= ?27679 [27679, 27678] by Demod 27835 with 418 at 3
-Id : 35831, {_}: add ?35916 (inverse (add (inverse (add ?35917 ?35916)) ?35917)) =>= ?35916 [35917, 35916] by Super 5973 with 27836 at 3
-Id : 35837, {_}: add ?35933 (inverse (add (inverse (add ?35933 ?35934)) ?35934)) =>= ?35933 [35934, 35933] by Super 35831 with 5973 at 1,1,1,2,2
-Id : 43017, {_}: add (inverse (add ?44930 ?44931)) ?44931 =>= add ?44931 (inverse ?44930) [44931, 44930] by Super 10051 with 35837 at 1,2,3
-Id : 43043, {_}: add (inverse (inverse ?45008)) (inverse ?45008) =<= add (inverse ?45008) (inverse (inverse (add ?45009 ?45008))) [45009, 45008] by Super 43017 with 2159 at 1,1,2
-Id : 43373, {_}: add ?45008 (inverse ?45008) =<= add (inverse ?45008) (inverse (inverse (add ?45009 ?45008))) [45009, 45008] by Demod 43043 with 427 at 1,2
-Id : 44805, {_}: add ?46602 (inverse ?46602) =<= add (inverse ?46602) (add ?46603 ?46602) [46603, 46602] by Demod 43373 with 427 at 2,3
-Id : 895, {_}: inverse (inverse (add ?1666 ?1665)) =<= add (inverse (inverse ?1665)) (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Super 446 with 738 at 1,1,3
-Id : 960, {_}: add ?1666 ?1665 =<= add (inverse (inverse ?1665)) (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 895 with 427 at 2
-Id : 961, {_}: add ?1666 ?1665 =<= add ?1665 (inverse (add (inverse (inverse (add (inverse ?1666) ?1665))) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 960 with 427 at 1,3
-Id : 962, {_}: add ?1666 ?1665 =<= add ?1665 (inverse (add (add (inverse ?1666) ?1665) (inverse (add ?1666 ?1665)))) [1665, 1666] by Demod 961 with 427 at 1,1,2,3
-Id : 5181, {_}: add (add ?6762 ?6763) ?6762 =<= add ?6762 (inverse (add (add (inverse (add ?6762 ?6763)) ?6762) (inverse (add ?6762 ?6763)))) [6763, 6762] by Super 962 with 5130 at 1,2,1,2,3
-Id : 5222, {_}: add ?6762 ?6763 =<= add ?6762 (inverse (add (add (inverse (add ?6762 ?6763)) ?6762) (inverse (add ?6762 ?6763)))) [6763, 6762] by Demod 5181 with 5130 at 2
-Id : 6255, {_}: add ?7893 ?7894 =<= add ?7893 (inverse (add (inverse (add ?7893 ?7894)) ?7893)) [7894, 7893] by Demod 5222 with 5130 at 1,2,3
-Id : 6261, {_}: add ?7910 ?7911 =<= add ?7910 (inverse (add (inverse (add ?7911 ?7910)) ?7910)) [7911, 7910] by Super 6255 with 5973 at 1,1,1,2,3
-Id : 27395, {_}: add (inverse (add ?27697 ?27698)) (inverse (add ?27698 ?27697)) =?= add (inverse (add ?27698 ?27697)) (inverse (add ?27698 ?27697)) [27698, 27697] by Super 27274 with 9644 at 1,2,3
-Id : 27857, {_}: add (inverse (add ?27697 ?27698)) (inverse (add ?27698 ?27697)) =>= inverse (add ?27698 ?27697) [27698, 27697] by Demod 27395 with 418 at 3
-Id : 28327, {_}: add (inverse (add ?28496 ?28495)) (inverse (add ?28495 ?28496)) =<= add (inverse (add ?28496 ?28495)) (inverse (add (inverse (inverse (add ?28496 ?28495))) (inverse (add ?28496 ?28495)))) [28495, 28496] by Super 6261 with 27857 at 1,1,1,2,3
-Id : 28628, {_}: inverse (add ?28495 ?28496) =<= add (inverse (add ?28496 ?28495)) (inverse (add (inverse (inverse (add ?28496 ?28495))) (inverse (add ?28496 ?28495)))) [28496, 28495] by Demod 28327 with 27857 at 2
-Id : 2450, {_}: inverse (inverse ?3637) =<= add ?3637 (inverse (add ?3638 (inverse ?3637))) [3638, 3637] by Super 427 with 2249 at 1,2
-Id : 2506, {_}: ?3637 =<= add ?3637 (inverse (add ?3638 (inverse ?3637))) [3638, 3637] by Demod 2450 with 427 at 2
-Id : 5163, {_}: ?6702 =<= add ?6702 (inverse (add (inverse ?6702) ?6701)) [6701, 6702] by Super 2506 with 5130 at 1,2,3
-Id : 28629, {_}: inverse (add ?28495 ?28496) =?= inverse (add ?28496 ?28495) [28496, 28495] by Demod 28628 with 5163 at 3
-Id : 44870, {_}: add (add ?46807 ?46808) (inverse (add ?46807 ?46808)) =<= add (inverse (add ?46808 ?46807)) (add ?46809 (add ?46807 ?46808)) [46809, 46808, 46807] by Super 44805 with 28629 at 1,3
-Id : 45240, {_}: add (inverse (add ?46807 ?46808)) (add ?46807 ?46808) =<= add (inverse (add ?46808 ?46807)) (add ?46809 (add ?46807 ?46808)) [46809, 46808, 46807] by Demod 44870 with 5973 at 2
-Id : 75570, {_}: inverse (add ?71946 (add ?71944 ?71945)) =<= add (inverse (add ?71945 (add ?71946 (add ?71944 ?71945)))) (inverse (add (inverse (add ?71944 ?71945)) (add ?71944 ?71945))) [71945, 71944, 71946] by Super 3344 with 45240 at 1,2,3
-Id : 2205, {_}: inverse ?3320 =<= add (inverse (add ?3321 ?3320)) (inverse ?3320) [3321, 3320] by Demod 2134 with 738 at 2
-Id : 2209, {_}: inverse (inverse ?3338) =<= add (inverse (add ?3339 (inverse ?3338))) ?3338 [3339, 3338] by Super 2205 with 427 at 2,3
-Id : 2281, {_}: ?3338 =<= add (inverse (add ?3339 (inverse ?3338))) ?3338 [3339, 3338] by Demod 2209 with 427 at 2
-Id : 5175, {_}: ?6743 =<= add (inverse (add (inverse ?6743) ?6742)) ?6743 [6742, 6743] by Super 2281 with 5130 at 1,1,3
-Id : 43053, {_}: add (inverse ?45043) ?45043 =<= add ?45043 (inverse (inverse (add (inverse ?45043) ?45042))) [45042, 45043] by Super 43017 with 5175 at 1,1,2
-Id : 43393, {_}: add (inverse ?45043) ?45043 =<= add ?45043 (add (inverse ?45043) ?45042) [45042, 45043] by Demod 43053 with 427 at 2,3
-Id : 46219, {_}: add (add (inverse ?47976) ?47977) ?47976 =>= add (inverse ?47976) ?47976 [47977, 47976] by Super 5973 with 43393 at 3
-Id : 2228, {_}: inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389)))))) =<= add ?3388 (inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389))))))) [3389, 3388, 3386] by Super 2205 with 4 at 1,3
-Id : 2327, {_}: add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389)))) =<= add ?3388 (inverse (inverse (add ?3386 (inverse (add (inverse ?3388) (inverse (add ?3388 ?3389))))))) [3389, 3388, 3386] by Demod 2228 with 427 at 2
-Id : 4116, {_}: add ?5774 (inverse (add (inverse ?5775) (inverse (add ?5775 ?5776)))) =<= add ?5775 (add ?5774 (inverse (add (inverse ?5775) (inverse (add ?5775 ?5776))))) [5776, 5775, 5774] by Demod 2327 with 427 at 2,3
-Id : 4147, {_}: add (inverse (inverse (add ?5900 ?5901))) (inverse (add (inverse ?5900) (inverse (add ?5900 ?5901)))) =>= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Super 4116 with 2501 at 2,3
-Id : 4368, {_}: inverse (inverse (add ?5900 ?5901)) =<= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Demod 4147 with 2501 at 2
-Id : 4369, {_}: add ?5900 ?5901 =<= add ?5900 (inverse (inverse (add ?5900 ?5901))) [5901, 5900] by Demod 4368 with 427 at 2
-Id : 4370, {_}: add ?5900 ?5901 =<= add ?5900 (add ?5900 ?5901) [5901, 5900] by Demod 4369 with 427 at 2,3
-Id : 43050, {_}: add (inverse (add ?45034 ?45033)) (add ?45034 ?45033) =>= add (add ?45034 ?45033) (inverse ?45034) [45033, 45034] by Super 43017 with 4370 at 1,1,2
-Id : 43389, {_}: add (inverse (add ?45034 ?45033)) (add ?45034 ?45033) =>= add (inverse ?45034) (add ?45034 ?45033) [45033, 45034] by Demod 43050 with 5973 at 3
-Id : 43042, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add (add ?45005 ?45006) (inverse ?45006) [45006, 45005] by Super 43017 with 2044 at 1,1,2
-Id : 43372, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add (inverse ?45006) (add ?45005 ?45006) [45006, 45005] by Demod 43042 with 5973 at 3
-Id : 43374, {_}: add ?45008 (inverse ?45008) =<= add (inverse ?45008) (add ?45009 ?45008) [45009, 45008] by Demod 43373 with 427 at 2,3
-Id : 48043, {_}: add (inverse (add ?45005 ?45006)) (add ?45005 ?45006) =>= add ?45006 (inverse ?45006) [45006, 45005] by Demod 43372 with 43374 at 3
-Id : 49303, {_}: add ?45033 (inverse ?45033) =?= add (inverse ?45034) (add ?45034 ?45033) [45034, 45033] by Demod 43389 with 48043 at 2
-Id : 5166, {_}: inverse ?6709 =<= add (inverse (add ?6709 ?6710)) (inverse ?6709) [6710, 6709] by Super 2159 with 5130 at 1,1,3
-Id : 43052, {_}: add (inverse (inverse ?45039)) (inverse ?45039) =<= add (inverse ?45039) (inverse (inverse (add ?45039 ?45040))) [45040, 45039] by Super 43017 with 5166 at 1,1,2
-Id : 43391, {_}: add ?45039 (inverse ?45039) =<= add (inverse ?45039) (inverse (inverse (add ?45039 ?45040))) [45040, 45039] by Demod 43052 with 427 at 1,2
-Id : 43392, {_}: add ?45039 (inverse ?45039) =<= add (inverse ?45039) (add ?45039 ?45040) [45040, 45039] by Demod 43391 with 427 at 2,3
-Id : 49304, {_}: add ?45033 (inverse ?45033) =?= add ?45034 (inverse ?45034) [45034, 45033] by Demod 49303 with 43392 at 3
-Id : 49415, {_}: ?50953 =<= add (inverse (add ?50954 (inverse ?50954))) ?50953 [50954, 50953] by Super 2281 with 49304 at 1,1,3
-Id : 50053, {_}: add ?51918 (add ?51919 (inverse ?51919)) =?= add (inverse (add ?51919 (inverse ?51919))) (add ?51919 (inverse ?51919)) [51919, 51918] by Super 46219 with 49415 at 1,2
-Id : 50133, {_}: add ?51918 (add ?51919 (inverse ?51919)) =?= add (inverse ?51919) (inverse (inverse ?51919)) [51919, 51918] by Demod 50053 with 48043 at 3
-Id : 50134, {_}: add ?51918 (add ?51919 (inverse ?51919)) =>= add (inverse ?51919) ?51919 [51919, 51918] by Demod 50133 with 427 at 2,3
-Id : 50710, {_}: ?52352 =<= add ?52352 (inverse (add (inverse ?52351) ?52351)) [52351, 52352] by Super 5163 with 50134 at 1,2,3
-Id : 75914, {_}: inverse (add ?71946 (add ?71944 ?71945)) =<= inverse (add ?71945 (add ?71946 (add ?71944 ?71945))) [71945, 71944, 71946] by Demod 75570 with 50710 at 3
-Id : 77144, {_}: add ?73328 (add ?73326 (add ?73327 ?73328)) =<= add (add ?73326 (add ?73327 ?73328)) (inverse (add (inverse (add ?73329 ?73328)) (inverse (add ?73326 (add ?73327 ?73328))))) [73329, 73327, 73326, 73328] by Super 9644 with 75914 at 2,1,2,3
-Id : 77399, {_}: add ?73328 (add ?73326 (add ?73327 ?73328)) =<= add (inverse (add (inverse (add ?73329 ?73328)) (inverse (add ?73326 (add ?73327 ?73328))))) (add ?73326 (add ?73327 ?73328)) [73329, 73327, 73326, 73328] by Demod 77144 with 5973 at 3
-Id : 77889, {_}: add ?74480 (add ?74481 (add ?74482 ?74480)) =>= add ?74481 (add ?74482 ?74480) [74482, 74481, 74480] by Demod 77399 with 2281 at 3
-Id : 77893, {_}: add ?74496 (add ?74497 (add ?74496 ?74495)) =?= add ?74497 (add (add ?74496 ?74495) ?74496) [74495, 74497, 74496] by Super 77889 with 5130 at 2,2,2
-Id : 78169, {_}: add ?74496 (add ?74497 (add ?74496 ?74495)) =>= add ?74497 (add ?74496 ?74495) [74495, 74497, 74496] by Demod 77893 with 5130 at 2,3
-Id : 77895, {_}: add ?74503 (add ?74504 (add ?74503 ?74505)) =>= add ?74504 (add ?74505 ?74503) [74505, 74504, 74503] by Super 77889 with 5973 at 2,2,2
-Id : 80396, {_}: add ?74497 (add ?74495 ?74496) =?= add ?74497 (add ?74496 ?74495) [74496, 74495, 74497] by Demod 78169 with 77895 at 2
-Id : 80521, {_}: add (add (add ?78514 ?78515) ?78516) (add ?78515 ?78514) =>= add (add ?78514 ?78515) ?78516 [78516, 78515, 78514] by Super 5130 with 80396 at 2
-Id : 79247, {_}: add ?76425 (add ?76426 (add ?76425 ?76427)) =>= add ?76426 (add ?76427 ?76425) [76427, 76426, 76425] by Super 77889 with 5973 at 2,2,2
-Id : 79331, {_}: add ?76775 (add (add ?76775 ?76776) ?76774) =<= add (add (add ?76775 ?76776) ?76774) (add ?76776 ?76775) [76774, 76776, 76775] by Super 79247 with 5130 at 2,2
-Id : 79332, {_}: add ?76778 (add (add ?76778 ?76780) ?76779) =>= add ?76779 (add ?76780 ?76778) [76779, 76780, 76778] by Super 79247 with 5973 at 2,2
-Id : 135898, {_}: add ?76774 (add ?76776 ?76775) =<= add (add (add ?76775 ?76776) ?76774) (add ?76776 ?76775) [76775, 76776, 76774] by Demod 79331 with 79332 at 2
-Id : 140658, {_}: add ?78516 (add ?78515 ?78514) =?= add (add ?78514 ?78515) ?78516 [78514, 78515, 78516] by Demod 80521 with 135898 at 2
-Id : 43039, {_}: add (inverse (inverse ?44995)) (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) [44997, 44996, 44995] by Super 43017 with 445 at 1,1,2
-Id : 43360, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) [44997, 44996, 44995] by Demod 43039 with 427 at 1,2
-Id : 43361, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (inverse (add (inverse (add ?44996 ?44997)) ?44995))) (inverse (add ?44996 ?44995)) [44997, 44996, 44995] by Demod 43360 with 5973 at 3
-Id : 43362, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (add (inverse (add ?44996 ?44997)) ?44995) (inverse (add ?44996 ?44995)) [44997, 44996, 44995] by Demod 43361 with 427 at 1,3
-Id : 43363, {_}: add ?44995 (inverse (add ?44996 ?44995)) =<= add (inverse (add ?44996 ?44995)) (add (inverse (add ?44996 ?44997)) ?44995) [44997, 44996, 44995] by Demod 43362 with 5973 at 3
-Id : 42258, {_}: add (inverse (add ?43873 ?43874)) ?43874 =>= add ?43874 (inverse ?43873) [43874, 43873] by Super 10051 with 35837 at 1,2,3
-Id : 42969, {_}: add ?44778 (inverse (add ?44777 ?44778)) =>= add ?44778 (inverse ?44777) [44777, 44778] by Super 5973 with 42258 at 3
-Id : 415299, {_}: add ?44995 (inverse ?44996) =<= add (inverse (add ?44996 ?44995)) (add (inverse (add ?44996 ?44997)) ?44995) [44997, 44996, 44995] by Demod 43363 with 42969 at 2
-Id : 415494, {_}: add (inverse (add ?628669 ?628668)) (add (inverse (add ?628669 ?628670)) ?628668) =<= add (add (inverse (add ?628669 ?628670)) ?628668) (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) [628670, 628668, 628669] by Super 10051 with 415299 at 1,2,1,2,3
-Id : 416655, {_}: add ?628668 (inverse ?628669) =<= add (add (inverse (add ?628669 ?628670)) ?628668) (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) [628670, 628669, 628668] by Demod 415494 with 415299 at 2
-Id : 416656, {_}: add ?628668 (inverse ?628669) =<= add (inverse (add ?628669 (inverse (add ?628668 (inverse ?628669))))) (add (inverse (add ?628669 ?628670)) ?628668) [628670, 628669, 628668] by Demod 416655 with 5973 at 3
-Id : 418876, {_}: add ?634385 (inverse ?634386) =<= add (inverse ?634386) (add (inverse (add ?634386 ?634387)) ?634385) [634387, 634386, 634385] by Demod 416656 with 2506 at 1,1,3
-Id : 9436, {_}: inverse ?10759 =<= add (inverse (add (inverse (add ?10760 ?10761)) ?10759)) (inverse (add ?10761 ?10759)) [10761, 10760, 10759] by Super 3282 with 866 at 1,1,1,1,3
-Id : 18533, {_}: inverse ?18554 =<= add (inverse (add (inverse (add ?18555 ?18556)) ?18554)) (inverse (add ?18554 ?18556)) [18556, 18555, 18554] by Super 9436 with 5973 at 1,2,3
-Id : 18582, {_}: inverse ?18755 =<= add (inverse (add (inverse ?18756) ?18755)) (inverse (add ?18755 ?18756)) [18756, 18755] by Super 18533 with 418 at 1,1,1,1,3
-Id : 19155, {_}: add (inverse (add ?19200 ?19201)) (inverse (add (inverse ?19201) ?19200)) =>= inverse ?19200 [19201, 19200] by Super 5973 with 18582 at 3
-Id : 418883, {_}: add ?634414 (inverse (inverse (add ?634412 ?634413))) =<= add (inverse (inverse (add ?634412 ?634413))) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Super 418876 with 19155 at 1,1,2,3
-Id : 420154, {_}: add ?634414 (add ?634412 ?634413) =<= add (inverse (inverse (add ?634412 ?634413))) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Demod 418883 with 427 at 2,2
-Id : 420155, {_}: add ?634414 (add ?634412 ?634413) =<= add (add ?634412 ?634413) (add (inverse (inverse ?634412)) ?634414) [634413, 634412, 634414] by Demod 420154 with 427 at 1,3
-Id : 420156, {_}: add ?634414 (add ?634412 ?634413) =<= add (add ?634412 ?634413) (add ?634412 ?634414) [634413, 634412, 634414] by Demod 420155 with 427 at 1,2,3
-Id : 421396, {_}: add (add ?637936 ?637935) (add ?637937 ?637936) =>= add ?637935 (add ?637936 ?637937) [637937, 637935, 637936] by Super 140658 with 420156 at 3
-Id : 421337, {_}: add (add ?637673 ?637674) (add ?637672 ?637673) =>= add ?637672 (add ?637673 ?637674) [637672, 637674, 637673] by Super 80396 with 420156 at 3
-Id : 428375, {_}: add ?637937 (add ?637936 ?637935) =?= add ?637935 (add ?637936 ?637937) [637935, 637936, 637937] by Demod 421396 with 421337 at 2
-Id : 421398, {_}: add ?637944 (add ?637945 ?637946) =<= add (add ?637944 ?637945) (add ?637945 ?637946) [637946, 637945, 637944] by Super 140658 with 420156 at 2
-Id : 418964, {_}: add ?634834 (inverse (inverse (add ?634833 ?634832))) =<= add (inverse (inverse (add ?634833 ?634832))) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Super 418876 with 446 at 1,1,2,3
-Id : 420298, {_}: add ?634834 (add ?634833 ?634832) =<= add (inverse (inverse (add ?634833 ?634832))) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Demod 418964 with 427 at 2,2
-Id : 420299, {_}: add ?634834 (add ?634833 ?634832) =<= add (add ?634833 ?634832) (add (inverse (inverse ?634832)) ?634834) [634832, 634833, 634834] by Demod 420298 with 427 at 1,3
-Id : 420300, {_}: add ?634834 (add ?634833 ?634832) =<= add (add ?634833 ?634832) (add ?634832 ?634834) [634832, 634833, 634834] by Demod 420299 with 427 at 1,2,3
-Id : 431824, {_}: add ?637944 (add ?637945 ?637946) =?= add ?637946 (add ?637944 ?637945) [637946, 637945, 637944] by Demod 421398 with 420300 at 3
-Id : 435227, {_}: add c (add b a) === add c (add b a) [] by Demod 435226 with 80396 at 3
-Id : 435226, {_}: add c (add b a) =<= add c (add a b) [] by Demod 431823 with 431824 at 3
-Id : 431823, {_}: add c (add b a) =<= add b (add c a) [] by Demod 6203 with 428375 at 3
-Id : 6203, {_}: add c (add b a) =<= add a (add c b) [] by Demod 6202 with 5973 at 2,3
-Id : 6202, {_}: add c (add b a) =<= add a (add b c) [] by Demod 6201 with 5973 at 2,2
-Id : 6201, {_}: add c (add a b) =<= add a (add b c) [] by Demod 2 with 5973 at 2
-Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-% SZS output end CNFRefutation for BOO073-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- nand is 95
- prove_meredith_2_basis_2 is 94
- sh_1 is 93
-Facts
- Id : 4, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-Last chance: 1246125322.97
-Last chance: all is indexed 1246125342.97
-Last chance: failed over 100 goal 1246125342.97
-FAILURE in 0 iterations
-% SZS status Timeout for BOO076-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246125613.41
-Last chance: all is indexed 1246125633.41
-Last chance: failed over 100 goal 1246125633.41
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-12.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246125903.86
-Last chance: all is indexed 1246125923.87
-Last chance: failed over 100 goal 1246125924.12
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246126194.44
-Last chance: all is indexed 1246126214.45
-Last chance: failed over 100 goal 1246126214.45
-FAILURE in 0 iterations
-% SZS status Timeout for COL003-20.p
-Order
- == is 100
- _ is 99
- apply is 96
- fixed_pt is 97
- k is 92
- k_definition is 91
- prove_strong_fixed_point is 95
- s is 94
- s_definition is 93
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
- Id : 6, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246126485.35
-Last chance: all is indexed 1246126505.41
-Last chance: failed over 100 goal 1246126505.41
-FAILURE in 0 iterations
-% SZS status Timeout for COL006-6.p
-Order
- == is 100
- _ is 99
- apply is 97
- combinator is 98
- o is 95
- o_definition is 94
- prove_fixed_point is 96
- q1 is 93
- q1_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
- Id : 6, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-Goal
- Id : 2, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-Last chance: 1246126776.98
-Last chance: all is indexed 1246126796.99
-Last chance: failed over 100 goal 1246126797.08
-FAILURE in 0 iterations
-% SZS status Timeout for COL011-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246127067.89
-Last chance: all is indexed 1246127087.95
-Last chance: failed over 100 goal 1246127088.09
-FAILURE in 0 iterations
-% SZS status Timeout for COL037-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 93
- m_definition is 92
- prove_fixed_point is 96
- v is 91
- v_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
- Id : 8, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246127360.45
-Last chance: all is indexed 1246127380.5
-Last chance: failed over 100 goal 1246127380.54
-FAILURE in 0 iterations
-% SZS status Timeout for COL038-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- h is 92
- h_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246127651.76
-Last chance: all is indexed 1246127671.76
-Last chance: failed over 100 goal 1246127671.76
-FAILURE in 0 iterations
-% SZS status Timeout for COL043-3.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- n is 92
- n_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Last chance: 1246127942.43
-Last chance: all is indexed 1246127962.43
-Last chance: failed over 100 goal 1246127962.43
-FAILURE in 0 iterations
-% SZS status Timeout for COL044-8.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- m is 91
- m_definition is 90
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Last chance: 1246128232.93
-Last chance: all is indexed 1246128253.01
-Last chance: failed over 100 goal 1246128253.19
-FAILURE in 0 iterations
-% SZS status Timeout for COL046-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 91
- m_definition is 90
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
- Id : 8, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246128524.07
-Last chance: all is indexed 1246128544.07
-Last chance: failed over 100 goal 1246128544.25
-FAILURE in 0 iterations
-% SZS status Timeout for COL049-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- i is 89
- i_definition is 88
- prove_strong_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
- Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Last chance: 1246128814.63
-Last chance: all is indexed 1246128834.73
-Goal subsumed
-Found proof, 290.682237s
-% SZS status Unsatisfiable for COL057-1.p
-% SZS output start CNFRefutation for COL057-1.p
-Id : 6, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
-Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Id : 4, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
-Id : 35, {_}: apply (apply (apply s i) ?113) ?112 =?= apply ?112 (apply ?113 ?112) [112, 113] by Super 4 with 10 at 1,3
-Id : 34, {_}: apply (apply (apply s ?110) i) ?109 =?= apply (apply ?110 ?109) ?109 [109, 110] by Super 4 with 10 at 2,3
-Id : 56, {_}: apply (apply (apply s (apply b ?164)) i) ?163 =?= apply ?164 (apply ?163 ?163) [163, 164] by Super 6 with 34 at 2
-Id : 761617, {_}: apply (apply (apply s i) (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i))) (f (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i))) === apply (apply (apply s i) (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i))) (f (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i))) [] by Super 4653 with 56 at 1,2
-Id : 4653, {_}: apply ?3570 (f ?3570) =<= apply (apply (apply s i) ?3570) (f ?3570) [3570] by Super 2 with 35 at 3
-Id : 2, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
-% SZS output end CNFRefutation for COL057-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-Goal subsumed
-Found proof, 0.123092s
-% SZS status Unsatisfiable for COL060-1.p
-% SZS output start CNFRefutation for COL060-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 410, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 408 with 4 at 2
-Id : 408, {_}: apply (apply (apply ?1205 (g (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1205)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1205)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1205)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1205)) (apply (apply b b) t)))) [1205] by Super 389 with 6 at 1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (apply (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (apply (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (g (apply (apply b (apply t ?57)) ?58)) (apply (f (apply (apply b (apply t ?57)) ?58)) (h (apply (apply b (apply t ?57)) ?58))) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (g (apply (apply b ?24) ?25)) (apply (f (apply (apply b ?24) ?25)) (h (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
-% SZS output end CNFRefutation for COL060-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q1_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-Goal subsumed
-Found proof, 0.122812s
-% SZS status Unsatisfiable for COL061-1.p
-% SZS output start CNFRefutation for COL061-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 410, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 409 with 6 at 2,2
-Id : 409, {_}: apply (f (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (apply (apply ?1207 (g (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1207)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1207)) (apply (apply b b) b)))) [1207] by Super 389 with 4 at 2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (f (apply (apply b (apply t ?57)) ?58)) (apply (h (apply (apply b (apply t ?57)) ?58)) (g (apply (apply b (apply t ?57)) ?58))) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (f (apply (apply b ?24) ?25)) (apply (h (apply (apply b ?24) ?25)) (g (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
-% SZS output end CNFRefutation for COL061-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_f_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-Goal subsumed
-Found proof, 2.025852s
-% SZS status Unsatisfiable for COL063-1.p
-% SZS output start CNFRefutation for COL063-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 3084, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3079 with 6 at 2
-Id : 3079, {_}: apply (apply ?9991 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?9991)))) [9991] by Super 3059 with 6 at 2,2
-Id : 3059, {_}: apply (apply ?9940 (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (apply (apply ?9941 (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) =>= apply (apply (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) [9941, 9940] by Super 405 with 4 at 2
-Id : 405, {_}: apply (apply (apply ?1195 (apply ?1196 (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (apply ?1197 (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) =>= apply (apply (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196))))) (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) [1197, 1196, 1195] by Super 389 with 4 at 1,1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (apply (h (apply (apply b (apply t ?57)) ?58)) (g (apply (apply b (apply t ?57)) ?58))) (f (apply (apply b (apply t ?57)) ?58)) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (apply (h (apply (apply b ?24) ?25)) (g (apply (apply b ?24) ?25))) (f (apply (apply b ?24) ?25)) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
-% SZS output end CNFRefutation for COL063-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_v_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-Goal subsumed
-Found proof, 14.670988s
-% SZS status Unsatisfiable for COL064-1.p
-% SZS output start CNFRefutation for COL064-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 10866, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10865 with 6 at 2
-Id : 10865, {_}: apply (apply ?36992 (g (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?36992))) (apply (apply b b) (apply (apply b b) t)))) [36992] by Super 3088 with 4 at 2
-Id : 3088, {_}: apply (apply (apply ?10013 (apply ?10014 (g (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10013) ?10014))) (apply (apply b b) (apply (apply b b) t)))) [10014, 10013] by Super 3083 with 4 at 1,1,2
-Id : 3083, {_}: apply (apply (apply ?10003 (g (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10003)) (apply (apply b b) (apply (apply b b) t)))) [10003] by Super 3059 with 6 at 2
-Id : 3059, {_}: apply (apply ?9940 (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (apply (apply ?9941 (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) =>= apply (apply (h (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) (f (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940))))) (g (apply (apply b (apply t ?9941)) (apply (apply b b) (apply (apply b b) ?9940)))) [9941, 9940] by Super 405 with 4 at 2
-Id : 405, {_}: apply (apply (apply ?1195 (apply ?1196 (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (apply ?1197 (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))))) (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) =>= apply (apply (h (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) (f (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196))))) (g (apply (apply b (apply t ?1197)) (apply (apply b b) (apply (apply b ?1195) ?1196)))) [1197, 1196, 1195] by Super 389 with 4 at 1,1,2
-Id : 389, {_}: apply (apply (apply ?1151 (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (apply ?1152 (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))))) (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) =>= apply (apply (h (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) (f (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151)))) (g (apply (apply b (apply t ?1152)) (apply (apply b b) ?1151))) [1152, 1151] by Super 50 with 4 at 1,2
-Id : 50, {_}: apply (apply (apply (apply ?123 (apply ?124 (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))))) ?125) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) =>= apply (apply (h (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) (f (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124)))) (g (apply (apply b (apply t ?125)) (apply (apply b ?123) ?124))) [125, 124, 123] by Super 25 with 4 at 1,1,1,2
-Id : 25, {_}: apply (apply (apply (apply ?58 (f (apply (apply b (apply t ?57)) ?58))) ?57) (g (apply (apply b (apply t ?57)) ?58))) (h (apply (apply b (apply t ?57)) ?58)) =>= apply (apply (h (apply (apply b (apply t ?57)) ?58)) (f (apply (apply b (apply t ?57)) ?58))) (g (apply (apply b (apply t ?57)) ?58)) [57, 58] by Super 11 with 6 at 1,1,2
-Id : 11, {_}: apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25)) =>= apply (apply (h (apply (apply b ?24) ?25)) (f (apply (apply b ?24) ?25))) (g (apply (apply b ?24) ?25)) [25, 24] by Super 2 with 4 at 1,1,2
-Id : 2, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
-% SZS output end CNFRefutation for COL064-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 92
- b_definition is 91
- f is 98
- g is 96
- h is 95
- i is 94
- prove_g_combinator is 93
- t is 90
- t_definition is 89
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-Goal subsumed
-Found proof, 71.486989s
-% SZS status Unsatisfiable for COL065-1.p
-% SZS output start CNFRefutation for COL065-1.p
-Id : 6, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 4, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 24512, {_}: apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) === apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))))) [] by Super 24511 with 6 at 2
-Id : 24511, {_}: apply (apply ?78509 (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))))) (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b b) ?78509))) (apply (apply b b) t))))) [78509] by Super 5051 with 4 at 2
-Id : 5051, {_}: apply (apply (apply ?14812 (apply ?14813 (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))))) (f (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t (apply (apply b ?14812) ?14813))) (apply (apply b b) t))))) [14813, 14812] by Super 5049 with 4 at 1,1,2
-Id : 5049, {_}: apply (apply (apply ?14808 (apply (g (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))))) (f (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) (i (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (i (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t)))) (h (apply (apply b b) (apply (apply b (apply t ?14808)) (apply (apply b b) t))))) [14808] by Super 5030 with 6 at 1,2
-Id : 5030, {_}: apply (apply (apply ?14754 (f (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) (apply ?14755 (apply (g (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (h (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))))) (i (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (i (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754)))) (h (apply (apply b b) (apply (apply b (apply t ?14755)) (apply (apply b b) ?14754))))) [14755, 14754] by Super 388 with 4 at 1,2
-Id : 388, {_}: apply (apply (apply (apply ?1025 (apply ?1026 (f (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))))) ?1027) (apply (g (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (h (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))))) (i (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (i (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026))))) (apply (g (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026)))) (h (apply (apply b b) (apply (apply b (apply t ?1027)) (apply (apply b ?1025) ?1026))))) [1027, 1026, 1025] by Super 132 with 4 at 1,1,1,2
-Id : 132, {_}: apply (apply (apply (apply ?316 (f (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) ?315) (apply (g (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (h (apply (apply b b) (apply (apply b (apply t ?315)) ?316))))) (i (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) =>= apply (apply (f (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (i (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) (apply (g (apply (apply b b) (apply (apply b (apply t ?315)) ?316))) (h (apply (apply b b) (apply (apply b (apply t ?315)) ?316)))) [315, 316] by Super 34 with 6 at 1,1,2
-Id : 34, {_}: apply (apply (apply ?76 (apply ?77 (f (apply (apply b b) (apply (apply b ?76) ?77))))) (apply (g (apply (apply b b) (apply (apply b ?76) ?77))) (h (apply (apply b b) (apply (apply b ?76) ?77))))) (i (apply (apply b b) (apply (apply b ?76) ?77))) =>= apply (apply (f (apply (apply b b) (apply (apply b ?76) ?77))) (i (apply (apply b b) (apply (apply b ?76) ?77)))) (apply (g (apply (apply b b) (apply (apply b ?76) ?77))) (h (apply (apply b b) (apply (apply b ?76) ?77)))) [77, 76] by Super 31 with 4 at 1,1,2
-Id : 31, {_}: apply (apply (apply ?69 (f (apply (apply b b) ?69))) (apply (g (apply (apply b b) ?69)) (h (apply (apply b b) ?69)))) (i (apply (apply b b) ?69)) =>= apply (apply (f (apply (apply b b) ?69)) (i (apply (apply b b) ?69))) (apply (g (apply (apply b b) ?69)) (h (apply (apply b b) ?69))) [69] by Super 11 with 4 at 1,2
-Id : 11, {_}: apply (apply (apply (apply ?24 (apply ?25 (f (apply (apply b ?24) ?25)))) (g (apply (apply b ?24) ?25))) (h (apply (apply b ?24) ?25))) (i (apply (apply b ?24) ?25)) =>= apply (apply (f (apply (apply b ?24) ?25)) (i (apply (apply b ?24) ?25))) (apply (g (apply (apply b ?24) ?25)) (h (apply (apply b ?24) ?25))) [25, 24] by Super 2 with 4 at 1,1,1,2
-Id : 2, {_}: apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) =>= apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) [1] by prove_g_combinator ?1
-% SZS output end CNFRefutation for COL065-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- group_axiom is 92
- inverse is 93
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 3.167539s
-% SZS status Unsatisfiable for GRP014-1.p
-% SZS output start CNFRefutation for GRP014-1.p
-Id : 5, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
-Id : 4, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Id : 7, {_}: multiply ?22 (inverse (multiply (multiply (inverse (multiply (inverse ?23) ?20)) ?24) (inverse (multiply ?23 ?24)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?19) (multiply (inverse (inverse ?22)) ?20))) ?21) (inverse (multiply ?19 ?21))) [21, 19, 24, 20, 23, 22] by Super 5 with 4 at 2,1,1,1,1,2,2
-Id : 65, {_}: multiply (inverse ?586) (multiply ?586 (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587, 586] by Super 4 with 7 at 2,2
-Id : 66, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?596) (multiply (inverse (inverse ?593)) (multiply (inverse ?593) ?598)))) ?597) (inverse (multiply ?596 ?597))) =>= ?598 [597, 598, 593, 596] by Super 4 with 7 at 2
-Id : 285, {_}: multiply (inverse ?2327) (multiply ?2327 ?2328) =?= multiply (inverse (inverse ?2329)) (multiply (inverse ?2329) ?2328) [2329, 2328, 2327] by Super 65 with 66 at 2,2,2
-Id : 188, {_}: multiply (inverse ?1696) (multiply ?1696 ?1694) =?= multiply (inverse (inverse ?1693)) (multiply (inverse ?1693) ?1694) [1693, 1694, 1696] by Super 65 with 66 at 2,2,2
-Id : 299, {_}: multiply (inverse ?2421) (multiply ?2421 ?2422) =?= multiply (inverse ?2420) (multiply ?2420 ?2422) [2420, 2422, 2421] by Super 285 with 188 at 3
-Id : 379, {_}: multiply ?2799 (inverse (multiply (multiply (inverse ?2798) (multiply ?2798 ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2798, 2799] by Super 4 with 299 at 1,1,2,2
-Id : 550, {_}: multiply ?3835 (inverse (multiply (multiply (inverse (multiply (inverse ?3836) (multiply ?3836 ?3837))) ?3838) (inverse (multiply (inverse ?3835) ?3838)))) =>= ?3837 [3838, 3837, 3836, 3835] by Super 4 with 188 at 1,1,1,1,2,2
-Id : 2860, {_}: multiply ?17926 (inverse (multiply (multiply (inverse (multiply (inverse ?17927) (multiply ?17927 ?17928))) (multiply ?17926 ?17929)) (inverse (multiply (inverse ?17930) (multiply ?17930 ?17929))))) =>= ?17928 [17930, 17929, 17928, 17927, 17926] by Super 550 with 299 at 1,2,1,2,2
-Id : 2947, {_}: multiply (multiply (inverse ?18671) (multiply ?18671 ?18672)) (inverse (multiply ?18669 (inverse (multiply (inverse ?18673) (multiply ?18673 (inverse (multiply (multiply (inverse (multiply (inverse ?18668) ?18669)) ?18670) (inverse (multiply ?18668 ?18670))))))))) =>= ?18672 [18670, 18668, 18673, 18669, 18672, 18671] by Super 2860 with 65 at 1,1,2,2
-Id : 2989, {_}: multiply (multiply (inverse ?18671) (multiply ?18671 ?18672)) (inverse (multiply ?18669 (inverse ?18669))) =>= ?18672 [18669, 18672, 18671] by Demod 2947 with 65 at 1,2,1,2,2
-Id : 3000, {_}: multiply ?18805 (inverse (multiply (multiply (inverse ?18806) (multiply ?18806 (inverse (multiply ?18804 (inverse ?18804))))) (inverse (multiply (inverse ?18805) ?18803)))) =>= ?18803 [18803, 18804, 18806, 18805] by Super 379 with 2989 at 2,1,2,1,2,2
-Id : 7432, {_}: multiply (inverse ?40377) (multiply (multiply (inverse (inverse ?40377)) ?40378) (inverse (multiply ?40379 (inverse ?40379)))) =>= ?40378 [40379, 40378, 40377] by Super 65 with 3000 at 2,2
-Id : 3646, {_}: multiply ?23036 (inverse (multiply (multiply (inverse ?23037) (multiply ?23037 (inverse (multiply ?23038 (inverse ?23038))))) (inverse (multiply (inverse ?23036) ?23039)))) =>= ?23039 [23039, 23038, 23037, 23036] by Super 379 with 2989 at 2,1,2,1,2,2
-Id : 3702, {_}: multiply ?23470 (inverse (inverse (multiply ?23472 (inverse ?23472)))) =>= inverse (inverse ?23470) [23472, 23470] by Super 3646 with 2989 at 1,2,2
-Id : 3804, {_}: multiply (inverse ?23847) (multiply ?23847 (inverse (inverse (multiply ?23846 (inverse ?23846))))) =?= multiply (inverse ?23845) (inverse (inverse ?23845)) [23845, 23846, 23847] by Super 299 with 3702 at 2,3
-Id : 4420, {_}: multiply (inverse ?26554) (inverse (inverse ?26554)) =?= multiply (inverse ?26555) (inverse (inverse ?26555)) [26555, 26554] by Demod 3804 with 3702 at 2,2
-Id : 190, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1706) (multiply (inverse (inverse ?1707)) (multiply (inverse ?1707) ?1708)))) ?1709) (inverse (multiply ?1706 ?1709))) =>= ?1708 [1709, 1708, 1707, 1706] by Super 4 with 7 at 2
-Id : 198, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1768) (multiply (inverse (inverse ?1769)) (multiply (inverse ?1769) ?1770)))) ?1771) (inverse (multiply ?1768 ?1771))))) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1771, 1770, 1769, 1768, 1772] by Super 190 with 66 at 1,2,2,1,1,1,1,2
-Id : 223, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse ?1770) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1770, 1772] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
-Id : 4421, {_}: multiply (inverse ?26561) (inverse (inverse ?26561)) =?= multiply (inverse (multiply (multiply (inverse (multiply (inverse ?26557) (multiply (inverse ?26558) (multiply ?26558 ?26559)))) ?26560) (inverse (multiply ?26557 ?26560)))) (inverse ?26559) [26560, 26559, 26558, 26557, 26561] by Super 4420 with 223 at 1,2,3
-Id : 4696, {_}: multiply (inverse ?27771) (inverse (inverse ?27771)) =?= multiply ?27772 (inverse ?27772) [27772, 27771] by Demod 4421 with 223 at 1,3
-Id : 4493, {_}: multiply (inverse ?26561) (inverse (inverse ?26561)) =?= multiply ?26559 (inverse ?26559) [26559, 26561] by Demod 4421 with 223 at 1,3
-Id : 4736, {_}: multiply ?27992 (inverse ?27992) =?= multiply ?27994 (inverse ?27994) [27994, 27992] by Super 4696 with 4493 at 2
-Id : 7526, {_}: multiply (inverse ?40902) (multiply ?40901 (inverse ?40901)) =>= inverse (inverse (inverse ?40902)) [40901, 40902] by Super 7432 with 4736 at 2,2
-Id : 7653, {_}: multiply (inverse ?41400) (multiply ?41400 (inverse ?41399)) =>= inverse (inverse (inverse ?41399)) [41399, 41400] by Super 299 with 7526 at 3
-Id : 8053, {_}: multiply ?18805 (inverse (multiply (inverse (inverse (inverse (multiply ?18804 (inverse ?18804))))) (inverse (multiply (inverse ?18805) ?18803)))) =>= ?18803 [18803, 18804, 18805] by Demod 3000 with 7653 at 1,1,2,2
-Id : 395, {_}: multiply (inverse ?2916) (multiply ?2916 (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915, 2916] by Super 65 with 299 at 1,1,1,1,2,2,2
-Id : 8051, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915] by Demod 395 with 7653 at 2
-Id : 8154, {_}: multiply (inverse ?43172) (multiply ?43172 (inverse ?43173)) =>= inverse (inverse (inverse ?43173)) [43173, 43172] by Super 299 with 7526 at 3
-Id : 474, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?3355) (multiply (inverse ?3356) (multiply ?3356 ?3357)))) ?3358) (inverse (multiply ?3355 ?3358))) =>= ?3357 [3358, 3357, 3356, 3355] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
-Id : 505, {_}: inverse (multiply (multiply (inverse ?3589) (multiply ?3589 ?3588)) (inverse (multiply ?3590 (multiply (multiply (inverse ?3590) (multiply (inverse ?3591) (multiply ?3591 ?3592))) ?3588)))) =>= ?3592 [3592, 3591, 3590, 3588, 3589] by Super 474 with 299 at 1,1,2
-Id : 3283, {_}: inverse (multiply (multiply (inverse ?20660) (multiply ?20660 (inverse (multiply ?20661 (inverse ?20661))))) (inverse (multiply (inverse ?20662) (multiply ?20662 ?20663)))) =>= ?20663 [20663, 20662, 20661, 20660] by Super 505 with 2989 at 2,1,2,1,2
-Id : 251, {_}: multiply ?2088 (inverse (multiply (multiply (inverse (multiply (inverse ?2086) (multiply ?2086 ?2087))) ?2089) (inverse (multiply (inverse ?2088) ?2089)))) =>= ?2087 [2089, 2087, 2086, 2088] by Super 4 with 188 at 1,1,1,1,2,2
-Id : 3330, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?21019) (multiply ?21019 ?21020))) ?21020) (inverse (multiply (inverse ?21022) (multiply ?21022 ?21023)))) =>= ?21023 [21023, 21022, 21020, 21019] by Super 3283 with 251 at 2,1,1,2
-Id : 8160, {_}: multiply (inverse ?43212) (multiply ?43212 ?43211) =?= inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?43208) (multiply ?43208 ?43209))) ?43209) (inverse (multiply (inverse ?43210) (multiply ?43210 ?43211)))))) [43210, 43209, 43208, 43211, 43212] by Super 8154 with 3330 at 2,2,2
-Id : 8246, {_}: multiply (inverse ?43212) (multiply ?43212 ?43211) =>= inverse (inverse ?43211) [43211, 43212] by Demod 8160 with 3330 at 1,1,3
-Id : 8276, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8051 with 8246 at 1,1,1,1,1,1,2
-Id : 3034, {_}: multiply (multiply (inverse ?19018) (multiply ?19018 ?19019)) (inverse (multiply ?19020 (inverse ?19020))) =>= ?19019 [19020, 19019, 19018] by Demod 2947 with 65 at 1,2,1,2,2
-Id : 3049, {_}: multiply (multiply (inverse (inverse ?19126)) (multiply (inverse ?19128) (multiply ?19128 ?19127))) (inverse (multiply ?19129 (inverse ?19129))) =>= multiply ?19126 ?19127 [19129, 19127, 19128, 19126] by Super 3034 with 299 at 2,1,2
-Id : 7592, {_}: multiply (multiply (inverse (inverse ?41055)) (multiply (inverse (inverse ?41053)) (inverse (inverse (inverse ?41053))))) (inverse (multiply ?41056 (inverse ?41056))) =?= multiply ?41055 (multiply ?41054 (inverse ?41054)) [41054, 41056, 41053, 41055] by Super 3049 with 7526 at 2,2,1,2
-Id : 6756, {_}: multiply (multiply (inverse ?37293) (multiply ?37294 (inverse ?37294))) (inverse (multiply ?37295 (inverse ?37295))) =>= inverse ?37293 [37295, 37294, 37293] by Super 2989 with 4736 at 2,1,2
-Id : 6813, {_}: multiply (multiply ?37621 (multiply ?37623 (inverse ?37623))) (inverse (multiply ?37624 (inverse ?37624))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?37619) (multiply (inverse ?37620) (multiply ?37620 ?37621)))) ?37622) (inverse (multiply ?37619 ?37622))) [37622, 37620, 37619, 37624, 37623, 37621] by Super 6756 with 223 at 1,1,2
-Id : 6857, {_}: multiply (multiply ?37621 (multiply ?37623 (inverse ?37623))) (inverse (multiply ?37624 (inverse ?37624))) =>= ?37621 [37624, 37623, 37621] by Demod 6813 with 223 at 3
-Id : 7919, {_}: inverse (inverse ?42462) =<= multiply ?42462 (multiply ?42463 (inverse ?42463)) [42463, 42462] by Demod 7592 with 6857 at 2
-Id : 2998, {_}: inverse (multiply (multiply (inverse ?18792) (multiply ?18792 (inverse (multiply ?18791 (inverse ?18791))))) (inverse (multiply (inverse ?18793) (multiply ?18793 ?18794)))) =>= ?18794 [18794, 18793, 18791, 18792] by Super 505 with 2989 at 2,1,2,1,2
-Id : 5265, {_}: inverse (multiply ?30443 (inverse ?30443)) =?= inverse (multiply ?30444 (inverse ?30444)) [30444, 30443] by Super 2998 with 4736 at 1,2
-Id : 5279, {_}: inverse (multiply ?30523 (inverse ?30523)) =?= inverse (inverse (inverse (inverse (multiply ?30522 (inverse ?30522))))) [30522, 30523] by Super 5265 with 3702 at 1,3
-Id : 7936, {_}: inverse (inverse ?42552) =<= multiply ?42552 (multiply (inverse (inverse (inverse (multiply ?42551 (inverse ?42551))))) (inverse (multiply ?42550 (inverse ?42550)))) [42550, 42551, 42552] by Super 7919 with 5279 at 2,2,3
-Id : 7778, {_}: inverse (inverse ?41055) =<= multiply ?41055 (multiply ?41054 (inverse ?41054)) [41054, 41055] by Demod 7592 with 6857 at 2
-Id : 7804, {_}: multiply (inverse (inverse ?37621)) (inverse (multiply ?37624 (inverse ?37624))) =>= ?37621 [37624, 37621] by Demod 6857 with 7778 at 1,2
-Id : 8036, {_}: inverse (inverse ?42552) =<= multiply ?42552 (inverse (multiply ?42551 (inverse ?42551))) [42551, 42552] by Demod 7936 with 7804 at 2,3
-Id : 8529, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?44275))) (inverse (multiply ?44274 (inverse ?44274)))) (inverse (inverse (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44274, 44275] by Super 8276 with 8036 at 1,2,1,1,1,2
-Id : 8588, {_}: inverse (inverse (inverse (multiply (inverse (inverse (inverse (inverse (inverse ?44275))))) (inverse (inverse (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8529 with 8036 at 1,1,1,1,2
-Id : 401, {_}: multiply (inverse ?2949) (multiply ?2949 ?2950) =?= multiply (inverse ?2951) (multiply ?2951 ?2950) [2951, 2950, 2949] by Super 285 with 188 at 3
-Id : 407, {_}: multiply (inverse ?2992) (multiply ?2992 (multiply ?2989 ?2990)) =?= multiply (inverse (inverse ?2989)) (multiply (inverse ?2991) (multiply ?2991 ?2990)) [2991, 2990, 2989, 2992] by Super 401 with 299 at 2,3
-Id : 8291, {_}: inverse (inverse (multiply ?2989 ?2990)) =<= multiply (inverse (inverse ?2989)) (multiply (inverse ?2991) (multiply ?2991 ?2990)) [2991, 2990, 2989] by Demod 407 with 8246 at 2
-Id : 8292, {_}: inverse (inverse (multiply ?2989 ?2990)) =<= multiply (inverse (inverse ?2989)) (inverse (inverse ?2990)) [2990, 2989] by Demod 8291 with 8246 at 2,3
-Id : 8589, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?44275))) (inverse ?44273)))))) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8588 with 8292 at 1,1,1,2
-Id : 8446, {_}: inverse (inverse (inverse (inverse ?37621))) =>= ?37621 [37621] by Demod 7804 with 8036 at 2
-Id : 8590, {_}: inverse (multiply (inverse (inverse (inverse ?44275))) (inverse ?44273)) =>= multiply ?44273 ?44275 [44273, 44275] by Demod 8589 with 8446 at 2
-Id : 8757, {_}: multiply ?18805 (multiply (multiply (inverse ?18805) ?18803) (multiply ?18804 (inverse ?18804))) =>= ?18803 [18804, 18803, 18805] by Demod 8053 with 8590 at 2,2
-Id : 8758, {_}: multiply ?18805 (inverse (inverse (multiply (inverse ?18805) ?18803))) =>= ?18803 [18803, 18805] by Demod 8757 with 7778 at 2,2
-Id : 8857, {_}: inverse (multiply (inverse (inverse (inverse ?44963))) (inverse ?44964)) =>= multiply ?44964 ?44963 [44964, 44963] by Demod 8589 with 8446 at 2
-Id : 8919, {_}: inverse (multiply ?45241 (inverse ?45242)) =>= multiply ?45242 (inverse ?45241) [45242, 45241] by Super 8857 with 8446 at 1,1,2
-Id : 9051, {_}: multiply ?2 (multiply (multiply ?3 ?5) (inverse (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5))) =>= ?4 [4, 5, 3, 2] by Demod 4 with 8919 at 2,2
-Id : 137, {_}: multiply (inverse ?1284) (multiply ?1284 (inverse (multiply (multiply (inverse (multiply (inverse ?1285) ?1286)) ?1287) (inverse (multiply ?1285 ?1287))))) =>= ?1286 [1287, 1286, 1285, 1284] by Super 4 with 7 at 2,2
-Id : 156, {_}: multiply (inverse ?1443) (multiply ?1443 (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439, 1443] by Super 137 with 7 at 2,2,2
-Id : 8285, {_}: inverse (inverse (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439] by Demod 156 with 8246 at 2
-Id : 9071, {_}: inverse (multiply (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442))) (inverse ?1439)) =>= multiply (inverse (inverse ?1439)) ?1441 [1439, 1442, 1441, 1440] by Demod 8285 with 8919 at 1,2
-Id : 9072, {_}: multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439] by Demod 9071 with 8919 at 2
-Id : 9073, {_}: multiply ?1439 (multiply (multiply ?1440 ?1442) (inverse (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442))) =>= multiply (inverse (inverse ?1439)) ?1441 [1441, 1442, 1440, 1439] by Demod 9072 with 8919 at 2,2
-Id : 9086, {_}: multiply (inverse (inverse ?2)) (multiply (inverse ?2) ?4) =>= ?4 [4, 2] by Demod 9051 with 9073 at 2
-Id : 9087, {_}: inverse (inverse ?4) =>= ?4 [4] by Demod 9086 with 8246 at 2
-Id : 9094, {_}: multiply ?18805 (multiply (inverse ?18805) ?18803) =>= ?18803 [18803, 18805] by Demod 8758 with 9087 at 2,2
-Id : 9160, {_}: inverse (multiply ?45446 (inverse ?45447)) =>= multiply ?45447 (inverse ?45446) [45447, 45446] by Super 8857 with 8446 at 1,1,2
-Id : 9162, {_}: inverse (multiply ?45454 ?45453) =<= multiply (inverse ?45453) (inverse ?45454) [45453, 45454] by Super 9160 with 9087 at 2,1,2
-Id : 9195, {_}: multiply ?45501 (inverse (multiply ?45500 ?45501)) =>= inverse ?45500 [45500, 45501] by Super 9094 with 9162 at 2,2
-Id : 8933, {_}: inverse ?45303 =<= multiply (inverse (multiply (inverse (inverse (inverse (inverse ?45304)))) ?45303)) ?45304 [45304, 45303] by Super 8857 with 8758 at 1,2
-Id : 9467, {_}: inverse ?46002 =<= multiply (inverse (multiply ?46003 ?46002)) ?46003 [46003, 46002] by Demod 8933 with 8446 at 1,1,1,3
-Id : 8287, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (inverse (inverse ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1772] by Demod 223 with 8246 at 2,1,1,1,1,2
-Id : 9069, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (inverse (multiply (inverse ?1772) (inverse (inverse ?1773)))) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 8287 with 8919 at 2
-Id : 9070, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (multiply (inverse ?1773) (inverse (inverse ?1772))) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 9069 with 8919 at 1,1,2,2
-Id : 9090, {_}: multiply (multiply ?1772 ?1774) (inverse (multiply (multiply (inverse ?1773) ?1772) ?1774)) =>= ?1773 [1773, 1774, 1772] by Demod 9070 with 9087 at 2,1,1,2,2
-Id : 9469, {_}: inverse (inverse (multiply (multiply (inverse ?46010) ?46008) ?46009)) =>= multiply (inverse ?46010) (multiply ?46008 ?46009) [46009, 46008, 46010] by Super 9467 with 9090 at 1,1,3
-Id : 9509, {_}: multiply (multiply (inverse ?46010) ?46008) ?46009 =>= multiply (inverse ?46010) (multiply ?46008 ?46009) [46009, 46008, 46010] by Demod 9469 with 9087 at 2
-Id : 9851, {_}: multiply ?46565 (inverse (multiply (inverse ?46563) (multiply ?46564 ?46565))) =>= inverse (multiply (inverse ?46563) ?46564) [46564, 46563, 46565] by Super 9195 with 9509 at 1,2,2
-Id : 9213, {_}: inverse (multiply ?45576 ?45577) =<= multiply (inverse ?45577) (inverse ?45576) [45577, 45576] by Super 9160 with 9087 at 2,1,2
-Id : 9215, {_}: inverse (multiply (inverse ?45583) ?45584) =>= multiply (inverse ?45584) ?45583 [45584, 45583] by Super 9213 with 9087 at 2,3
-Id : 9934, {_}: multiply ?46565 (multiply (inverse (multiply ?46564 ?46565)) ?46563) =>= inverse (multiply (inverse ?46563) ?46564) [46563, 46564, 46565] by Demod 9851 with 9215 at 2,2
-Id : 12550, {_}: multiply ?50696 (multiply (inverse (multiply ?50697 ?50696)) ?50698) =>= multiply (inverse ?50697) ?50698 [50698, 50697, 50696] by Demod 9934 with 9215 at 3
-Id : 9075, {_}: inverse (inverse (multiply (multiply ?2913 ?2917) (inverse (multiply (inverse (inverse (inverse ?2914))) ?2917)))) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 8276 with 8919 at 1,1,2
-Id : 9076, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 9075 with 8919 at 1,2
-Id : 9077, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse (inverse (inverse ?2914))) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9076 with 8919 at 2
-Id : 9102, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse ?2914) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9077 with 9087 at 1,1,2,2
-Id : 9248, {_}: multiply (multiply ?2913 ?2917) (multiply (inverse ?2917) ?2914) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 9102 with 9215 at 2,2
-Id : 9533, {_}: multiply (inverse ?46084) (multiply (inverse (inverse (multiply ?46084 ?46083))) ?46085) =>= multiply ?46083 ?46085 [46085, 46083, 46084] by Super 9248 with 9195 at 1,2
-Id : 9598, {_}: multiply (inverse ?46084) (multiply (multiply ?46084 ?46083) ?46085) =>= multiply ?46083 ?46085 [46085, 46083, 46084] by Demod 9533 with 9087 at 1,2,2
-Id : 12590, {_}: multiply ?50874 (multiply ?50872 ?50873) =<= multiply (inverse ?50875) (multiply (multiply (multiply ?50875 ?50874) ?50872) ?50873) [50875, 50873, 50872, 50874] by Super 12550 with 9598 at 2,2
-Id : 12312, {_}: multiply (multiply ?50214 ?50215) ?50216 =<= multiply (inverse ?50213) (multiply (multiply (multiply ?50213 ?50214) ?50215) ?50216) [50213, 50216, 50215, 50214] by Super 9509 with 9598 at 1,2
-Id : 29878, {_}: multiply ?50874 (multiply ?50872 ?50873) =?= multiply (multiply ?50874 ?50872) ?50873 [50873, 50872, 50874] by Demod 12590 with 12312 at 3
-Id : 30629, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 2 with 29878 at 3
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for GRP014-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_commutator is 86
- b is 97
- c is 96
- commutator is 95
- identity is 92
- inverse is 90
- left_identity is 91
- left_inverse is 89
- multiply is 94
- name is 87
- prove_center is 93
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
- Id : 12, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-Goal
- Id : 2, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-Last chance: 1246129199.8
-Last chance: all is indexed 1246129219.81
-Last chance: failed over 100 goal 1246129219.81
-FAILURE in 0 iterations
-% SZS status Timeout for GRP024-5.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- identity is 93
- intersection is 85
- intersection_associative is 79
- intersection_commutative is 81
- intersection_idempotent is 84
- intersection_union_absorbtion is 76
- inverse is 91
- inverse_involution is 87
- inverse_of_identity is 88
- inverse_product_lemma is 86
- left_identity is 92
- left_inverse is 90
- multiply is 95
- multiply_intersection1 is 74
- multiply_intersection2 is 72
- multiply_union1 is 75
- multiply_union2 is 73
- negative_part is 96
- positive_part is 97
- prove_product is 94
- union is 83
- union_associative is 78
- union_commutative is 80
- union_idempotent is 82
- union_intersection_absorbtion is 77
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
- Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
- Id : 14, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
- Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
- Id : 18, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
- Id : 20, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
- Id : 22, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
- Id : 24, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
- Id : 26, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
- Id : 28, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
- Id : 30, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
- Id : 32, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
- Id : 34, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
- Id : 36, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
- Id : 38, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
- Id : 40, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
- Id : 42, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-Goal
- Id : 2, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-Found proof, 2.757502s
-% SZS status Unsatisfiable for GRP114-1.p
-% SZS output start CNFRefutation for GRP114-1.p
-Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-Id : 24, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
-Id : 34, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-Id : 28, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
-Id : 26, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
-Id : 267, {_}: multiply (union ?680 ?681) ?682 =<= union (multiply ?680 ?682) (multiply ?681 ?682) [682, 681, 680] by multiply_union2 ?680 ?681 ?682
-Id : 30, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
-Id : 230, {_}: multiply ?593 (intersection ?594 ?595) =<= intersection (multiply ?593 ?594) (multiply ?593 ?595) [595, 594, 593] by multiply_intersection1 ?593 ?594 ?595
-Id : 42, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
-Id : 20, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
-Id : 303, {_}: multiply (intersection ?770 ?771) ?772 =<= intersection (multiply ?770 ?772) (multiply ?771 ?772) [772, 771, 770] by multiply_intersection2 ?770 ?771 ?772
-Id : 14, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
-Id : 22, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
-Id : 40, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
-Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
-Id : 32, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-Id : 79, {_}: inverse (multiply ?142 ?143) =<= multiply (inverse ?143) (inverse ?142) [143, 142] by inverse_product_lemma ?142 ?143
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 47, {_}: multiply (multiply ?68 ?69) ?70 =?= multiply ?68 (multiply ?69 ?70) [70, 69, 68] by associativity ?68 ?69 ?70
-Id : 56, {_}: multiply identity ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Super 47 with 6 at 1,2
-Id : 8890, {_}: ?10861 =<= multiply (inverse ?10862) (multiply ?10862 ?10861) [10862, 10861] by Demod 56 with 4 at 2
-Id : 81, {_}: inverse (multiply (inverse ?147) ?148) =>= multiply (inverse ?148) ?147 [148, 147] by Super 79 with 12 at 2,3
-Id : 80, {_}: inverse (multiply identity ?145) =<= multiply (inverse ?145) identity [145] by Super 79 with 10 at 2,3
-Id : 450, {_}: inverse ?990 =<= multiply (inverse ?990) identity [990] by Demod 80 with 4 at 1,2
-Id : 452, {_}: inverse (inverse ?993) =<= multiply ?993 identity [993] by Super 450 with 12 at 1,3
-Id : 467, {_}: ?993 =<= multiply ?993 identity [993] by Demod 452 with 12 at 2
-Id : 472, {_}: multiply ?1004 (union ?1005 identity) =?= union (multiply ?1004 ?1005) ?1004 [1005, 1004] by Super 32 with 467 at 2,3
-Id : 3162, {_}: multiply ?4224 (positive_part ?4225) =<= union (multiply ?4224 ?4225) ?4224 [4225, 4224] by Demod 472 with 40 at 2,2
-Id : 3164, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= union identity (inverse ?4229) [4229] by Super 3162 with 6 at 1,3
-Id : 336, {_}: union identity ?835 =>= positive_part ?835 [835] by Super 22 with 40 at 3
-Id : 3201, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= positive_part (inverse ?4229) [4229] by Demod 3164 with 336 at 3
-Id : 3231, {_}: inverse (positive_part (inverse ?4304)) =<= multiply (inverse (positive_part ?4304)) ?4304 [4304] by Super 81 with 3201 at 1,2
-Id : 8905, {_}: ?10899 =<= multiply (inverse (inverse (positive_part ?10899))) (inverse (positive_part (inverse ?10899))) [10899] by Super 8890 with 3231 at 2,3
-Id : 8940, {_}: ?10899 =<= inverse (multiply (positive_part (inverse ?10899)) (inverse (positive_part ?10899))) [10899] by Demod 8905 with 14 at 3
-Id : 83, {_}: inverse (multiply ?153 (inverse ?152)) =>= multiply ?152 (inverse ?153) [152, 153] by Super 79 with 12 at 1,3
-Id : 8941, {_}: ?10899 =<= multiply (positive_part ?10899) (inverse (positive_part (inverse ?10899))) [10899] by Demod 8940 with 83 at 3
-Id : 310, {_}: multiply (intersection (inverse ?798) ?797) ?798 =>= intersection identity (multiply ?797 ?798) [797, 798] by Super 303 with 6 at 1,3
-Id : 355, {_}: intersection identity ?867 =>= negative_part ?867 [867] by Super 20 with 42 at 3
-Id : 15926, {_}: multiply (intersection (inverse ?16735) ?16736) ?16735 =>= negative_part (multiply ?16736 ?16735) [16736, 16735] by Demod 310 with 355 at 3
-Id : 15951, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part (multiply identity ?16817) [16817] by Super 15926 with 42 at 1,2
-Id : 15996, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15951 with 4 at 1,3
-Id : 237, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= intersection identity (multiply (inverse ?620) ?621) [621, 620] by Super 230 with 6 at 1,3
-Id : 9389, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= negative_part (multiply (inverse ?620) ?621) [621, 620] by Demod 237 with 355 at 3
-Id : 387, {_}: intersection (positive_part ?915) ?915 =>= ?915 [915] by Super 30 with 336 at 1,2
-Id : 274, {_}: multiply (union (inverse ?708) ?707) ?708 =>= union identity (multiply ?707 ?708) [707, 708] by Super 267 with 6 at 1,3
-Id : 9866, {_}: multiply (union (inverse ?12356) ?12357) ?12356 =>= positive_part (multiply ?12357 ?12356) [12357, 12356] by Demod 274 with 336 at 3
-Id : 384, {_}: union identity (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Super 26 with 336 at 1,3
-Id : 394, {_}: positive_part (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Demod 384 with 336 at 2
-Id : 339, {_}: union ?842 (union ?843 identity) =>= positive_part (union ?842 ?843) [843, 842] by Super 26 with 40 at 3
-Id : 350, {_}: union ?842 (positive_part ?843) =<= positive_part (union ?842 ?843) [843, 842] by Demod 339 with 40 at 2,2
-Id : 667, {_}: union ?906 (positive_part ?907) =?= union (positive_part ?906) ?907 [907, 906] by Demod 394 with 350 at 2
-Id : 414, {_}: union (negative_part ?942) ?942 =>= ?942 [942] by Super 28 with 355 at 1,2
-Id : 479, {_}: multiply ?1021 (intersection ?1022 identity) =?= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Super 34 with 467 at 2,3
-Id : 2583, {_}: multiply ?3618 (negative_part ?3619) =<= intersection (multiply ?3618 ?3619) ?3618 [3619, 3618] by Demod 479 with 42 at 2,2
-Id : 2585, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= intersection identity (inverse ?3623) [3623] by Super 2583 with 6 at 1,3
-Id : 2636, {_}: multiply (inverse ?3692) (negative_part ?3692) =>= negative_part (inverse ?3692) [3692] by Demod 2585 with 355 at 3
-Id : 358, {_}: intersection ?874 (intersection ?875 identity) =>= negative_part (intersection ?874 ?875) [875, 874] by Super 24 with 42 at 3
-Id : 603, {_}: intersection ?1157 (negative_part ?1158) =<= negative_part (intersection ?1157 ?1158) [1158, 1157] by Demod 358 with 42 at 2,2
-Id : 613, {_}: intersection ?1189 (negative_part identity) =>= negative_part (negative_part ?1189) [1189] by Super 603 with 42 at 1,3
-Id : 354, {_}: negative_part identity =>= identity [] by Super 16 with 42 at 2
-Id : 624, {_}: intersection ?1189 identity =<= negative_part (negative_part ?1189) [1189] by Demod 613 with 354 at 2,2
-Id : 625, {_}: negative_part ?1189 =<= negative_part (negative_part ?1189) [1189] by Demod 624 with 42 at 2
-Id : 2642, {_}: multiply (inverse (negative_part ?3706)) (negative_part ?3706) =>= negative_part (inverse (negative_part ?3706)) [3706] by Super 2636 with 625 at 2,2
-Id : 2662, {_}: identity =<= negative_part (inverse (negative_part ?3706)) [3706] by Demod 2642 with 6 at 2
-Id : 2732, {_}: union identity (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Super 414 with 2662 at 1,2
-Id : 2769, {_}: positive_part (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Demod 2732 with 336 at 2
-Id : 2879, {_}: union (inverse (negative_part ?3906)) (positive_part ?3907) =>= union (inverse (negative_part ?3906)) ?3907 [3907, 3906] by Super 667 with 2769 at 1,3
-Id : 9889, {_}: multiply (union (inverse (negative_part ?12432)) ?12433) (negative_part ?12432) =>= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12433, 12432] by Super 9866 with 2879 at 1,2
-Id : 9846, {_}: multiply (union (inverse ?708) ?707) ?708 =>= positive_part (multiply ?707 ?708) [707, 708] by Demod 274 with 336 at 3
-Id : 9923, {_}: positive_part (multiply ?12433 (negative_part ?12432)) =<= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12432, 12433] by Demod 9889 with 9846 at 2
-Id : 492, {_}: multiply ?1021 (negative_part ?1022) =<= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Demod 479 with 42 at 2,2
-Id : 9892, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part (multiply identity ?12441) [12441] by Super 9866 with 40 at 1,2
-Id : 9926, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part ?12441 [12441] by Demod 9892 with 4 at 1,3
-Id : 9949, {_}: multiply (positive_part (inverse ?12495)) (negative_part ?12495) =>= intersection (positive_part ?12495) (positive_part (inverse ?12495)) [12495] by Super 492 with 9926 at 1,3
-Id : 10776, {_}: positive_part (multiply (inverse ?13313) (negative_part ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Super 9923 with 9949 at 1,3
-Id : 2613, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= negative_part (inverse ?3623) [3623] by Demod 2585 with 355 at 3
-Id : 10814, {_}: positive_part (negative_part (inverse ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10776 with 2613 at 1,2
-Id : 334, {_}: positive_part (intersection ?832 identity) =>= identity [832] by Super 28 with 40 at 2
-Id : 507, {_}: positive_part (negative_part ?832) =>= identity [832] by Demod 334 with 42 at 1,2
-Id : 10815, {_}: identity =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10814 with 507 at 2
-Id : 51491, {_}: intersection identity (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Super 387 with 10815 at 1,2
-Id : 51798, {_}: negative_part (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51491 with 355 at 2
-Id : 369, {_}: intersection ?874 (negative_part ?875) =<= negative_part (intersection ?874 ?875) [875, 874] by Demod 358 with 42 at 2,2
-Id : 51799, {_}: intersection (positive_part ?50477) (negative_part (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51798 with 369 at 2
-Id : 51800, {_}: intersection (negative_part (positive_part (inverse ?50477))) (positive_part ?50477) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51799 with 20 at 2
-Id : 411, {_}: intersection identity (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Super 24 with 355 at 1,3
-Id : 421, {_}: negative_part (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Demod 411 with 355 at 2
-Id : 795, {_}: intersection ?1452 (negative_part ?1453) =?= intersection (negative_part ?1452) ?1453 [1453, 1452] by Demod 421 with 369 at 2
-Id : 353, {_}: negative_part (union ?864 identity) =>= identity [864] by Super 30 with 42 at 2
-Id : 371, {_}: negative_part (positive_part ?864) =>= identity [864] by Demod 353 with 40 at 1,2
-Id : 797, {_}: intersection (positive_part ?1457) (negative_part ?1458) =>= intersection identity ?1458 [1458, 1457] by Super 795 with 371 at 1,3
-Id : 834, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= intersection identity ?1458 [1457, 1458] by Demod 797 with 20 at 2
-Id : 835, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= negative_part ?1458 [1457, 1458] by Demod 834 with 355 at 3
-Id : 51801, {_}: negative_part (positive_part (inverse ?50477)) =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51800 with 835 at 2
-Id : 51802, {_}: identity =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51801 with 371 at 2
-Id : 52174, {_}: multiply (inverse (positive_part ?50853)) identity =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Super 9389 with 51802 at 2,2
-Id : 52262, {_}: inverse (positive_part ?50853) =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Demod 52174 with 467 at 2
-Id : 65, {_}: ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Demod 56 with 4 at 2
-Id : 9954, {_}: multiply (positive_part (inverse ?12505)) ?12505 =>= positive_part ?12505 [12505] by Demod 9892 with 4 at 1,3
-Id : 9956, {_}: multiply (positive_part ?12508) (inverse ?12508) =>= positive_part (inverse ?12508) [12508] by Super 9954 with 12 at 1,1,2
-Id : 10049, {_}: inverse ?12562 =<= multiply (inverse (positive_part ?12562)) (positive_part (inverse ?12562)) [12562] by Super 65 with 9956 at 2,3
-Id : 52263, {_}: inverse (positive_part ?50853) =<= negative_part (inverse ?50853) [50853] by Demod 52262 with 10049 at 1,3
-Id : 52532, {_}: multiply (inverse (positive_part ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15996 with 52263 at 1,2
-Id : 52563, {_}: inverse (positive_part (inverse ?16817)) =>= negative_part ?16817 [16817] by Demod 52532 with 3231 at 2
-Id : 52572, {_}: ?10899 =<= multiply (positive_part ?10899) (negative_part ?10899) [10899] by Demod 8941 with 52563 at 2,3
-Id : 52951, {_}: a === a [] by Demod 2 with 52572 at 2
-Id : 2, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
-% SZS output end CNFRefutation for GRP114-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 87
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 89
- least_upper_bound is 95
- left_identity is 90
- left_inverse is 88
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 91
- prove_distrun is 93
- symmetry_of_glb is 86
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-Last chance: 1246129493.23
-Last chance: all is indexed 1246129513.23
-Last chance: failed over 100 goal 1246129513.24
-FAILURE in 0 iterations
-% SZS status Timeout for GRP164-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 84
- associativity_of_lub is 83
- glb_absorbtion is 79
- greatest_lower_bound is 88
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 93
- inverse is 91
- lat4_1 is 74
- lat4_2 is 73
- lat4_3 is 72
- lat4_4 is 71
- least_upper_bound is 86
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- negative_part is 96
- positive_part is 97
- prove_lat4 is 94
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
- Id : 36, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
- Id : 38, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
- Id : 40, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-Goal
- Id : 2, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-Found proof, 4.832821s
-% SZS status Unsatisfiable for GRP167-1.p
-% SZS output start CNFRefutation for GRP167-1.p
-Id : 202, {_}: multiply ?551 (greatest_lower_bound ?552 ?553) =<= greatest_lower_bound (multiply ?551 ?552) (multiply ?551 ?553) [553, 552, 551] by monotony_glb1 ?551 ?552 ?553
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 171, {_}: multiply ?475 (least_upper_bound ?476 ?477) =<= least_upper_bound (multiply ?475 ?476) (multiply ?475 ?477) [477, 476, 475] by monotony_lub1 ?475 ?476 ?477
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 384, {_}: greatest_lower_bound ?977 (least_upper_bound ?978 ?979) =<= least_upper_bound (greatest_lower_bound ?977 ?978) (greatest_lower_bound ?977 ?979) [979, 978, 977] by lat4_4 ?977 ?978 ?979
-Id : 34, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 236, {_}: multiply (least_upper_bound ?630 ?631) ?632 =<= least_upper_bound (multiply ?630 ?632) (multiply ?631 ?632) [632, 631, 630] by monotony_lub2 ?630 ?631 ?632
-Id : 36, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 269, {_}: multiply (greatest_lower_bound ?712 ?713) ?714 =<= greatest_lower_bound (multiply ?712 ?714) (multiply ?713 ?714) [714, 713, 712] by monotony_glb2 ?712 ?713 ?714
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 45, {_}: multiply (multiply ?70 ?71) ?72 =?= multiply ?70 (multiply ?71 ?72) [72, 71, 70] by associativity ?70 ?71 ?72
-Id : 54, {_}: multiply identity ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Super 45 with 6 at 1,2
-Id : 63, {_}: ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Demod 54 with 4 at 2
-Id : 275, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= greatest_lower_bound identity (multiply ?735 ?736) [735, 736] by Super 269 with 6 at 1,3
-Id : 314, {_}: greatest_lower_bound identity ?795 =>= negative_part ?795 [795] by Super 10 with 36 at 3
-Id : 16391, {_}: multiply (greatest_lower_bound (inverse ?19768) ?19769) ?19768 =>= negative_part (multiply ?19769 ?19768) [19769, 19768] by Demod 275 with 314 at 3
-Id : 16415, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part (multiply identity ?19845) [19845] by Super 16391 with 36 at 1,2
-Id : 16452, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part ?19845 [19845] by Demod 16415 with 4 at 1,3
-Id : 16463, {_}: ?19856 =<= multiply (inverse (negative_part (inverse ?19856))) (negative_part ?19856) [19856] by Super 63 with 16452 at 2,3
-Id : 242, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= least_upper_bound identity (multiply ?653 ?654) [653, 654] by Super 236 with 6 at 1,3
-Id : 298, {_}: least_upper_bound identity ?767 =>= positive_part ?767 [767] by Super 12 with 34 at 3
-Id : 14215, {_}: multiply (least_upper_bound (inverse ?17599) ?17600) ?17599 =>= positive_part (multiply ?17600 ?17599) [17600, 17599] by Demod 242 with 298 at 3
-Id : 14238, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part (multiply identity ?17673) [17673] by Super 14215 with 34 at 1,2
-Id : 14268, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14238 with 4 at 1,3
-Id : 14200, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= positive_part (multiply ?653 ?654) [653, 654] by Demod 242 with 298 at 3
-Id : 393, {_}: greatest_lower_bound ?1016 (least_upper_bound ?1017 identity) =<= least_upper_bound (greatest_lower_bound ?1016 ?1017) (negative_part ?1016) [1017, 1016] by Super 384 with 36 at 2,3
-Id : 17844, {_}: greatest_lower_bound ?21384 (positive_part ?21385) =<= least_upper_bound (greatest_lower_bound ?21384 ?21385) (negative_part ?21384) [21385, 21384] by Demod 393 with 34 at 2,2
-Id : 17873, {_}: greatest_lower_bound ?21489 (positive_part ?21490) =<= least_upper_bound (greatest_lower_bound ?21490 ?21489) (negative_part ?21489) [21490, 21489] by Super 17844 with 10 at 1,3
-Id : 16475, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19889)) ?19890) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Super 32 with 16452 at 1,3
-Id : 480, {_}: greatest_lower_bound identity (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Super 14 with 314 at 1,3
-Id : 492, {_}: negative_part (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 480 with 314 at 2
-Id : 317, {_}: greatest_lower_bound ?802 (greatest_lower_bound ?803 identity) =>= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Super 14 with 36 at 3
-Id : 326, {_}: greatest_lower_bound ?802 (negative_part ?803) =<= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Demod 317 with 36 at 2,2
-Id : 770, {_}: greatest_lower_bound ?1137 (negative_part ?1138) =?= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 492 with 326 at 2
-Id : 16503, {_}: multiply (greatest_lower_bound (inverse ?19889) (negative_part ?19890)) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Demod 16475 with 770 at 1,2
-Id : 16376, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= negative_part (multiply ?735 ?736) [735, 736] by Demod 275 with 314 at 3
-Id : 16504, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19889, 19890] by Demod 16503 with 16376 at 2
-Id : 16505, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (multiply ?19890 ?19889) (negative_part ?19889) [19889, 19890] by Demod 16504 with 10 at 3
-Id : 47, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= multiply ?77 identity [78, 77] by Super 45 with 6 at 2,3
-Id : 4534, {_}: multiply (multiply ?6403 (inverse ?6404)) ?6404 =>= multiply ?6403 identity [6404, 6403] by Super 45 with 6 at 2,3
-Id : 4537, {_}: multiply identity ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Super 4534 with 6 at 1,2
-Id : 4552, {_}: ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Demod 4537 with 4 at 2
-Id : 46, {_}: multiply (multiply ?74 identity) ?75 =>= multiply ?74 ?75 [75, 74] by Super 45 with 4 at 2,3
-Id : 4557, {_}: multiply ?6432 ?6433 =<= multiply (inverse (inverse ?6432)) ?6433 [6433, 6432] by Super 46 with 4552 at 1,2
-Id : 4577, {_}: ?6410 =<= multiply ?6410 identity [6410] by Demod 4552 with 4557 at 3
-Id : 4578, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= ?77 [78, 77] by Demod 47 with 4577 at 3
-Id : 4593, {_}: inverse (inverse ?6519) =<= multiply ?6519 identity [6519] by Super 4577 with 4557 at 3
-Id : 4599, {_}: inverse (inverse ?6519) =>= ?6519 [6519] by Demod 4593 with 4577 at 3
-Id : 4627, {_}: multiply (multiply ?6536 ?6535) (inverse ?6535) =>= ?6536 [6535, 6536] by Super 4578 with 4599 at 2,1,2
-Id : 62773, {_}: inverse ?65768 =<= multiply (inverse (multiply ?65769 ?65768)) ?65769 [65769, 65768] by Super 63 with 4627 at 2,3
-Id : 177, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= least_upper_bound identity (multiply (inverse ?498) ?499) [499, 498] by Super 171 with 6 at 1,3
-Id : 4722, {_}: multiply (inverse ?6711) (least_upper_bound ?6711 ?6712) =>= positive_part (multiply (inverse ?6711) ?6712) [6712, 6711] by Demod 177 with 298 at 3
-Id : 4745, {_}: multiply (inverse ?6778) (positive_part ?6778) =?= positive_part (multiply (inverse ?6778) identity) [6778] by Super 4722 with 34 at 2,2
-Id : 4793, {_}: multiply (inverse ?6833) (positive_part ?6833) =>= positive_part (inverse ?6833) [6833] by Demod 4745 with 4577 at 1,3
-Id : 4805, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part (inverse (inverse ?6862)) [6862] by Super 4793 with 4599 at 1,2
-Id : 4824, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part ?6862 [6862] by Demod 4805 with 4599 at 1,3
-Id : 62790, {_}: inverse (positive_part (inverse ?65816)) =<= multiply (inverse (positive_part ?65816)) ?65816 [65816] by Super 62773 with 4824 at 1,1,3
-Id : 63210, {_}: negative_part (multiply (negative_part (inverse (positive_part ?66345))) ?66345) =>= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Super 16505 with 62790 at 1,3
-Id : 303, {_}: greatest_lower_bound ?780 (positive_part ?780) =>= ?780 [780] by Super 24 with 34 at 2,2
-Id : 535, {_}: greatest_lower_bound (positive_part ?1185) ?1185 =>= ?1185 [1185] by Super 10 with 303 at 3
-Id : 301, {_}: least_upper_bound ?774 (least_upper_bound ?775 identity) =>= positive_part (least_upper_bound ?774 ?775) [775, 774] by Super 16 with 34 at 3
-Id : 566, {_}: least_upper_bound ?1228 (positive_part ?1229) =<= positive_part (least_upper_bound ?1228 ?1229) [1229, 1228] by Demod 301 with 34 at 2,2
-Id : 576, {_}: least_upper_bound ?1260 (positive_part identity) =>= positive_part (positive_part ?1260) [1260] by Super 566 with 34 at 1,3
-Id : 297, {_}: positive_part identity =>= identity [] by Super 18 with 34 at 2
-Id : 590, {_}: least_upper_bound ?1260 identity =<= positive_part (positive_part ?1260) [1260] by Demod 576 with 297 at 2,2
-Id : 591, {_}: positive_part ?1260 =<= positive_part (positive_part ?1260) [1260] by Demod 590 with 34 at 2
-Id : 4802, {_}: multiply (inverse (positive_part ?6856)) (positive_part ?6856) =>= positive_part (inverse (positive_part ?6856)) [6856] by Super 4793 with 591 at 2,2
-Id : 4819, {_}: identity =<= positive_part (inverse (positive_part ?6856)) [6856] by Demod 4802 with 6 at 2
-Id : 4905, {_}: greatest_lower_bound identity (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Super 535 with 4819 at 1,2
-Id : 4952, {_}: negative_part (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Demod 4905 with 314 at 2
-Id : 63307, {_}: negative_part (multiply (inverse (positive_part ?66345)) ?66345) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63210 with 4952 at 1,1,2
-Id : 63308, {_}: negative_part (inverse (positive_part (inverse ?66345))) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63307 with 62790 at 1,2
-Id : 63309, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63308 with 4952 at 2
-Id : 5097, {_}: greatest_lower_bound (inverse (positive_part ?7140)) (negative_part ?7141) =>= greatest_lower_bound (inverse (positive_part ?7140)) ?7141 [7141, 7140] by Super 770 with 4952 at 1,3
-Id : 63310, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) ?66345 [66345] by Demod 63309 with 5097 at 3
-Id : 63817, {_}: greatest_lower_bound ?66966 (positive_part (inverse (positive_part (inverse ?66966)))) =>= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Super 17873 with 63310 at 1,3
-Id : 64085, {_}: greatest_lower_bound ?66966 identity =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 63817 with 4819 at 2,2
-Id : 64086, {_}: negative_part ?66966 =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 64085 with 36 at 2
-Id : 81154, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (positive_part (inverse ?80770))) [80770] by Super 14200 with 64086 at 1,2
-Id : 4710, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= positive_part (multiply (inverse ?498) ?499) [499, 498] by Demod 177 with 298 at 3
-Id : 444, {_}: least_upper_bound identity (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Super 16 with 298 at 1,3
-Id : 455, {_}: positive_part (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 444 with 298 at 2
-Id : 310, {_}: least_upper_bound ?774 (positive_part ?775) =<= positive_part (least_upper_bound ?774 ?775) [775, 774] by Demod 301 with 34 at 2,2
-Id : 677, {_}: least_upper_bound ?1100 (positive_part ?1101) =?= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 455 with 310 at 2
-Id : 483, {_}: least_upper_bound identity (negative_part ?1146) =>= identity [1146] by Super 22 with 314 at 2,2
-Id : 491, {_}: positive_part (negative_part ?1146) =>= identity [1146] by Demod 483 with 298 at 2
-Id : 4795, {_}: multiply (inverse (negative_part ?6836)) identity =>= positive_part (inverse (negative_part ?6836)) [6836] by Super 4793 with 491 at 2,2
-Id : 4816, {_}: inverse (negative_part ?6836) =<= positive_part (inverse (negative_part ?6836)) [6836] by Demod 4795 with 4577 at 2
-Id : 4838, {_}: least_upper_bound (inverse (negative_part ?6900)) (positive_part ?6901) =>= least_upper_bound (inverse (negative_part ?6900)) ?6901 [6901, 6900] by Super 677 with 4816 at 1,3
-Id : 6365, {_}: multiply (inverse (inverse (negative_part ?8525))) (least_upper_bound (inverse (negative_part ?8525)) ?8526) =>= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Super 4710 with 4838 at 2,2
-Id : 6403, {_}: positive_part (multiply (inverse (inverse (negative_part ?8525))) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6365 with 4710 at 2
-Id : 6404, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6403 with 4599 at 1,1,2
-Id : 6405, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (negative_part ?8525) (positive_part ?8526)) [8526, 8525] by Demod 6404 with 4599 at 1,1,3
-Id : 81274, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (inverse ?80770)) [80770] by Demod 81154 with 6405 at 3
-Id : 16478, {_}: multiply (negative_part (inverse ?19896)) ?19896 =>= negative_part ?19896 [19896] by Demod 16415 with 4 at 1,3
-Id : 16480, {_}: multiply (negative_part ?19899) (inverse ?19899) =>= negative_part (inverse ?19899) [19899] by Super 16478 with 4599 at 1,1,2
-Id : 81275, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= positive_part (negative_part (inverse ?80770)) [80770] by Demod 81274 with 16480 at 1,3
-Id : 81276, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= identity [80770] by Demod 81275 with 491 at 3
-Id : 81601, {_}: positive_part (inverse ?81005) =<= multiply (inverse (negative_part ?81005)) identity [81005] by Super 63 with 81276 at 2,3
-Id : 81716, {_}: positive_part (inverse ?81005) =>= inverse (negative_part ?81005) [81005] by Demod 81601 with 4577 at 3
-Id : 81904, {_}: multiply (inverse (negative_part ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14268 with 81716 at 1,2
-Id : 208, {_}: multiply (inverse ?574) (greatest_lower_bound ?574 ?575) =>= greatest_lower_bound identity (multiply (inverse ?574) ?575) [575, 574] by Super 202 with 6 at 1,3
-Id : 13518, {_}: multiply (inverse ?16653) (greatest_lower_bound ?16653 ?16654) =>= negative_part (multiply (inverse ?16653) ?16654) [16654, 16653] by Demod 208 with 314 at 3
-Id : 13544, {_}: multiply (inverse ?16729) (negative_part ?16729) =?= negative_part (multiply (inverse ?16729) identity) [16729] by Super 13518 with 36 at 2,2
-Id : 13624, {_}: multiply (inverse ?16816) (negative_part ?16816) =>= negative_part (inverse ?16816) [16816] by Demod 13544 with 4577 at 1,3
-Id : 13651, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part (inverse (inverse ?16885)) [16885] by Super 13624 with 4599 at 1,2
-Id : 13713, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part ?16885 [16885] by Demod 13651 with 4599 at 1,3
-Id : 62794, {_}: inverse (negative_part (inverse ?65826)) =<= multiply (inverse (negative_part ?65826)) ?65826 [65826] by Super 62773 with 13713 at 1,1,3
-Id : 81928, {_}: inverse (negative_part (inverse ?17673)) =>= positive_part ?17673 [17673] by Demod 81904 with 62794 at 2
-Id : 81935, {_}: ?19856 =<= multiply (positive_part ?19856) (negative_part ?19856) [19856] by Demod 16463 with 81928 at 1,3
-Id : 82404, {_}: a === a [] by Demod 2 with 81935 at 3
-Id : 2, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 90
- least_upper_bound is 86
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- p09b_1 is 74
- p09b_2 is 73
- p09b_3 is 72
- p09b_4 is 71
- prove_p09b is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
- Id : 36, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
- Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
- Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-Found proof, 198.990674s
-% SZS status Unsatisfiable for GRP178-2.p
-% SZS output start CNFRefutation for GRP178-2.p
-Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 171, {_}: multiply ?467 (least_upper_bound ?468 ?469) =<= least_upper_bound (multiply ?467 ?468) (multiply ?467 ?469) [469, 468, 467] by monotony_lub1 ?467 ?468 ?469
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 202, {_}: multiply ?543 (greatest_lower_bound ?544 ?545) =<= greatest_lower_bound (multiply ?543 ?544) (multiply ?543 ?545) [545, 544, 543] by monotony_glb1 ?543 ?544 ?545
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 45, {_}: multiply (multiply ?62 ?63) ?64 =?= multiply ?62 (multiply ?63 ?64) [64, 63, 62] by associativity ?62 ?63 ?64
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 54, {_}: multiply identity ?97 =<= multiply (inverse ?96) (multiply ?96 ?97) [96, 97] by Super 45 with 6 at 1,2
-Id : 63, {_}: ?97 =<= multiply (inverse ?96) (multiply ?96 ?97) [96, 97] by Demod 54 with 4 at 2
-Id : 47, {_}: multiply (multiply ?69 (inverse ?70)) ?70 =>= multiply ?69 identity [70, 69] by Super 45 with 6 at 2,3
-Id : 9265, {_}: multiply (multiply ?8232 (inverse ?8233)) ?8233 =>= multiply ?8232 identity [8233, 8232] by Super 45 with 6 at 2,3
-Id : 9268, {_}: multiply identity ?8239 =<= multiply (inverse (inverse ?8239)) identity [8239] by Super 9265 with 6 at 1,2
-Id : 9283, {_}: ?8239 =<= multiply (inverse (inverse ?8239)) identity [8239] by Demod 9268 with 4 at 2
-Id : 46, {_}: multiply (multiply ?66 identity) ?67 =>= multiply ?66 ?67 [67, 66] by Super 45 with 4 at 2,3
-Id : 9288, {_}: multiply ?8261 ?8262 =<= multiply (inverse (inverse ?8261)) ?8262 [8262, 8261] by Super 46 with 9283 at 1,2
-Id : 9304, {_}: ?8239 =<= multiply ?8239 identity [8239] by Demod 9283 with 9288 at 3
-Id : 9305, {_}: multiply (multiply ?69 (inverse ?70)) ?70 =>= ?69 [70, 69] by Demod 47 with 9304 at 3
-Id : 9320, {_}: inverse (inverse ?8348) =<= multiply ?8348 identity [8348] by Super 9304 with 9288 at 3
-Id : 9326, {_}: inverse (inverse ?8348) =>= ?8348 [8348] by Demod 9320 with 9304 at 3
-Id : 9354, {_}: multiply (multiply ?8365 ?8364) (inverse ?8364) =>= ?8365 [8364, 8365] by Super 9305 with 9326 at 2,1,2
-Id : 9315, {_}: multiply ?8330 (inverse ?8330) =>= identity [8330] by Super 6 with 9288 at 2
-Id : 9365, {_}: multiply ?8382 (greatest_lower_bound ?8383 (inverse ?8382)) =>= greatest_lower_bound (multiply ?8382 ?8383) identity [8383, 8382] by Super 28 with 9315 at 2,3
-Id : 9386, {_}: multiply ?8382 (greatest_lower_bound ?8383 (inverse ?8382)) =>= greatest_lower_bound identity (multiply ?8382 ?8383) [8383, 8382] by Demod 9365 with 10 at 3
-Id : 137579, {_}: multiply (inverse ?85743) (greatest_lower_bound ?85743 ?85744) =>= greatest_lower_bound identity (multiply (inverse ?85743) ?85744) [85744, 85743] by Super 202 with 6 at 1,3
-Id : 4862, {_}: greatest_lower_bound (least_upper_bound ?4719 ?4720) ?4719 =>= ?4719 [4720, 4719] by Super 10 with 24 at 3
-Id : 4863, {_}: greatest_lower_bound (least_upper_bound ?4723 ?4722) ?4722 =>= ?4722 [4722, 4723] by Super 4862 with 12 at 1,2
-Id : 173, {_}: multiply (inverse ?475) (least_upper_bound ?474 ?475) =>= least_upper_bound (multiply (inverse ?475) ?474) identity [474, 475] by Super 171 with 6 at 2,3
-Id : 9616, {_}: multiply (inverse ?8736) (least_upper_bound ?8737 ?8736) =>= least_upper_bound identity (multiply (inverse ?8736) ?8737) [8737, 8736] by Demod 173 with 12 at 3
-Id : 336, {_}: greatest_lower_bound b a =>= identity [] by Demod 40 with 10 at 2
-Id : 337, {_}: least_upper_bound b identity =>= b [] by Super 22 with 336 at 2,2
-Id : 349, {_}: least_upper_bound identity b =>= b [] by Demod 337 with 12 at 2
-Id : 9624, {_}: multiply (inverse b) b =<= least_upper_bound identity (multiply (inverse b) identity) [] by Super 9616 with 349 at 2,2
-Id : 9699, {_}: identity =<= least_upper_bound identity (multiply (inverse b) identity) [] by Demod 9624 with 6 at 2
-Id : 9700, {_}: identity =<= least_upper_bound identity (inverse b) [] by Demod 9699 with 9304 at 2,3
-Id : 9734, {_}: greatest_lower_bound identity (inverse b) =>= inverse b [] by Super 4863 with 9700 at 1,2
-Id : 9886, {_}: greatest_lower_bound ?8962 (inverse b) =<= greatest_lower_bound (greatest_lower_bound ?8962 identity) (inverse b) [8962] by Super 14 with 9734 at 2,2
-Id : 9910, {_}: greatest_lower_bound ?8962 (inverse b) =<= greatest_lower_bound (inverse b) (greatest_lower_bound ?8962 identity) [8962] by Demod 9886 with 10 at 3
-Id : 138060, {_}: multiply (inverse (inverse b)) (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply (inverse (inverse b)) (greatest_lower_bound ?86438 identity)) [86438] by Super 137579 with 9910 at 2,2
-Id : 139832, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply (inverse (inverse b)) (greatest_lower_bound ?86438 identity)) [86438] by Demod 138060 with 9326 at 1,2
-Id : 139833, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?86438 identity)) [86438] by Demod 139832 with 9326 at 1,2,3
-Id : 190, {_}: multiply (inverse ?475) (least_upper_bound ?474 ?475) =>= least_upper_bound identity (multiply (inverse ?475) ?474) [474, 475] by Demod 173 with 12 at 3
-Id : 299, {_}: greatest_lower_bound ?761 identity =<= greatest_lower_bound (greatest_lower_bound ?761 identity) a [761] by Super 14 with 34 at 2,2
-Id : 308, {_}: greatest_lower_bound ?761 identity =<= greatest_lower_bound a (greatest_lower_bound ?761 identity) [761] by Demod 299 with 10 at 3
-Id : 691, {_}: least_upper_bound a (greatest_lower_bound ?1150 identity) =>= a [1150] by Super 22 with 308 at 2,2
-Id : 693, {_}: least_upper_bound a identity =>= a [] by Super 691 with 20 at 2,2
-Id : 704, {_}: least_upper_bound identity a =>= a [] by Demod 693 with 12 at 2
-Id : 707, {_}: least_upper_bound ?1166 a =<= least_upper_bound (least_upper_bound ?1166 identity) a [1166] by Super 16 with 704 at 2,2
-Id : 1790, {_}: least_upper_bound ?1985 a =<= least_upper_bound a (least_upper_bound ?1985 identity) [1985] by Demod 707 with 12 at 3
-Id : 1791, {_}: least_upper_bound ?1987 a =<= least_upper_bound a (least_upper_bound identity ?1987) [1987] by Super 1790 with 12 at 2,3
-Id : 9745, {_}: least_upper_bound (inverse b) a =>= least_upper_bound a identity [] by Super 1791 with 9700 at 2,3
-Id : 9760, {_}: least_upper_bound a (inverse b) =>= least_upper_bound a identity [] by Demod 9745 with 12 at 2
-Id : 9761, {_}: least_upper_bound a (inverse b) =>= least_upper_bound identity a [] by Demod 9760 with 12 at 3
-Id : 9762, {_}: least_upper_bound a (inverse b) =>= a [] by Demod 9761 with 704 at 3
-Id : 9940, {_}: multiply (inverse (inverse b)) a =<= least_upper_bound identity (multiply (inverse (inverse b)) a) [] by Super 190 with 9762 at 2,2
-Id : 9943, {_}: multiply b a =<= least_upper_bound identity (multiply (inverse (inverse b)) a) [] by Demod 9940 with 9326 at 1,2
-Id : 9944, {_}: multiply b a =<= least_upper_bound identity (multiply b a) [] by Demod 9943 with 9326 at 1,2,3
-Id : 10784, {_}: greatest_lower_bound identity (multiply b a) =>= identity [] by Super 24 with 9944 at 2,2
-Id : 47323, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply b a) ?32510) =>= greatest_lower_bound identity ?32510 [32510] by Super 14 with 10784 at 1,3
-Id : 69234, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound a ?46169)) =>= greatest_lower_bound identity (multiply b ?46169) [46169] by Super 47323 with 28 at 2,2
-Id : 339, {_}: greatest_lower_bound ?788 identity =<= greatest_lower_bound (greatest_lower_bound ?788 b) a [788] by Super 14 with 336 at 2,2
-Id : 348, {_}: greatest_lower_bound ?788 identity =<= greatest_lower_bound a (greatest_lower_bound ?788 b) [788] by Demod 339 with 10 at 3
-Id : 69253, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 identity)) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 b)) [46206] by Super 69234 with 348 at 2,2,2
-Id : 353, {_}: least_upper_bound ?797 b =<= least_upper_bound (least_upper_bound ?797 identity) b [797] by Super 16 with 349 at 2,2
-Id : 607, {_}: least_upper_bound ?1066 b =<= least_upper_bound b (least_upper_bound ?1066 identity) [1066] by Demod 353 with 12 at 3
-Id : 608, {_}: least_upper_bound ?1068 b =<= least_upper_bound b (least_upper_bound identity ?1068) [1068] by Super 607 with 12 at 2,3
-Id : 9739, {_}: least_upper_bound (inverse b) b =>= least_upper_bound b identity [] by Super 608 with 9700 at 2,3
-Id : 9768, {_}: least_upper_bound b (inverse b) =>= least_upper_bound b identity [] by Demod 9739 with 12 at 2
-Id : 9769, {_}: least_upper_bound b (inverse b) =>= least_upper_bound identity b [] by Demod 9768 with 12 at 3
-Id : 9770, {_}: least_upper_bound b (inverse b) =>= b [] by Demod 9769 with 349 at 3
-Id : 9967, {_}: multiply (inverse (inverse b)) b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Super 190 with 9770 at 2,2
-Id : 10010, {_}: multiply b b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Demod 9967 with 9326 at 1,2
-Id : 10011, {_}: multiply b b =<= least_upper_bound identity (multiply b b) [] by Demod 10010 with 9326 at 1,2,3
-Id : 10830, {_}: greatest_lower_bound identity (multiply b b) =>= identity [] by Super 24 with 10011 at 2,2
-Id : 11235, {_}: greatest_lower_bound ?9614 identity =<= greatest_lower_bound (greatest_lower_bound ?9614 identity) (multiply b b) [9614] by Super 14 with 10830 at 2,2
-Id : 394, {_}: greatest_lower_bound ?844 identity =<= greatest_lower_bound a (greatest_lower_bound ?844 identity) [844] by Demod 299 with 10 at 3
-Id : 395, {_}: greatest_lower_bound ?846 identity =<= greatest_lower_bound a (greatest_lower_bound identity ?846) [846] by Super 394 with 10 at 2,3
-Id : 721, {_}: greatest_lower_bound a (greatest_lower_bound (greatest_lower_bound identity ?1178) ?1179) =>= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Super 14 with 395 at 1,3
-Id : 751, {_}: greatest_lower_bound a (greatest_lower_bound identity (greatest_lower_bound ?1178 ?1179)) =>= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 721 with 14 at 2,2
-Id : 752, {_}: greatest_lower_bound (greatest_lower_bound ?1178 ?1179) identity =?= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 751 with 395 at 2
-Id : 753, {_}: greatest_lower_bound identity (greatest_lower_bound ?1178 ?1179) =<= greatest_lower_bound (greatest_lower_bound ?1178 identity) ?1179 [1179, 1178] by Demod 752 with 10 at 2
-Id : 47765, {_}: greatest_lower_bound ?32774 identity =<= greatest_lower_bound identity (greatest_lower_bound ?32774 (multiply b b)) [32774] by Demod 11235 with 753 at 3
-Id : 47777, {_}: greatest_lower_bound (multiply b ?32794) identity =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?32794 b)) [32794] by Super 47765 with 28 at 2,3
-Id : 47888, {_}: greatest_lower_bound identity (multiply b ?32794) =<= greatest_lower_bound identity (multiply b (greatest_lower_bound ?32794 b)) [32794] by Demod 47777 with 10 at 2
-Id : 112860, {_}: greatest_lower_bound identity (multiply b (greatest_lower_bound ?46206 identity)) =>= greatest_lower_bound identity (multiply b ?46206) [46206] by Demod 69253 with 47888 at 3
-Id : 139834, {_}: multiply b (greatest_lower_bound ?86438 (inverse b)) =>= greatest_lower_bound identity (multiply b ?86438) [86438] by Demod 139833 with 112860 at 3
-Id : 758814, {_}: greatest_lower_bound ?433915 (inverse b) =<= multiply (inverse b) (greatest_lower_bound identity (multiply b ?433915)) [433915] by Super 63 with 139834 at 2,3
-Id : 9363, {_}: multiply (greatest_lower_bound ?8377 ?8376) (inverse ?8376) =>= greatest_lower_bound (multiply ?8377 (inverse ?8376)) identity [8376, 8377] by Super 32 with 9315 at 2,3
-Id : 389839, {_}: multiply (greatest_lower_bound ?219201 ?219202) (inverse ?219202) =>= greatest_lower_bound identity (multiply ?219201 (inverse ?219202)) [219202, 219201] by Demod 9363 with 10 at 3
-Id : 389867, {_}: multiply identity (inverse a) =<= greatest_lower_bound identity (multiply b (inverse a)) [] by Super 389839 with 336 at 1,2
-Id : 390920, {_}: inverse a =<= greatest_lower_bound identity (multiply b (inverse a)) [] by Demod 389867 with 4 at 2
-Id : 758889, {_}: greatest_lower_bound (inverse a) (inverse b) =<= multiply (inverse b) (inverse a) [] by Super 758814 with 390920 at 2,3
-Id : 759137, {_}: greatest_lower_bound (inverse b) (inverse a) =<= multiply (inverse b) (inverse a) [] by Demod 758889 with 10 at 2
-Id : 9373, {_}: multiply (least_upper_bound ?8405 ?8404) (inverse ?8404) =>= least_upper_bound (multiply ?8405 (inverse ?8404)) identity [8404, 8405] by Super 30 with 9315 at 2,3
-Id : 379748, {_}: multiply (least_upper_bound ?213200 ?213201) (inverse ?213201) =>= least_upper_bound identity (multiply ?213200 (inverse ?213201)) [213201, 213200] by Demod 9373 with 12 at 3
-Id : 9632, {_}: multiply (inverse a) a =<= least_upper_bound identity (multiply (inverse a) identity) [] by Super 9616 with 704 at 2,2
-Id : 9704, {_}: identity =<= least_upper_bound identity (multiply (inverse a) identity) [] by Demod 9632 with 6 at 2
-Id : 9705, {_}: identity =<= least_upper_bound identity (inverse a) [] by Demod 9704 with 9304 at 2,3
-Id : 9791, {_}: least_upper_bound (inverse a) b =>= least_upper_bound b identity [] by Super 608 with 9705 at 2,3
-Id : 9810, {_}: least_upper_bound b (inverse a) =>= least_upper_bound b identity [] by Demod 9791 with 12 at 2
-Id : 9811, {_}: least_upper_bound b (inverse a) =>= least_upper_bound identity b [] by Demod 9810 with 12 at 3
-Id : 9812, {_}: least_upper_bound b (inverse a) =>= b [] by Demod 9811 with 349 at 3
-Id : 10144, {_}: multiply (inverse (inverse a)) b =<= least_upper_bound identity (multiply (inverse (inverse a)) b) [] by Super 190 with 9812 at 2,2
-Id : 10186, {_}: multiply a b =<= least_upper_bound identity (multiply (inverse (inverse a)) b) [] by Demod 10144 with 9326 at 1,2
-Id : 10187, {_}: multiply a b =<= least_upper_bound identity (multiply a b) [] by Demod 10186 with 9326 at 1,2,3
-Id : 380544, {_}: multiply (multiply a b) (inverse (multiply a b)) =>= least_upper_bound identity (multiply identity (inverse (multiply a b))) [] by Super 379748 with 10187 at 1,2
-Id : 382056, {_}: multiply a (multiply b (inverse (multiply a b))) =>= least_upper_bound identity (multiply identity (inverse (multiply a b))) [] by Demod 380544 with 8 at 2
-Id : 382057, {_}: multiply a (multiply b (inverse (multiply a b))) =>= least_upper_bound identity (inverse (multiply a b)) [] by Demod 382056 with 4 at 2,3
-Id : 10969, {_}: multiply (inverse (multiply a b)) (multiply a b) =>= least_upper_bound identity (multiply (inverse (multiply a b)) identity) [] by Super 190 with 10187 at 2,2
-Id : 10972, {_}: identity =<= least_upper_bound identity (multiply (inverse (multiply a b)) identity) [] by Demod 10969 with 6 at 2
-Id : 10973, {_}: identity =<= least_upper_bound identity (inverse (multiply a b)) [] by Demod 10972 with 9304 at 2,3
-Id : 382058, {_}: multiply a (multiply b (inverse (multiply a b))) =>= identity [] by Demod 382057 with 10973 at 3
-Id : 383433, {_}: multiply b (inverse (multiply a b)) =>= multiply (inverse a) identity [] by Super 63 with 382058 at 2,3
-Id : 383436, {_}: multiply b (inverse (multiply a b)) =>= inverse a [] by Demod 383433 with 9304 at 3
-Id : 383449, {_}: inverse (multiply a b) =<= multiply (inverse b) (inverse a) [] by Super 63 with 383436 at 2,3
-Id : 759138, {_}: greatest_lower_bound (inverse b) (inverse a) =>= inverse (multiply a b) [] by Demod 759137 with 383449 at 3
-Id : 759204, {_}: multiply a (inverse (multiply a b)) =>= greatest_lower_bound identity (multiply a (inverse b)) [] by Super 9386 with 759138 at 2,2
-Id : 368035, {_}: multiply (greatest_lower_bound ?208569 ?208570) (inverse ?208569) =>= greatest_lower_bound identity (multiply ?208570 (inverse ?208569)) [208570, 208569] by Super 32 with 9315 at 1,3
-Id : 368063, {_}: multiply identity (inverse b) =<= greatest_lower_bound identity (multiply a (inverse b)) [] by Super 368035 with 336 at 1,2
-Id : 369182, {_}: inverse b =<= greatest_lower_bound identity (multiply a (inverse b)) [] by Demod 368063 with 4 at 2
-Id : 759234, {_}: multiply a (inverse (multiply a b)) =>= inverse b [] by Demod 759204 with 369182 at 3
-Id : 759348, {_}: inverse (multiply a b) =<= multiply (inverse a) (inverse b) [] by Super 63 with 759234 at 2,3
-Id : 380530, {_}: multiply (multiply b a) (inverse (multiply b a)) =>= least_upper_bound identity (multiply identity (inverse (multiply b a))) [] by Super 379748 with 9944 at 1,2
-Id : 382029, {_}: multiply b (multiply a (inverse (multiply b a))) =>= least_upper_bound identity (multiply identity (inverse (multiply b a))) [] by Demod 380530 with 8 at 2
-Id : 382030, {_}: multiply b (multiply a (inverse (multiply b a))) =>= least_upper_bound identity (inverse (multiply b a)) [] by Demod 382029 with 4 at 2,3
-Id : 10793, {_}: multiply (inverse (multiply b a)) (multiply b a) =>= least_upper_bound identity (multiply (inverse (multiply b a)) identity) [] by Super 190 with 9944 at 2,2
-Id : 10796, {_}: identity =<= least_upper_bound identity (multiply (inverse (multiply b a)) identity) [] by Demod 10793 with 6 at 2
-Id : 10797, {_}: identity =<= least_upper_bound identity (inverse (multiply b a)) [] by Demod 10796 with 9304 at 2,3
-Id : 382031, {_}: multiply b (multiply a (inverse (multiply b a))) =>= identity [] by Demod 382030 with 10797 at 3
-Id : 382929, {_}: multiply a (inverse (multiply b a)) =>= multiply (inverse b) identity [] by Super 63 with 382031 at 2,3
-Id : 382932, {_}: multiply a (inverse (multiply b a)) =>= inverse b [] by Demod 382929 with 9304 at 3
-Id : 382945, {_}: inverse (multiply b a) =<= multiply (inverse a) (inverse b) [] by Super 63 with 382932 at 2,3
-Id : 759368, {_}: inverse (multiply a b) =>= inverse (multiply b a) [] by Demod 759348 with 382945 at 3
-Id : 759573, {_}: inverse (inverse (multiply b a)) =>= multiply a b [] by Super 9326 with 759368 at 1,2
-Id : 759596, {_}: multiply b a =<= multiply a b [] by Demod 759573 with 9326 at 2
-Id : 760017, {_}: multiply (multiply b a) (inverse b) =>= a [] by Super 9354 with 759596 at 1,2
-Id : 760034, {_}: multiply b (multiply a (inverse b)) =>= a [] by Demod 760017 with 8 at 2
-Id : 760418, {_}: multiply a (inverse b) =<= multiply (inverse b) a [] by Super 63 with 760034 at 2,3
-Id : 760473, {_}: multiply (multiply a (inverse b)) ?434336 =>= multiply (inverse b) (multiply a ?434336) [434336] by Super 8 with 760418 at 1,2
-Id : 760489, {_}: multiply a (multiply (inverse b) ?434336) =<= multiply (inverse b) (multiply a ?434336) [434336] by Demod 760473 with 8 at 2
-Id : 763912, {_}: multiply a (greatest_lower_bound b ?436084) =<= greatest_lower_bound (multiply b a) (multiply a ?436084) [436084] by Super 28 with 759596 at 1,3
-Id : 760023, {_}: multiply (multiply b a) ?434182 =>= multiply a (multiply b ?434182) [434182] by Super 8 with 759596 at 1,2
-Id : 760032, {_}: multiply b (multiply a ?434182) =<= multiply a (multiply b ?434182) [434182] by Demod 760023 with 8 at 2
-Id : 763932, {_}: multiply a (greatest_lower_bound b (multiply b ?436118)) =<= greatest_lower_bound (multiply b a) (multiply b (multiply a ?436118)) [436118] by Super 763912 with 760032 at 2,3
-Id : 764080, {_}: multiply a (greatest_lower_bound b (multiply b ?436118)) =>= multiply b (greatest_lower_bound a (multiply a ?436118)) [436118] by Demod 763932 with 28 at 3
-Id : 768933, {_}: multiply a (multiply (inverse b) (greatest_lower_bound b (multiply b ?438632))) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Super 760489 with 764080 at 2,3
-Id : 208, {_}: multiply (inverse ?566) (greatest_lower_bound ?566 ?567) =>= greatest_lower_bound identity (multiply (inverse ?566) ?567) [567, 566] by Super 202 with 6 at 1,3
-Id : 768988, {_}: multiply a (greatest_lower_bound identity (multiply (inverse b) (multiply b ?438632))) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Demod 768933 with 208 at 2,2
-Id : 768989, {_}: multiply a (greatest_lower_bound identity ?438632) =<= multiply (inverse b) (multiply b (greatest_lower_bound a (multiply a ?438632))) [438632] by Demod 768988 with 63 at 2,2,2
-Id : 769075, {_}: multiply a (greatest_lower_bound identity ?438774) =>= greatest_lower_bound a (multiply a ?438774) [438774] by Demod 768989 with 63 at 3
-Id : 325, {_}: greatest_lower_bound ?779 identity =<= greatest_lower_bound (greatest_lower_bound ?779 identity) c [779] by Super 14 with 38 at 2,2
-Id : 334, {_}: greatest_lower_bound ?779 identity =<= greatest_lower_bound c (greatest_lower_bound ?779 identity) [779] by Demod 325 with 10 at 3
-Id : 1055, {_}: least_upper_bound c (greatest_lower_bound ?1435 identity) =>= c [1435] by Super 22 with 334 at 2,2
-Id : 1057, {_}: least_upper_bound c identity =>= c [] by Super 1055 with 20 at 2,2
-Id : 1068, {_}: least_upper_bound identity c =>= c [] by Demod 1057 with 12 at 2
-Id : 1072, {_}: least_upper_bound ?1452 c =<= least_upper_bound (least_upper_bound ?1452 identity) c [1452] by Super 16 with 1068 at 2,2
-Id : 2044, {_}: least_upper_bound ?2196 c =<= least_upper_bound c (least_upper_bound ?2196 identity) [2196] by Demod 1072 with 12 at 3
-Id : 2045, {_}: least_upper_bound ?2198 c =<= least_upper_bound c (least_upper_bound identity ?2198) [2198] by Super 2044 with 12 at 2,3
-Id : 9738, {_}: least_upper_bound (inverse b) c =>= least_upper_bound c identity [] by Super 2045 with 9700 at 2,3
-Id : 9771, {_}: least_upper_bound c (inverse b) =>= least_upper_bound c identity [] by Demod 9738 with 12 at 2
-Id : 9772, {_}: least_upper_bound c (inverse b) =>= least_upper_bound identity c [] by Demod 9771 with 12 at 3
-Id : 9773, {_}: least_upper_bound c (inverse b) =>= c [] by Demod 9772 with 1068 at 3
-Id : 10029, {_}: multiply (inverse (inverse b)) c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Super 190 with 9773 at 2,2
-Id : 10032, {_}: multiply b c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Demod 10029 with 9326 at 1,2
-Id : 10033, {_}: multiply b c =<= least_upper_bound identity (multiply b c) [] by Demod 10032 with 9326 at 1,2,3
-Id : 10872, {_}: greatest_lower_bound identity (multiply b c) =>= identity [] by Super 24 with 10033 at 2,2
-Id : 47955, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply b c) ?32868) =>= greatest_lower_bound identity ?32868 [32868] by Super 14 with 10872 at 1,3
-Id : 70757, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound b ?47489) c) =>= greatest_lower_bound identity (multiply ?47489 c) [47489] by Super 47955 with 32 at 2,2
-Id : 338, {_}: greatest_lower_bound b (greatest_lower_bound a ?786) =>= greatest_lower_bound identity ?786 [786] by Super 14 with 336 at 1,3
-Id : 70764, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound identity ?47501) c) =<= greatest_lower_bound identity (multiply (greatest_lower_bound a ?47501) c) [47501] by Super 70757 with 338 at 1,2,2
-Id : 9792, {_}: least_upper_bound (inverse a) c =>= least_upper_bound c identity [] by Super 2045 with 9705 at 2,3
-Id : 9807, {_}: least_upper_bound c (inverse a) =>= least_upper_bound c identity [] by Demod 9792 with 12 at 2
-Id : 9808, {_}: least_upper_bound c (inverse a) =>= least_upper_bound identity c [] by Demod 9807 with 12 at 3
-Id : 9809, {_}: least_upper_bound c (inverse a) =>= c [] by Demod 9808 with 1068 at 3
-Id : 10119, {_}: multiply (inverse (inverse a)) c =<= least_upper_bound identity (multiply (inverse (inverse a)) c) [] by Super 190 with 9809 at 2,2
-Id : 10122, {_}: multiply a c =<= least_upper_bound identity (multiply (inverse (inverse a)) c) [] by Demod 10119 with 9326 at 1,2
-Id : 10123, {_}: multiply a c =<= least_upper_bound identity (multiply a c) [] by Demod 10122 with 9326 at 1,2,3
-Id : 10918, {_}: greatest_lower_bound identity (multiply a c) =>= identity [] by Super 24 with 10123 at 2,2
-Id : 48295, {_}: greatest_lower_bound identity (greatest_lower_bound (multiply a c) ?33053) =>= greatest_lower_bound identity ?33053 [33053] by Super 14 with 10918 at 1,3
-Id : 48305, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound a ?33073) c) =>= greatest_lower_bound identity (multiply ?33073 c) [33073] by Super 48295 with 32 at 2,2
-Id : 115728, {_}: greatest_lower_bound identity (multiply (greatest_lower_bound identity ?47501) c) =>= greatest_lower_bound identity (multiply ?47501 c) [47501] by Demod 70764 with 48305 at 3
-Id : 204, {_}: multiply (inverse ?551) (greatest_lower_bound ?550 ?551) =>= greatest_lower_bound (multiply (inverse ?551) ?550) identity [550, 551] by Super 202 with 6 at 2,3
-Id : 142360, {_}: multiply (inverse ?87937) (greatest_lower_bound ?87938 ?87937) =>= greatest_lower_bound identity (multiply (inverse ?87937) ?87938) [87938, 87937] by Demod 204 with 10 at 3
-Id : 142374, {_}: multiply (inverse a) identity =<= greatest_lower_bound identity (multiply (inverse a) b) [] by Super 142360 with 336 at 2,2
-Id : 143139, {_}: inverse a =<= greatest_lower_bound identity (multiply (inverse a) b) [] by Demod 142374 with 9304 at 2
-Id : 144455, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (multiply (multiply (inverse a) b) c) [] by Super 115728 with 143139 at 1,2,2
-Id : 144470, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (multiply (inverse a) (multiply b c)) [] by Demod 144455 with 8 at 2,3
-Id : 769471, {_}: multiply a (greatest_lower_bound identity (multiply (inverse a) c)) =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Super 769075 with 144470 at 2,2
-Id : 768990, {_}: multiply a (greatest_lower_bound identity ?438632) =>= greatest_lower_bound a (multiply a ?438632) [438632] by Demod 768989 with 63 at 3
-Id : 770016, {_}: greatest_lower_bound a (multiply a (multiply (inverse a) c)) =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 769471 with 768990 at 2
-Id : 9368, {_}: multiply identity ?8392 =<= multiply ?8391 (multiply (inverse ?8391) ?8392) [8391, 8392] by Super 8 with 9315 at 1,2
-Id : 9385, {_}: ?8392 =<= multiply ?8391 (multiply (inverse ?8391) ?8392) [8391, 8392] by Demod 9368 with 4 at 2
-Id : 770017, {_}: greatest_lower_bound a c =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 770016 with 9385 at 2,2
-Id : 770018, {_}: greatest_lower_bound c a =<= greatest_lower_bound a (multiply a (multiply (inverse a) (multiply b c))) [] by Demod 770017 with 10 at 2
-Id : 770019, {_}: greatest_lower_bound c a =<= greatest_lower_bound a (multiply b c) [] by Demod 770018 with 9385 at 2,3
-Id : 770827, {_}: greatest_lower_bound c a === greatest_lower_bound c a [] by Demod 350 with 770019 at 2
-Id : 350, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound c a [] by Demod 2 with 10 at 3
-Id : 2, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c [] by prove_p09b
-% SZS output end CNFRefutation for GRP178-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- c is 72
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 94
- p12x_1 is 75
- p12x_2 is 74
- p12x_3 is 73
- p12x_4 is 71
- p12x_5 is 70
- p12x_6 is 69
- p12x_7 is 68
- prove_p12x is 96
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p12x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
- Id : 40, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
- Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
- Id : 44, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
- Id : 46, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-Goal
- Id : 2, {_}: a =>= b [] by prove_p12x
-Found proof, 11.815356s
-% SZS status Unsatisfiable for GRP181-4.p
-% SZS output start CNFRefutation for GRP181-4.p
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-Id : 177, {_}: multiply ?477 (least_upper_bound ?478 ?479) =<= least_upper_bound (multiply ?477 ?478) (multiply ?477 ?479) [479, 478, 477] by monotony_lub1 ?477 ?478 ?479
-Id : 46, {_}: inverse (least_upper_bound ?61 ?62) =<= greatest_lower_bound (inverse ?61) (inverse ?62) [62, 61] by p12x_7 ?61 ?62
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 40, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 44, {_}: inverse (greatest_lower_bound ?58 ?59) =<= least_upper_bound (inverse ?58) (inverse ?59) [59, 58] by p12x_6 ?58 ?59
-Id : 375, {_}: inverse (greatest_lower_bound ?877 ?878) =<= least_upper_bound (inverse ?877) (inverse ?878) [878, 877] by p12x_6 ?877 ?878
-Id : 398, {_}: inverse (least_upper_bound ?920 ?921) =<= greatest_lower_bound (inverse ?920) (inverse ?921) [921, 920] by p12x_7 ?920 ?921
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 208, {_}: multiply ?553 (greatest_lower_bound ?554 ?555) =<= greatest_lower_bound (multiply ?553 ?554) (multiply ?553 ?555) [555, 554, 553] by monotony_glb1 ?553 ?554 ?555
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 34, {_}: inverse identity =>= identity [] by p12x_1
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 51, {_}: multiply (multiply ?72 ?73) ?74 =?= multiply ?72 (multiply ?73 ?74) [74, 73, 72] by associativity ?72 ?73 ?74
-Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-Id : 324, {_}: inverse (multiply ?822 ?823) =<= multiply (inverse ?823) (inverse ?822) [823, 822] by p12x_3 ?822 ?823
-Id : 328, {_}: inverse (multiply ?833 (inverse ?832)) =>= multiply ?832 (inverse ?833) [832, 833] by Super 324 with 36 at 1,3
-Id : 53, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= multiply ?79 identity [80, 79] by Super 51 with 6 at 2,3
-Id : 325, {_}: inverse (multiply identity ?825) =<= multiply (inverse ?825) identity [825] by Super 324 with 34 at 2,3
-Id : 428, {_}: inverse ?975 =<= multiply (inverse ?975) identity [975] by Demod 325 with 4 at 1,2
-Id : 430, {_}: inverse (inverse ?978) =<= multiply ?978 identity [978] by Super 428 with 36 at 1,3
-Id : 441, {_}: ?978 =<= multiply ?978 identity [978] by Demod 430 with 36 at 2
-Id : 28686, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= ?79 [80, 79] by Demod 53 with 441 at 3
-Id : 28700, {_}: inverse ?20638 =<= multiply ?20639 (inverse (multiply ?20638 (inverse (inverse ?20639)))) [20639, 20638] by Super 328 with 28686 at 1,2
-Id : 28729, {_}: inverse ?20638 =<= multiply ?20639 (multiply (inverse ?20639) (inverse ?20638)) [20639, 20638] by Demod 28700 with 328 at 2,3
-Id : 28730, {_}: inverse ?20638 =<= multiply ?20639 (inverse (multiply ?20638 ?20639)) [20639, 20638] by Demod 28729 with 38 at 2,3
-Id : 307, {_}: multiply ?771 (inverse ?771) =>= identity [771] by Super 6 with 36 at 1,2
-Id : 598, {_}: multiply (multiply ?1178 ?1177) (inverse ?1177) =>= multiply ?1178 identity [1177, 1178] by Super 8 with 307 at 2,3
-Id : 42163, {_}: multiply (multiply ?33679 ?33680) (inverse ?33680) =>= ?33679 [33680, 33679] by Demod 598 with 441 at 3
-Id : 210, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound (multiply (inverse ?561) ?560) identity [560, 561] by Super 208 with 6 at 2,3
-Id : 229, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound identity (multiply (inverse ?561) ?560) [560, 561] by Demod 210 with 10 at 3
-Id : 401, {_}: inverse (least_upper_bound identity ?928) =>= greatest_lower_bound identity (inverse ?928) [928] by Super 398 with 34 at 1,3
-Id : 534, {_}: inverse (multiply (least_upper_bound identity ?1106) ?1107) =<= multiply (inverse ?1107) (greatest_lower_bound identity (inverse ?1106)) [1107, 1106] by Super 38 with 401 at 2,3
-Id : 34883, {_}: inverse (multiply (least_upper_bound identity ?27004) (inverse ?27004)) =>= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Super 229 with 534 at 2
-Id : 34945, {_}: multiply ?27004 (inverse (least_upper_bound identity ?27004)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Demod 34883 with 328 at 2
-Id : 34946, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?27004)) identity) [27004] by Demod 34945 with 401 at 2,2
-Id : 34947, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =>= greatest_lower_bound identity (inverse (inverse ?27004)) [27004] by Demod 34946 with 441 at 2,3
-Id : 34948, {_}: multiply ?27004 (greatest_lower_bound identity (inverse ?27004)) =>= greatest_lower_bound identity ?27004 [27004] by Demod 34947 with 36 at 2,3
-Id : 42223, {_}: multiply (greatest_lower_bound identity ?33882) (inverse (greatest_lower_bound identity (inverse ?33882))) =>= ?33882 [33882] by Super 42163 with 34948 at 1,2
-Id : 377, {_}: inverse (greatest_lower_bound ?883 (inverse ?882)) =>= least_upper_bound (inverse ?883) ?882 [882, 883] by Super 375 with 36 at 2,3
-Id : 42257, {_}: multiply (greatest_lower_bound identity ?33882) (least_upper_bound (inverse identity) ?33882) =>= ?33882 [33882] by Demod 42223 with 377 at 2,2
-Id : 118341, {_}: multiply (greatest_lower_bound identity ?85951) (least_upper_bound identity ?85951) =>= ?85951 [85951] by Demod 42257 with 34 at 1,2,2
-Id : 376, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound (inverse ?880) identity [880] by Super 375 with 34 at 2,3
-Id : 388, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound identity (inverse ?880) [880] by Demod 376 with 12 at 3
-Id : 509, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (inverse ?1077) (least_upper_bound identity (inverse ?1076)) [1076, 1077] by Super 44 with 388 at 2,3
-Id : 519, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (least_upper_bound identity (inverse ?1076)) (inverse ?1077) [1076, 1077] by Demod 509 with 12 at 3
-Id : 520, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound identity (least_upper_bound (inverse ?1076) (inverse ?1077)) [1076, 1077] by Demod 519 with 16 at 3
-Id : 521, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 520 with 44 at 2,3
-Id : 512, {_}: inverse (greatest_lower_bound ?1083 identity) =>= least_upper_bound identity (inverse ?1083) [1083] by Demod 376 with 12 at 3
-Id : 516, {_}: inverse (greatest_lower_bound ?1090 (greatest_lower_bound ?1091 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1090 ?1091)) [1091, 1090] by Super 512 with 14 at 1,2
-Id : 2150, {_}: least_upper_bound identity (inverse (greatest_lower_bound ?1077 ?1076)) =?= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 521 with 516 at 2
-Id : 30474, {_}: multiply (inverse ?22001) (greatest_lower_bound ?22001 ?22002) =>= greatest_lower_bound identity (multiply (inverse ?22001) ?22002) [22002, 22001] by Super 208 with 6 at 1,3
-Id : 337, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 40 with 10 at 2
-Id : 338, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 337 with 10 at 3
-Id : 30482, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 30474 with 338 at 2,2
-Id : 214, {_}: multiply (inverse ?576) (greatest_lower_bound ?576 ?577) =>= greatest_lower_bound identity (multiply (inverse ?576) ?577) [577, 576] by Super 208 with 6 at 1,3
-Id : 30627, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 30482 with 214 at 2
-Id : 30842, {_}: least_upper_bound identity (inverse (greatest_lower_bound (multiply (inverse c) a) identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Super 2150 with 30627 at 1,2,3
-Id : 30855, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) a))) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30842 with 2150 at 2
-Id : 378, {_}: inverse (greatest_lower_bound identity ?885) =>= least_upper_bound identity (inverse ?885) [885] by Super 375 with 34 at 1,3
-Id : 30856, {_}: least_upper_bound identity (least_upper_bound identity (inverse (multiply (inverse c) a))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30855 with 378 at 2,2
-Id : 112, {_}: least_upper_bound ?298 (least_upper_bound ?298 ?299) =>= least_upper_bound ?298 ?299 [299, 298] by Super 16 with 18 at 1,3
-Id : 30857, {_}: least_upper_bound identity (inverse (multiply (inverse c) a)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30856 with 112 at 2
-Id : 326, {_}: inverse (multiply (inverse ?827) ?828) =>= multiply (inverse ?828) ?827 [828, 827] by Super 324 with 36 at 2,3
-Id : 30858, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply (inverse c) b))) [] by Demod 30857 with 326 at 2,2
-Id : 30859, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (least_upper_bound identity (inverse (multiply (inverse c) b))) [] by Demod 30858 with 378 at 2,3
-Id : 30860, {_}: least_upper_bound identity (multiply (inverse a) c) =<= least_upper_bound identity (inverse (multiply (inverse c) b)) [] by Demod 30859 with 112 at 3
-Id : 30861, {_}: least_upper_bound identity (multiply (inverse a) c) =>= least_upper_bound identity (multiply (inverse b) c) [] by Demod 30860 with 326 at 2,3
-Id : 118363, {_}: multiply (greatest_lower_bound identity (multiply (inverse a) c)) (least_upper_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 118341 with 30861 at 2,2
-Id : 399, {_}: inverse (least_upper_bound ?923 identity) =>= greatest_lower_bound (inverse ?923) identity [923] by Super 398 with 34 at 2,3
-Id : 413, {_}: inverse (least_upper_bound ?923 identity) =>= greatest_lower_bound identity (inverse ?923) [923] by Demod 399 with 10 at 3
-Id : 560, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound (inverse ?1130) (greatest_lower_bound identity (inverse ?1129)) [1129, 1130] by Super 46 with 413 at 2,3
-Id : 580, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound (greatest_lower_bound identity (inverse ?1129)) (inverse ?1130) [1129, 1130] by Demod 560 with 10 at 3
-Id : 581, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =<= greatest_lower_bound identity (greatest_lower_bound (inverse ?1129) (inverse ?1130)) [1129, 1130] by Demod 580 with 14 at 3
-Id : 582, {_}: inverse (least_upper_bound ?1130 (least_upper_bound ?1129 identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound ?1129 ?1130)) [1129, 1130] by Demod 581 with 46 at 2,3
-Id : 569, {_}: inverse (least_upper_bound ?1152 identity) =>= greatest_lower_bound identity (inverse ?1152) [1152] by Demod 399 with 10 at 3
-Id : 573, {_}: inverse (least_upper_bound ?1159 (least_upper_bound ?1160 identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound ?1159 ?1160)) [1160, 1159] by Super 569 with 16 at 1,2
-Id : 2778, {_}: greatest_lower_bound identity (inverse (least_upper_bound ?1130 ?1129)) =?= greatest_lower_bound identity (inverse (least_upper_bound ?1129 ?1130)) [1129, 1130] by Demod 582 with 573 at 2
-Id : 28815, {_}: multiply (inverse ?20915) (least_upper_bound ?20915 ?20916) =>= least_upper_bound identity (multiply (inverse ?20915) ?20916) [20916, 20915] by Super 177 with 6 at 1,3
-Id : 353, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 42 with 12 at 2
-Id : 354, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 353 with 12 at 3
-Id : 28823, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 28815 with 354 at 2,2
-Id : 183, {_}: multiply (inverse ?500) (least_upper_bound ?500 ?501) =>= least_upper_bound identity (multiply (inverse ?500) ?501) [501, 500] by Super 177 with 6 at 1,3
-Id : 28958, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 28823 with 183 at 2
-Id : 29161, {_}: greatest_lower_bound identity (inverse (least_upper_bound (multiply (inverse c) a) identity)) =>= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Super 2778 with 28958 at 1,2,3
-Id : 29185, {_}: greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) a))) =>= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29161 with 2778 at 2
-Id : 29186, {_}: greatest_lower_bound identity (greatest_lower_bound identity (inverse (multiply (inverse c) a))) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29185 with 401 at 2,2
-Id : 124, {_}: greatest_lower_bound ?324 (greatest_lower_bound ?324 ?325) =>= greatest_lower_bound ?324 ?325 [325, 324] by Super 14 with 20 at 1,3
-Id : 29187, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) a)) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29186 with 124 at 2
-Id : 29188, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (multiply (inverse c) b))) [] by Demod 29187 with 326 at 2,2
-Id : 29189, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (greatest_lower_bound identity (inverse (multiply (inverse c) b))) [] by Demod 29188 with 401 at 2,3
-Id : 29190, {_}: greatest_lower_bound identity (multiply (inverse a) c) =<= greatest_lower_bound identity (inverse (multiply (inverse c) b)) [] by Demod 29189 with 124 at 3
-Id : 29191, {_}: greatest_lower_bound identity (multiply (inverse a) c) =>= greatest_lower_bound identity (multiply (inverse b) c) [] by Demod 29190 with 326 at 2,3
-Id : 118571, {_}: multiply (greatest_lower_bound identity (multiply (inverse b) c)) (least_upper_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 118363 with 29191 at 1,2
-Id : 42258, {_}: multiply (greatest_lower_bound identity ?33882) (least_upper_bound identity ?33882) =>= ?33882 [33882] by Demod 42257 with 34 at 1,2,2
-Id : 118572, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 118571 with 42258 at 2
-Id : 118655, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 28730 with 118572 at 1,2,3
-Id : 118658, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 118655 with 36 at 2
-Id : 118659, {_}: a =<= inverse (inverse b) [] by Demod 118658 with 28730 at 3
-Id : 118660, {_}: a =>= b [] by Demod 118659 with 36 at 3
-Id : 119303, {_}: b === b [] by Demod 2 with 118660 at 2
-Id : 2, {_}: a =>= b [] by prove_p12x
-% SZS output end CNFRefutation for GRP181-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 94
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 95
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 92
- p20x_1 is 76
- p20x_3 is 75
- prove_20x is 93
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p20x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-Last chance: 1246130000.01
-Last chance: all is indexed 1246130020.02
-Last chance: failed over 100 goal 1246130020.02
-FAILURE in 0 iterations
-% SZS status Timeout for GRP183-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21 is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-Found proof, 112.009971s
-% SZS status Unsatisfiable for GRP184-1.p
-% SZS output start CNFRefutation for GRP184-1.p
-Id : 265, {_}: multiply (greatest_lower_bound ?703 ?704) ?705 =<= greatest_lower_bound (multiply ?703 ?705) (multiply ?704 ?705) [705, 704, 703] by monotony_glb2 ?703 ?704 ?705
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 145, {_}: greatest_lower_bound ?406 (least_upper_bound ?406 ?407) =>= ?406 [407, 406] by glb_absorbtion ?406 ?407
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 127, {_}: least_upper_bound ?353 (greatest_lower_bound ?353 ?354) =>= ?353 [354, 353] by lub_absorbtion ?353 ?354
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 230, {_}: multiply (least_upper_bound ?621 ?622) ?623 =<= least_upper_bound (multiply ?621 ?623) (multiply ?622 ?623) [623, 622, 621] by monotony_lub2 ?621 ?622 ?623
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 38, {_}: multiply (multiply ?61 ?62) ?63 =?= multiply ?61 (multiply ?62 ?63) [63, 62, 61] by associativity ?61 ?62 ?63
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 2065, {_}: multiply (multiply ?3204 (inverse ?3205)) ?3205 =>= multiply ?3204 identity [3205, 3204] by Super 38 with 6 at 2,3
-Id : 2068, {_}: multiply identity ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Super 2065 with 6 at 1,2
-Id : 2091, {_}: ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Demod 2068 with 4 at 2
-Id : 2111, {_}: multiply (inverse (inverse ?3262)) (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Super 26 with 2091 at 2,3
-Id : 39, {_}: multiply (multiply ?65 identity) ?66 =>= multiply ?65 ?66 [66, 65] by Super 38 with 4 at 2,3
-Id : 2108, {_}: multiply ?3253 ?3254 =<= multiply (inverse (inverse ?3253)) ?3254 [3254, 3253] by Super 39 with 2091 at 1,2
-Id : 2129, {_}: ?3211 =<= multiply ?3211 identity [3211] by Demod 2091 with 2108 at 3
-Id : 2149, {_}: inverse (inverse ?3356) =>= multiply ?3356 identity [3356] by Super 2129 with 2108 at 3
-Id : 2156, {_}: inverse (inverse ?3356) =>= ?3356 [3356] by Demod 2149 with 2129 at 3
-Id : 9722, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Demod 2111 with 2156 at 1,2
-Id : 9764, {_}: multiply ?11921 (least_upper_bound ?11922 identity) =<= least_upper_bound (multiply ?11921 ?11922) ?11921 [11922, 11921] by Demod 9722 with 2156 at 1,1,3
-Id : 701, {_}: multiply (least_upper_bound ?1544 identity) ?1545 =<= least_upper_bound (multiply ?1544 ?1545) ?1545 [1545, 1544] by Super 230 with 4 at 2,3
-Id : 703, {_}: multiply (least_upper_bound (inverse ?1549) identity) ?1549 =>= least_upper_bound identity ?1549 [1549] by Super 701 with 6 at 1,3
-Id : 729, {_}: multiply (least_upper_bound identity (inverse ?1549)) ?1549 =>= least_upper_bound identity ?1549 [1549] by Demod 703 with 12 at 1,2
-Id : 2193, {_}: multiply (least_upper_bound identity ?3378) (inverse ?3378) =>= least_upper_bound identity (inverse ?3378) [3378] by Super 729 with 2156 at 2,1,2
-Id : 9777, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound (inverse ?11957) identity) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Super 9764 with 2193 at 1,3
-Id : 9888, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Demod 9777 with 12 at 2,2
-Id : 9889, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound identity (least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957)) [11957] by Demod 9888 with 16 at 3
-Id : 523, {_}: least_upper_bound (greatest_lower_bound ?1203 ?1204) ?1203 =>= ?1203 [1204, 1203] by Super 12 with 22 at 3
-Id : 524, {_}: least_upper_bound (greatest_lower_bound ?1207 ?1206) ?1206 =>= ?1206 [1206, 1207] by Super 523 with 10 at 1,2
-Id : 139, {_}: greatest_lower_bound (least_upper_bound ?385 ?386) ?385 =>= ?385 [386, 385] by Super 10 with 24 at 3
-Id : 40, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= multiply ?68 identity [69, 68] by Super 38 with 6 at 2,3
-Id : 2130, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= ?68 [69, 68] by Demod 40 with 2129 at 3
-Id : 231, {_}: multiply (least_upper_bound ?625 identity) ?626 =<= least_upper_bound (multiply ?625 ?626) ?626 [626, 625] by Super 230 with 4 at 2,3
-Id : 693, {_}: least_upper_bound ?1518 (multiply ?1517 ?1518) =>= multiply (least_upper_bound ?1517 identity) ?1518 [1517, 1518] by Super 12 with 231 at 3
-Id : 235, {_}: multiply (least_upper_bound identity ?641) ?642 =<= least_upper_bound ?642 (multiply ?641 ?642) [642, 641] by Super 230 with 4 at 1,3
-Id : 1616, {_}: multiply (least_upper_bound identity ?1517) ?1518 =?= multiply (least_upper_bound ?1517 identity) ?1518 [1518, 1517] by Demod 693 with 235 at 2
-Id : 1625, {_}: multiply (least_upper_bound (least_upper_bound identity ?2728) ?2730) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Super 30 with 1616 at 1,3
-Id : 1699, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Demod 1625 with 16 at 1,2
-Id : 1700, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= multiply (least_upper_bound (least_upper_bound ?2728 identity) ?2730) ?2729 [2729, 2730, 2728] by Demod 1699 with 30 at 3
-Id : 4487, {_}: multiply (multiply (least_upper_bound identity (least_upper_bound ?5822 ?5823)) (inverse ?5824)) ?5824 =>= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5824, 5823, 5822] by Super 2130 with 1700 at 1,2
-Id : 4634, {_}: least_upper_bound identity (least_upper_bound ?6053 ?6054) =<= least_upper_bound (least_upper_bound ?6053 identity) ?6054 [6054, 6053] by Demod 4487 with 2130 at 2
-Id : 122, {_}: least_upper_bound (greatest_lower_bound ?335 ?336) ?335 =>= ?335 [336, 335] by Super 12 with 22 at 3
-Id : 4738, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound identity ?6182) ?6183) =>= least_upper_bound identity ?6183 [6183, 6182] by Super 4634 with 122 at 1,3
-Id : 4751, {_}: least_upper_bound identity (least_upper_bound ?6221 (greatest_lower_bound identity ?6220)) =>= least_upper_bound identity ?6221 [6220, 6221] by Super 4738 with 12 at 2,2
-Id : 4923, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (least_upper_bound identity ?6418) (greatest_lower_bound identity ?6419) [6419, 6418] by Super 16 with 4751 at 2
-Id : 4974, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (greatest_lower_bound identity ?6419) (least_upper_bound identity ?6418) [6419, 6418] by Demod 4923 with 12 at 3
-Id : 5424, {_}: greatest_lower_bound (least_upper_bound identity ?7110) (greatest_lower_bound identity ?7111) =>= greatest_lower_bound identity ?7111 [7111, 7110] by Super 139 with 4974 at 1,2
-Id : 5471, {_}: greatest_lower_bound (greatest_lower_bound identity ?7111) (least_upper_bound identity ?7110) =>= greatest_lower_bound identity ?7111 [7110, 7111] by Demod 5424 with 10 at 2
-Id : 6383, {_}: greatest_lower_bound identity (greatest_lower_bound ?8259 (least_upper_bound identity ?8260)) =>= greatest_lower_bound identity ?8259 [8260, 8259] by Demod 5471 with 14 at 2
-Id : 605, {_}: greatest_lower_bound (least_upper_bound ?1361 ?1362) ?1361 =>= ?1361 [1362, 1361] by Super 10 with 24 at 3
-Id : 606, {_}: greatest_lower_bound (least_upper_bound ?1365 ?1364) ?1364 =>= ?1364 [1364, 1365] by Super 605 with 12 at 1,2
-Id : 6408, {_}: greatest_lower_bound identity (least_upper_bound identity ?8337) =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8336, 8337] by Super 6383 with 606 at 2,2
-Id : 6477, {_}: identity =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8337, 8336] by Demod 6408 with 24 at 2
-Id : 8574, {_}: least_upper_bound identity (least_upper_bound ?10550 (least_upper_bound identity ?10551)) =>= least_upper_bound ?10550 (least_upper_bound identity ?10551) [10551, 10550] by Super 524 with 6477 at 1,2
-Id : 9890, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957) [11957] by Demod 9889 with 8574 at 3
-Id : 382, {_}: least_upper_bound ?896 (least_upper_bound ?896 ?897) =>= least_upper_bound ?896 ?897 [897, 896] by Super 16 with 18 at 1,3
-Id : 383, {_}: least_upper_bound ?899 (least_upper_bound ?900 ?899) =>= least_upper_bound ?899 ?900 [900, 899] by Super 382 with 12 at 2,2
-Id : 9723, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply ?3262 ?3263) ?3262 [3263, 3262] by Demod 9722 with 2156 at 1,1,3
-Id : 9944, {_}: least_upper_bound ?12111 (multiply ?12111 ?12112) =>= multiply ?12111 (least_upper_bound ?12112 identity) [12112, 12111] by Super 12 with 9723 at 3
-Id : 9957, {_}: least_upper_bound (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Super 9944 with 2193 at 2,2
-Id : 10090, {_}: least_upper_bound identity (least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147))) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 9957 with 16 at 2
-Id : 10091, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 10090 with 8574 at 2
-Id : 10092, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) [12147] by Demod 10091 with 12 at 2,3
-Id : 50296, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound (inverse ?12147) (least_upper_bound identity ?12147) [12147] by Demod 10092 with 9890 at 3
-Id : 50343, {_}: least_upper_bound (least_upper_bound identity (inverse ?46312)) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Super 383 with 50296 at 2,2
-Id : 50540, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312))) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50343 with 16 at 2
-Id : 100, {_}: least_upper_bound ?287 (least_upper_bound ?287 ?288) =>= least_upper_bound ?287 ?288 [288, 287] by Super 16 with 18 at 1,3
-Id : 50541, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50540 with 100 at 2,2
-Id : 50542, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =<= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50541 with 8574 at 2
-Id : 50543, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =>= least_upper_bound identity (least_upper_bound (inverse ?46312) ?46312) [46312] by Demod 50542 with 16 at 3
-Id : 51165, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound identity (least_upper_bound (inverse ?11957) ?11957) [11957] by Demod 9890 with 50543 at 3
-Id : 51164, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 50296 with 50543 at 3
-Id : 1772, {_}: multiply (multiply ?2886 (least_upper_bound identity (inverse ?2885))) ?2885 =>= multiply ?2886 (least_upper_bound identity ?2885) [2885, 2886] by Super 8 with 729 at 2,3
-Id : 2194, {_}: multiply (multiply ?3381 ?3380) (inverse ?3380) =>= ?3381 [3380, 3381] by Super 2130 with 2156 at 2,1,2
-Id : 2142, {_}: multiply ?3332 (inverse ?3332) =>= identity [3332] by Super 6 with 2108 at 2
-Id : 2212, {_}: multiply identity ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Super 8 with 2142 at 1,2
-Id : 2238, {_}: ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Demod 2212 with 4 at 2
-Id : 4219, {_}: multiply ?5438 (inverse (multiply (inverse ?5439) ?5438)) =>= ?5439 [5439, 5438] by Super 2194 with 2238 at 1,2
-Id : 18113, {_}: inverse (multiply (inverse ?20071) (inverse ?20072)) =>= multiply ?20072 ?20071 [20072, 20071] by Super 2238 with 4219 at 2,3
-Id : 18209, {_}: inverse (multiply ?20210 ?20209) =<= multiply (inverse ?20209) (inverse ?20210) [20209, 20210] by Super 2156 with 18113 at 1,2
-Id : 18309, {_}: multiply (inverse (multiply ?20330 ?20331)) ?20330 =>= inverse ?20331 [20331, 20330] by Super 2130 with 18209 at 1,2
-Id : 20618, {_}: multiply (least_upper_bound identity (inverse (multiply ?22269 ?22270))) ?22269 =>= least_upper_bound ?22269 (inverse ?22270) [22270, 22269] by Super 235 with 18309 at 2,3
-Id : 379959, {_}: multiply (least_upper_bound ?332905 (inverse ?332906)) (inverse ?332905) =>= least_upper_bound identity (inverse (multiply ?332905 ?332906)) [332906, 332905] by Super 2194 with 20618 at 1,2
-Id : 243389, {_}: multiply (least_upper_bound identity (multiply ?228491 ?228492)) (inverse ?228492) =>= least_upper_bound (inverse ?228492) ?228491 [228492, 228491] by Super 235 with 2194 at 2,3
-Id : 177106, {_}: multiply (multiply ?175304 (least_upper_bound identity (inverse ?175305))) ?175305 =>= multiply ?175304 (least_upper_bound identity ?175305) [175305, 175304] by Super 8 with 729 at 2,3
-Id : 10132, {_}: multiply (inverse ?12250) (least_upper_bound ?12250 identity) =>= least_upper_bound identity (inverse ?12250) [12250] by Super 9764 with 6 at 1,3
-Id : 10133, {_}: multiply (inverse ?12252) (least_upper_bound identity ?12252) =>= least_upper_bound identity (inverse ?12252) [12252] by Super 10132 with 12 at 2,2
-Id : 10242, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound (least_upper_bound identity ?12325) (least_upper_bound identity (inverse ?12325)) [12325] by Super 235 with 10133 at 2,3
-Id : 10288, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound identity (least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325))) [12325] by Demod 10242 with 16 at 3
-Id : 10289, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325)) [12325] by Demod 10288 with 8574 at 3
-Id : 177160, {_}: multiply (least_upper_bound (inverse ?175487) (least_upper_bound identity (inverse (inverse ?175487)))) ?175487 =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Super 177106 with 10289 at 1,2
-Id : 236, {_}: multiply (least_upper_bound (inverse ?645) ?644) ?645 =>= least_upper_bound identity (multiply ?644 ?645) [644, 645] by Super 230 with 6 at 1,3
-Id : 177356, {_}: least_upper_bound identity (multiply (least_upper_bound identity (inverse (inverse ?175487))) ?175487) =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177160 with 236 at 2
-Id : 177357, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =<= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177356 with 2156 at 2,1,2,2
-Id : 177519, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175800) ?175800) =>= multiply (least_upper_bound identity ?175800) (least_upper_bound identity ?175800) [175800] by Demod 177357 with 2156 at 2,1,3
-Id : 177520, {_}: least_upper_bound identity (multiply (least_upper_bound ?175802 identity) ?175802) =>= multiply (least_upper_bound identity ?175802) (least_upper_bound identity ?175802) [175802] by Super 177519 with 12 at 1,2,2
-Id : 3515, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?4381) ?4382)) ?4381 =>= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4382, 4381] by Super 235 with 236 at 2,3
-Id : 1778, {_}: multiply (least_upper_bound (least_upper_bound identity (inverse ?2903)) ?2904) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Super 30 with 729 at 1,3
-Id : 1803, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Demod 1778 with 16 at 1,2
-Id : 1804, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (multiply ?2904 ?2903) (least_upper_bound identity ?2903) [2904, 2903] by Demod 1803 with 12 at 3
-Id : 102, {_}: least_upper_bound ?294 ?293 =<= least_upper_bound (least_upper_bound ?294 ?293) ?293 [293, 294] by Super 16 with 18 at 2,2
-Id : 29053, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27543 ?27544) ?27545) =<= least_upper_bound (least_upper_bound ?27543 (least_upper_bound ?27544 identity)) ?27545 [27545, 27544, 27543] by Super 4634 with 16 at 1,3
-Id : 29054, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27547 ?27548) ?27549) =<= least_upper_bound (least_upper_bound ?27547 (least_upper_bound identity ?27548)) ?27549 [27549, 27548, 27547] by Super 29053 with 12 at 2,1,3
-Id : 93172, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324)) [78324, 78323] by Super 102 with 29054 at 3
-Id : 93561, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324) [78324, 78323] by Demod 93172 with 8574 at 3
-Id : 4534, {_}: least_upper_bound identity (least_upper_bound ?5822 ?5823) =<= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5823, 5822] by Demod 4487 with 2130 at 2
-Id : 27996, {_}: least_upper_bound ?26567 (least_upper_bound identity (least_upper_bound ?26568 ?26567)) =>= least_upper_bound ?26567 (least_upper_bound ?26568 identity) [26568, 26567] by Super 383 with 4534 at 2,2
-Id : 28002, {_}: least_upper_bound ?26586 (least_upper_bound identity ?26586) =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Super 27996 with 122 at 2,2,2
-Id : 28236, {_}: least_upper_bound ?26586 identity =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Demod 28002 with 383 at 2
-Id : 8916, {_}: least_upper_bound identity (least_upper_bound ?11024 (least_upper_bound identity ?11025)) =>= least_upper_bound ?11024 (least_upper_bound identity ?11025) [11025, 11024] by Super 524 with 6477 at 1,2
-Id : 8917, {_}: least_upper_bound identity (least_upper_bound ?11027 (least_upper_bound ?11028 identity)) =>= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Super 8916 with 12 at 2,2,2
-Id : 4835, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound ?6313 identity) ?6314) =>= least_upper_bound identity ?6314 [6314, 6313] by Super 4634 with 524 at 1,3
-Id : 4847, {_}: least_upper_bound identity (greatest_lower_bound ?6349 identity) =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Super 4835 with 22 at 2,2
-Id : 128, {_}: least_upper_bound ?356 (greatest_lower_bound ?357 ?356) =>= ?356 [357, 356] by Super 127 with 10 at 2,2
-Id : 4903, {_}: identity =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Demod 4847 with 128 at 2
-Id : 5840, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631) =>= greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631 [7631, 7630] by Super 606 with 4903 at 1,2
-Id : 5845, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7645) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Super 5840 with 606 at 1,2,2
-Id : 112, {_}: greatest_lower_bound ?313 (greatest_lower_bound ?313 ?314) =>= greatest_lower_bound ?313 ?314 [314, 313] by Super 14 with 20 at 1,3
-Id : 5908, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Demod 5845 with 112 at 2
-Id : 5909, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound ?7644 identity)) ?7645 [7644, 7645] by Demod 5908 with 10 at 1,3
-Id : 7862, {_}: greatest_lower_bound identity ?10013 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound ?10014 identity) ?10013) [10014, 10013] by Demod 5909 with 14 at 3
-Id : 146, {_}: greatest_lower_bound ?409 (least_upper_bound ?410 ?409) =>= ?409 [410, 409] by Super 145 with 12 at 2,2
-Id : 7879, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= greatest_lower_bound identity (least_upper_bound ?10064 identity) [10064, 10063] by Super 7862 with 146 at 2,3
-Id : 7984, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= identity [10064, 10063] by Demod 7879 with 146 at 3
-Id : 8758, {_}: least_upper_bound identity (least_upper_bound ?10813 (least_upper_bound ?10814 identity)) =>= least_upper_bound ?10813 (least_upper_bound ?10814 identity) [10814, 10813] by Super 524 with 7984 at 1,2
-Id : 9284, {_}: least_upper_bound ?11027 (least_upper_bound ?11028 identity) =?= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Demod 8917 with 8758 at 2
-Id : 89245, {_}: least_upper_bound ?75550 identity =<= least_upper_bound ?75550 (least_upper_bound identity (greatest_lower_bound ?75550 ?75551)) [75551, 75550] by Demod 28236 with 9284 at 3
-Id : 89255, {_}: least_upper_bound (least_upper_bound ?75580 ?75581) identity =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Super 89245 with 606 at 2,2,3
-Id : 89821, {_}: least_upper_bound identity (least_upper_bound ?75580 ?75581) =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Demod 89255 with 12 at 2
-Id : 113848, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =?= least_upper_bound identity (least_upper_bound ?78323 ?78324) [78324, 78323] by Demod 93561 with 89821 at 3
-Id : 181989, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (least_upper_bound (multiply ?2904 ?2903) ?2903) [2904, 2903] by Demod 1804 with 113848 at 3
-Id : 181990, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (multiply (least_upper_bound ?2904 identity) ?2903) [2904, 2903] by Demod 181989 with 231 at 2,3
-Id : 230272, {_}: least_upper_bound identity (multiply (least_upper_bound ?4382 identity) ?4381) =?= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4381, 4382] by Demod 3515 with 181990 at 2
-Id : 230301, {_}: least_upper_bound ?219571 (least_upper_bound identity (multiply ?219571 ?219571)) =>= multiply (least_upper_bound identity ?219571) (least_upper_bound identity ?219571) [219571] by Super 177520 with 230272 at 2
-Id : 232386, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (least_upper_bound ?221067 identity) (multiply ?221067 ?221067) [221067] by Super 16 with 230301 at 2
-Id : 233006, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (multiply ?221067 ?221067) (least_upper_bound ?221067 identity) [221067] by Demod 232386 with 12 at 3
-Id : 4614, {_}: greatest_lower_bound ?5993 (least_upper_bound identity (least_upper_bound ?5992 ?5993)) =>= ?5993 [5992, 5993] by Super 146 with 4534 at 2,2
-Id : 27608, {_}: least_upper_bound ?26112 (least_upper_bound identity (least_upper_bound ?26113 ?26112)) =>= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Super 524 with 4614 at 1,2
-Id : 4631, {_}: least_upper_bound ?6045 (least_upper_bound identity (least_upper_bound ?6044 ?6045)) =>= least_upper_bound ?6045 (least_upper_bound ?6044 identity) [6044, 6045] by Super 383 with 4534 at 2,2
-Id : 83798, {_}: least_upper_bound ?26112 (least_upper_bound ?26113 identity) =?= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Demod 27608 with 4631 at 2
-Id : 233007, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound identity (least_upper_bound ?221067 (multiply ?221067 ?221067)) [221067] by Demod 233006 with 83798 at 3
-Id : 9743, {_}: least_upper_bound ?11859 (multiply ?11859 ?11860) =>= multiply ?11859 (least_upper_bound ?11860 identity) [11860, 11859] by Super 12 with 9723 at 3
-Id : 233595, {_}: multiply (least_upper_bound identity ?221617) (least_upper_bound identity ?221617) =<= least_upper_bound identity (multiply ?221617 (least_upper_bound ?221617 identity)) [221617] by Demod 233007 with 9743 at 2,3
-Id : 233596, {_}: multiply (least_upper_bound identity ?221619) (least_upper_bound identity ?221619) =<= least_upper_bound identity (multiply ?221619 (least_upper_bound identity ?221619)) [221619] by Super 233595 with 12 at 2,2,3
-Id : 243525, {_}: multiply (multiply (least_upper_bound identity ?228868) (least_upper_bound identity ?228868)) (inverse (least_upper_bound identity ?228868)) =>= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Super 243389 with 233596 at 1,2
-Id : 243950, {_}: least_upper_bound identity ?228868 =<= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Demod 243525 with 2194 at 2
-Id : 244049, {_}: least_upper_bound ?229075 (inverse (least_upper_bound identity ?229075)) =>= least_upper_bound identity ?229075 [229075] by Super 12 with 243950 at 3
-Id : 380052, {_}: multiply (least_upper_bound identity ?333235) (inverse ?333235) =<= least_upper_bound identity (inverse (multiply ?333235 (least_upper_bound identity ?333235))) [333235] by Super 379959 with 244049 at 1,2
-Id : 381402, {_}: least_upper_bound identity (inverse ?334503) =<= least_upper_bound identity (inverse (multiply ?334503 (least_upper_bound identity ?334503))) [334503] by Demod 380052 with 2193 at 2
-Id : 177358, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =>= multiply (least_upper_bound identity ?175487) (least_upper_bound identity ?175487) [175487] by Demod 177357 with 2156 at 2,1,3
-Id : 177476, {_}: multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (multiply (least_upper_bound identity ?175688) (least_upper_bound identity ?175688)) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Super 10133 with 177358 at 2,2
-Id : 177670, {_}: multiply (multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (least_upper_bound identity ?175688)) (least_upper_bound identity ?175688) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177476 with 8 at 2
-Id : 177671, {_}: multiply (inverse ?175688) (least_upper_bound identity ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177670 with 18309 at 1,2
-Id : 177672, {_}: least_upper_bound identity (inverse ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177671 with 10133 at 2
-Id : 381492, {_}: least_upper_bound identity (inverse (inverse (multiply (least_upper_bound identity ?334735) ?334735))) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Super 381402 with 177672 at 2,1,2,3
-Id : 382266, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?334735) ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 381492 with 2156 at 2,2
-Id : 382267, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 382266 with 177358 at 2
-Id : 18224, {_}: inverse (multiply (inverse ?20261) (inverse ?20262)) =>= multiply ?20262 ?20261 [20262, 20261] by Super 2238 with 4219 at 2,3
-Id : 18226, {_}: inverse (multiply (inverse ?20267) ?20266) =>= multiply (inverse ?20266) ?20267 [20266, 20267] by Super 18224 with 2156 at 2,1,2
-Id : 382268, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (inverse (least_upper_bound identity (inverse ?334735))) (multiply (least_upper_bound identity ?334735) ?334735)) [334735] by Demod 382267 with 18226 at 2,3
-Id : 382269, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (multiply (inverse (least_upper_bound identity (inverse ?334735))) (least_upper_bound identity ?334735)) ?334735) [334735] by Demod 382268 with 8 at 2,3
-Id : 18545, {_}: inverse (multiply ?20706 (inverse ?20707)) =>= multiply ?20707 (inverse ?20706) [20707, 20706] by Super 18224 with 2156 at 1,1,2
-Id : 18566, {_}: inverse (least_upper_bound identity (inverse ?20767)) =<= multiply ?20767 (inverse (least_upper_bound identity ?20767)) [20767] by Super 18545 with 2193 at 1,2
-Id : 19741, {_}: multiply (inverse (least_upper_bound identity (inverse ?21554))) (least_upper_bound identity ?21554) =>= ?21554 [21554] by Super 2130 with 18566 at 1,2
-Id : 382270, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =>= least_upper_bound identity (multiply ?334735 ?334735) [334735] by Demod 382269 with 19741 at 1,2,3
-Id : 382385, {_}: multiply (least_upper_bound identity (multiply (inverse ?334827) (inverse ?334827))) ?334827 =>= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Super 1772 with 382270 at 1,2
-Id : 2064, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 (multiply ?3201 identity) [3202, 3201] by Super 235 with 40 at 2,3
-Id : 223367, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 ?3201 [3202, 3201] by Demod 2064 with 2129 at 2,3
-Id : 382807, {_}: least_upper_bound ?334827 (inverse ?334827) =<= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Demod 382385 with 223367 at 2
-Id : 382808, {_}: least_upper_bound ?334827 (inverse ?334827) =<= least_upper_bound ?334827 (least_upper_bound identity (inverse ?334827)) [334827] by Demod 382807 with 10289 at 3
-Id : 383798, {_}: least_upper_bound ?12147 (inverse ?12147) =<= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 51164 with 382808 at 2
-Id : 383800, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 51165 with 383798 at 3
-Id : 2115, {_}: multiply (inverse (inverse ?3274)) (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Super 28 with 2091 at 2,3
-Id : 10659, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Demod 2115 with 2156 at 1,2
-Id : 10660, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply ?3274 ?3275) ?3274 [3275, 3274] by Demod 10659 with 2156 at 1,1,3
-Id : 10678, {_}: greatest_lower_bound ?12834 (multiply ?12834 ?12835) =>= multiply ?12834 (greatest_lower_bound ?12835 identity) [12835, 12834] by Super 10 with 10660 at 3
-Id : 18328, {_}: greatest_lower_bound (inverse ?20397) (inverse (multiply ?20396 ?20397)) =>= multiply (inverse ?20397) (greatest_lower_bound (inverse ?20396) identity) [20396, 20397] by Super 10678 with 18209 at 2,2
-Id : 2116, {_}: multiply (inverse (inverse ?3277)) (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Super 28 with 2091 at 1,3
-Id : 11396, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Demod 2116 with 2156 at 1,2
-Id : 11397, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply ?3277 ?3278) [3278, 3277] by Demod 11396 with 2156 at 1,2,3
-Id : 11398, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =?= multiply ?3277 (greatest_lower_bound ?3278 identity) [3278, 3277] by Demod 11397 with 10678 at 3
-Id : 78468, {_}: greatest_lower_bound (inverse ?65596) (inverse (multiply ?65597 ?65596)) =>= multiply (inverse ?65596) (greatest_lower_bound identity (inverse ?65597)) [65597, 65596] by Demod 18328 with 11398 at 3
-Id : 78507, {_}: greatest_lower_bound (inverse ?65693) (inverse (inverse ?65692)) =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Super 78468 with 18309 at 1,2,2
-Id : 78731, {_}: greatest_lower_bound (inverse ?65693) ?65692 =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Demod 78507 with 2156 at 2,2
-Id : 443714, {_}: greatest_lower_bound (inverse ?378148) ?378149 =<= multiply (inverse ?378148) (greatest_lower_bound identity (multiply ?378148 ?378149)) [378149, 378148] by Demod 78731 with 2156 at 2,2,3
-Id : 842, {_}: multiply (greatest_lower_bound ?1730 identity) ?1731 =<= greatest_lower_bound (multiply ?1730 ?1731) ?1731 [1731, 1730] by Super 265 with 4 at 2,3
-Id : 844, {_}: multiply (greatest_lower_bound (inverse ?1735) identity) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Super 842 with 6 at 1,3
-Id : 874, {_}: multiply (greatest_lower_bound identity (inverse ?1735)) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Demod 844 with 10 at 1,2
-Id : 2191, {_}: multiply (greatest_lower_bound identity ?3374) (inverse ?3374) =>= greatest_lower_bound identity (inverse ?3374) [3374] by Super 874 with 2156 at 2,1,2
-Id : 9776, {_}: multiply (greatest_lower_bound identity ?11955) (least_upper_bound (inverse ?11955) identity) =<= least_upper_bound (greatest_lower_bound identity (inverse ?11955)) (greatest_lower_bound identity ?11955) [11955] by Super 9764 with 2191 at 1,3
-Id : 47906, {_}: multiply (greatest_lower_bound identity ?45245) (least_upper_bound identity (inverse ?45245)) =<= least_upper_bound (greatest_lower_bound identity (inverse ?45245)) (greatest_lower_bound identity ?45245) [45245] by Demod 9776 with 12 at 2,2
-Id : 47957, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity (inverse (inverse ?45371))) =>= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Super 47906 with 2156 at 2,1,3
-Id : 48268, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =<= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Demod 47957 with 2156 at 2,2,2
-Id : 9956, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound (inverse ?12145) identity) [12145] by Super 9944 with 2191 at 2,2
-Id : 10089, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound identity (inverse ?12145)) [12145] by Demod 9956 with 12 at 2,3
-Id : 105582, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =?= multiply (greatest_lower_bound identity ?45371) (least_upper_bound identity (inverse ?45371)) [45371] by Demod 48268 with 10089 at 3
-Id : 443814, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?378412) (least_upper_bound identity (inverse ?378412)))) [378412] by Super 443714 with 105582 at 2,2,3
-Id : 5843, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7639) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Super 5840 with 139 at 1,2,2
-Id : 5900, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Demod 5843 with 112 at 2
-Id : 5901, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound identity ?7638)) ?7639 [7638, 7639] by Demod 5900 with 10 at 1,3
-Id : 7645, {_}: greatest_lower_bound identity ?9767 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound identity ?9768) ?9767) [9768, 9767] by Demod 5901 with 14 at 3
-Id : 270, {_}: multiply (greatest_lower_bound identity ?723) ?724 =<= greatest_lower_bound ?724 (multiply ?723 ?724) [724, 723] by Super 265 with 4 at 1,3
-Id : 7676, {_}: greatest_lower_bound identity (multiply ?9863 (least_upper_bound identity ?9864)) =<= greatest_lower_bound identity (multiply (greatest_lower_bound identity ?9863) (least_upper_bound identity ?9864)) [9864, 9863] by Super 7645 with 270 at 2,3
-Id : 444411, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply ?378412 (least_upper_bound identity (inverse ?378412)))) [378412] by Demod 443814 with 7676 at 2,3
-Id : 2215, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound (multiply ?3422 ?3423) identity [3423, 3422] by Super 26 with 2142 at 2,3
-Id : 2235, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound identity (multiply ?3422 ?3423) [3423, 3422] by Demod 2215 with 12 at 3
-Id : 444412, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?378412 identity))) [378412] by Demod 444411 with 2235 at 2,2,3
-Id : 444413, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) identity [378412] by Demod 444412 with 24 at 2,3
-Id : 444414, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= inverse (greatest_lower_bound identity (inverse ?378412)) [378412] by Demod 444413 with 2129 at 3
-Id : 761747, {_}: least_upper_bound (least_upper_bound identity ?693163) (inverse (greatest_lower_bound identity (inverse ?693163))) =>= least_upper_bound identity ?693163 [693163] by Super 128 with 444414 at 2,2
-Id : 762288, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) (least_upper_bound identity ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 761747 with 12 at 2
-Id : 1150, {_}: least_upper_bound (least_upper_bound ?2078 ?2079) ?2078 =>= least_upper_bound ?2078 ?2079 [2079, 2078] by Super 12 with 100 at 3
-Id : 158742, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?149635 ?149636) ?149637) ?149635 =>= least_upper_bound ?149635 (least_upper_bound ?149636 ?149637) [149637, 149636, 149635] by Super 1150 with 16 at 1,2
-Id : 375, {_}: least_upper_bound (least_upper_bound ?872 ?873) ?872 =>= least_upper_bound ?872 ?873 [873, 872] by Super 12 with 100 at 3
-Id : 1142, {_}: least_upper_bound (least_upper_bound ?2051 ?2052) (least_upper_bound ?2051 ?2053) =>= least_upper_bound (least_upper_bound ?2051 ?2052) ?2053 [2053, 2052, 2051] by Super 16 with 375 at 1,3
-Id : 158880, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?150190 ?150191) ?150189) ?150190 =?= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Super 158742 with 1142 at 1,2
-Id : 1152, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?2086 ?2084) ?2085) ?2086 =>= least_upper_bound ?2086 (least_upper_bound ?2084 ?2085) [2085, 2084, 2086] by Super 1150 with 16 at 1,2
-Id : 159604, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =<= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Demod 158880 with 1152 at 2
-Id : 126, {_}: least_upper_bound ?351 ?349 =<= least_upper_bound (least_upper_bound ?351 ?349) (greatest_lower_bound ?349 ?350) [350, 349, 351] by Super 16 with 22 at 2,2
-Id : 135029, {_}: least_upper_bound ?113864 ?113865 =<= least_upper_bound (greatest_lower_bound ?113865 ?113866) (least_upper_bound ?113864 ?113865) [113866, 113865, 113864] by Demod 126 with 12 at 3
-Id : 135153, {_}: least_upper_bound ?114345 (least_upper_bound ?114346 ?114344) =<= least_upper_bound ?114346 (least_upper_bound ?114345 (least_upper_bound ?114346 ?114344)) [114344, 114346, 114345] by Super 135029 with 139 at 1,3
-Id : 503059, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =?= least_upper_bound ?150191 (least_upper_bound ?150190 ?150189) [150189, 150191, 150190] by Demod 159604 with 135153 at 3
-Id : 762289, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 762288 with 503059 at 2
-Id : 2280, {_}: multiply (greatest_lower_bound identity ?3504) (inverse ?3504) =>= greatest_lower_bound identity (inverse ?3504) [3504] by Super 874 with 2156 at 2,1,2
-Id : 2286, {_}: multiply (greatest_lower_bound identity ?3514) (inverse (greatest_lower_bound identity ?3514)) =>= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Super 2280 with 112 at 1,2
-Id : 2335, {_}: identity =<= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Demod 2286 with 2142 at 2
-Id : 2422, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity ?3608)) =>= inverse (greatest_lower_bound identity ?3608) [3608] by Super 524 with 2335 at 1,2
-Id : 2722, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827) =>= least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827 [3827, 3826] by Super 16 with 2422 at 1,3
-Id : 762290, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163 =>= least_upper_bound identity ?693163 [693163] by Demod 762289 with 2722 at 2
-Id : 18327, {_}: multiply (inverse ?20394) (least_upper_bound (inverse ?20393) identity) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Super 9723 with 18209 at 1,3
-Id : 2112, {_}: multiply (inverse (inverse ?3265)) (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Super 26 with 2091 at 1,3
-Id : 10376, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Demod 2112 with 2156 at 1,2
-Id : 10377, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply ?3265 ?3266) [3266, 3265] by Demod 10376 with 2156 at 1,2,3
-Id : 10378, {_}: multiply ?3265 (least_upper_bound identity ?3266) =?= multiply ?3265 (least_upper_bound ?3266 identity) [3266, 3265] by Demod 10377 with 9743 at 3
-Id : 18347, {_}: multiply (inverse ?20394) (least_upper_bound identity (inverse ?20393)) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Demod 18327 with 10378 at 2
-Id : 2048, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 (multiply ?3142 identity) [3143, 3142] by Super 270 with 40 at 2,3
-Id : 194485, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 ?3142 [3143, 3142] by Demod 2048 with 2129 at 2,3
-Id : 194529, {_}: multiply (inverse ?186266) (least_upper_bound identity (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Super 18347 with 194485 at 1,1,3
-Id : 194632, {_}: multiply (inverse ?186266) (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266)))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Demod 194529 with 2422 at 2,2
-Id : 194633, {_}: inverse (multiply (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))) ?186266) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186266, 186265] by Demod 194632 with 18209 at 2
-Id : 195668, {_}: inverse (greatest_lower_bound ?187604 ?187605) =<= least_upper_bound (inverse (greatest_lower_bound ?187604 ?187605)) (inverse ?187604) [187605, 187604] by Demod 194633 with 194485 at 1,2
-Id : 201008, {_}: inverse (greatest_lower_bound (inverse ?193412) ?193413) =<= least_upper_bound (inverse (greatest_lower_bound (inverse ?193412) ?193413)) ?193412 [193413, 193412] by Super 195668 with 2156 at 2,3
-Id : 201035, {_}: inverse (greatest_lower_bound (inverse ?193516) ?193517) =<= least_upper_bound (inverse (greatest_lower_bound ?193517 (inverse ?193516))) ?193516 [193517, 193516] by Super 201008 with 10 at 1,1,3
-Id : 762291, {_}: inverse (greatest_lower_bound (inverse ?693163) identity) =>= least_upper_bound identity ?693163 [693163] by Demod 762290 with 201035 at 2
-Id : 18116, {_}: multiply ?20080 (inverse (multiply (inverse ?20081) ?20080)) =>= ?20081 [20081, 20080] by Super 2194 with 2238 at 1,2
-Id : 20397, {_}: multiply ?22035 (inverse (multiply ?22036 ?22035)) =>= inverse ?22036 [22036, 22035] by Super 18116 with 2156 at 1,1,2,2
-Id : 267, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound (multiply ?710 ?711) identity [711, 710] by Super 265 with 6 at 2,3
-Id : 287, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound identity (multiply ?710 ?711) [711, 710] by Demod 267 with 10 at 3
-Id : 20404, {_}: multiply ?22056 (inverse (greatest_lower_bound identity (multiply ?22055 ?22056))) =>= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Super 20397 with 287 at 1,2,2
-Id : 271, {_}: multiply (greatest_lower_bound (inverse ?727) ?726) ?727 =>= greatest_lower_bound identity (multiply ?726 ?727) [726, 727] by Super 265 with 6 at 1,3
-Id : 20403, {_}: multiply ?22053 (inverse (greatest_lower_bound identity (multiply ?22052 ?22053))) =>= inverse (greatest_lower_bound (inverse ?22053) ?22052) [22052, 22053] by Super 20397 with 271 at 1,2,2
-Id : 354211, {_}: inverse (greatest_lower_bound (inverse ?22056) ?22055) =?= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Demod 20404 with 20403 at 2
-Id : 763705, {_}: inverse (greatest_lower_bound identity (inverse ?694794)) =>= least_upper_bound identity ?694794 [694794] by Demod 762291 with 354211 at 2
-Id : 763707, {_}: inverse (greatest_lower_bound identity ?694797) =<= least_upper_bound identity (inverse ?694797) [694797] by Super 763705 with 2156 at 2,1,2
-Id : 766509, {_}: multiply (least_upper_bound identity ?11957) (inverse (greatest_lower_bound identity ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 383800 with 763707 at 2,2
-Id : 383797, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 10289 with 382808 at 3
-Id : 766508, {_}: multiply (inverse (greatest_lower_bound identity ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 383797 with 763707 at 1,2
-Id : 768092, {_}: least_upper_bound a (inverse a) === least_upper_bound a (inverse a) [] by Demod 768091 with 766508 at 3
-Id : 768091, {_}: least_upper_bound a (inverse a) =<= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 298 with 766509 at 2
-Id : 298, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 297 with 12 at 2,3
-Id : 297, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound a identity) [] by Demod 296 with 10 at 1,1,3
-Id : 296, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 295 with 10 at 1,2,2
-Id : 295, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 2 with 12 at 1,2
-Id : 2, {_}: multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by prove_p21
-% SZS output end CNFRefutation for GRP184-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21x is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-Found proof, 111.081739s
-% SZS status Unsatisfiable for GRP184-3.p
-% SZS output start CNFRefutation for GRP184-3.p
-Id : 265, {_}: multiply (greatest_lower_bound ?703 ?704) ?705 =<= greatest_lower_bound (multiply ?703 ?705) (multiply ?704 ?705) [705, 704, 703] by monotony_glb2 ?703 ?704 ?705
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 145, {_}: greatest_lower_bound ?406 (least_upper_bound ?406 ?407) =>= ?406 [407, 406] by glb_absorbtion ?406 ?407
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 127, {_}: least_upper_bound ?353 (greatest_lower_bound ?353 ?354) =>= ?353 [354, 353] by lub_absorbtion ?353 ?354
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 230, {_}: multiply (least_upper_bound ?621 ?622) ?623 =<= least_upper_bound (multiply ?621 ?623) (multiply ?622 ?623) [623, 622, 621] by monotony_lub2 ?621 ?622 ?623
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 38, {_}: multiply (multiply ?61 ?62) ?63 =?= multiply ?61 (multiply ?62 ?63) [63, 62, 61] by associativity ?61 ?62 ?63
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 2065, {_}: multiply (multiply ?3204 (inverse ?3205)) ?3205 =>= multiply ?3204 identity [3205, 3204] by Super 38 with 6 at 2,3
-Id : 2068, {_}: multiply identity ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Super 2065 with 6 at 1,2
-Id : 2091, {_}: ?3211 =<= multiply (inverse (inverse ?3211)) identity [3211] by Demod 2068 with 4 at 2
-Id : 2111, {_}: multiply (inverse (inverse ?3262)) (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Super 26 with 2091 at 2,3
-Id : 39, {_}: multiply (multiply ?65 identity) ?66 =>= multiply ?65 ?66 [66, 65] by Super 38 with 4 at 2,3
-Id : 2108, {_}: multiply ?3253 ?3254 =<= multiply (inverse (inverse ?3253)) ?3254 [3254, 3253] by Super 39 with 2091 at 1,2
-Id : 2129, {_}: ?3211 =<= multiply ?3211 identity [3211] by Demod 2091 with 2108 at 3
-Id : 2149, {_}: inverse (inverse ?3356) =>= multiply ?3356 identity [3356] by Super 2129 with 2108 at 3
-Id : 2156, {_}: inverse (inverse ?3356) =>= ?3356 [3356] by Demod 2149 with 2129 at 3
-Id : 9722, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply (inverse (inverse ?3262)) ?3263) ?3262 [3263, 3262] by Demod 2111 with 2156 at 1,2
-Id : 9764, {_}: multiply ?11921 (least_upper_bound ?11922 identity) =<= least_upper_bound (multiply ?11921 ?11922) ?11921 [11922, 11921] by Demod 9722 with 2156 at 1,1,3
-Id : 701, {_}: multiply (least_upper_bound ?1544 identity) ?1545 =<= least_upper_bound (multiply ?1544 ?1545) ?1545 [1545, 1544] by Super 230 with 4 at 2,3
-Id : 703, {_}: multiply (least_upper_bound (inverse ?1549) identity) ?1549 =>= least_upper_bound identity ?1549 [1549] by Super 701 with 6 at 1,3
-Id : 729, {_}: multiply (least_upper_bound identity (inverse ?1549)) ?1549 =>= least_upper_bound identity ?1549 [1549] by Demod 703 with 12 at 1,2
-Id : 2193, {_}: multiply (least_upper_bound identity ?3378) (inverse ?3378) =>= least_upper_bound identity (inverse ?3378) [3378] by Super 729 with 2156 at 2,1,2
-Id : 9777, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound (inverse ?11957) identity) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Super 9764 with 2193 at 1,3
-Id : 9888, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound (least_upper_bound identity (inverse ?11957)) (least_upper_bound identity ?11957) [11957] by Demod 9777 with 12 at 2,2
-Id : 9889, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =<= least_upper_bound identity (least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957)) [11957] by Demod 9888 with 16 at 3
-Id : 523, {_}: least_upper_bound (greatest_lower_bound ?1203 ?1204) ?1203 =>= ?1203 [1204, 1203] by Super 12 with 22 at 3
-Id : 524, {_}: least_upper_bound (greatest_lower_bound ?1207 ?1206) ?1206 =>= ?1206 [1206, 1207] by Super 523 with 10 at 1,2
-Id : 139, {_}: greatest_lower_bound (least_upper_bound ?385 ?386) ?385 =>= ?385 [386, 385] by Super 10 with 24 at 3
-Id : 40, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= multiply ?68 identity [69, 68] by Super 38 with 6 at 2,3
-Id : 2130, {_}: multiply (multiply ?68 (inverse ?69)) ?69 =>= ?68 [69, 68] by Demod 40 with 2129 at 3
-Id : 231, {_}: multiply (least_upper_bound ?625 identity) ?626 =<= least_upper_bound (multiply ?625 ?626) ?626 [626, 625] by Super 230 with 4 at 2,3
-Id : 693, {_}: least_upper_bound ?1518 (multiply ?1517 ?1518) =>= multiply (least_upper_bound ?1517 identity) ?1518 [1517, 1518] by Super 12 with 231 at 3
-Id : 235, {_}: multiply (least_upper_bound identity ?641) ?642 =<= least_upper_bound ?642 (multiply ?641 ?642) [642, 641] by Super 230 with 4 at 1,3
-Id : 1616, {_}: multiply (least_upper_bound identity ?1517) ?1518 =?= multiply (least_upper_bound ?1517 identity) ?1518 [1518, 1517] by Demod 693 with 235 at 2
-Id : 1625, {_}: multiply (least_upper_bound (least_upper_bound identity ?2728) ?2730) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Super 30 with 1616 at 1,3
-Id : 1699, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= least_upper_bound (multiply (least_upper_bound ?2728 identity) ?2729) (multiply ?2730 ?2729) [2729, 2730, 2728] by Demod 1625 with 16 at 1,2
-Id : 1700, {_}: multiply (least_upper_bound identity (least_upper_bound ?2728 ?2730)) ?2729 =<= multiply (least_upper_bound (least_upper_bound ?2728 identity) ?2730) ?2729 [2729, 2730, 2728] by Demod 1699 with 30 at 3
-Id : 4487, {_}: multiply (multiply (least_upper_bound identity (least_upper_bound ?5822 ?5823)) (inverse ?5824)) ?5824 =>= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5824, 5823, 5822] by Super 2130 with 1700 at 1,2
-Id : 4634, {_}: least_upper_bound identity (least_upper_bound ?6053 ?6054) =<= least_upper_bound (least_upper_bound ?6053 identity) ?6054 [6054, 6053] by Demod 4487 with 2130 at 2
-Id : 122, {_}: least_upper_bound (greatest_lower_bound ?335 ?336) ?335 =>= ?335 [336, 335] by Super 12 with 22 at 3
-Id : 4738, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound identity ?6182) ?6183) =>= least_upper_bound identity ?6183 [6183, 6182] by Super 4634 with 122 at 1,3
-Id : 4751, {_}: least_upper_bound identity (least_upper_bound ?6221 (greatest_lower_bound identity ?6220)) =>= least_upper_bound identity ?6221 [6220, 6221] by Super 4738 with 12 at 2,2
-Id : 4923, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (least_upper_bound identity ?6418) (greatest_lower_bound identity ?6419) [6419, 6418] by Super 16 with 4751 at 2
-Id : 4974, {_}: least_upper_bound identity ?6418 =<= least_upper_bound (greatest_lower_bound identity ?6419) (least_upper_bound identity ?6418) [6419, 6418] by Demod 4923 with 12 at 3
-Id : 5424, {_}: greatest_lower_bound (least_upper_bound identity ?7110) (greatest_lower_bound identity ?7111) =>= greatest_lower_bound identity ?7111 [7111, 7110] by Super 139 with 4974 at 1,2
-Id : 5471, {_}: greatest_lower_bound (greatest_lower_bound identity ?7111) (least_upper_bound identity ?7110) =>= greatest_lower_bound identity ?7111 [7110, 7111] by Demod 5424 with 10 at 2
-Id : 6383, {_}: greatest_lower_bound identity (greatest_lower_bound ?8259 (least_upper_bound identity ?8260)) =>= greatest_lower_bound identity ?8259 [8260, 8259] by Demod 5471 with 14 at 2
-Id : 605, {_}: greatest_lower_bound (least_upper_bound ?1361 ?1362) ?1361 =>= ?1361 [1362, 1361] by Super 10 with 24 at 3
-Id : 606, {_}: greatest_lower_bound (least_upper_bound ?1365 ?1364) ?1364 =>= ?1364 [1364, 1365] by Super 605 with 12 at 1,2
-Id : 6408, {_}: greatest_lower_bound identity (least_upper_bound identity ?8337) =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8336, 8337] by Super 6383 with 606 at 2,2
-Id : 6477, {_}: identity =<= greatest_lower_bound identity (least_upper_bound ?8336 (least_upper_bound identity ?8337)) [8337, 8336] by Demod 6408 with 24 at 2
-Id : 8574, {_}: least_upper_bound identity (least_upper_bound ?10550 (least_upper_bound identity ?10551)) =>= least_upper_bound ?10550 (least_upper_bound identity ?10551) [10551, 10550] by Super 524 with 6477 at 1,2
-Id : 9890, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound (inverse ?11957) (least_upper_bound identity ?11957) [11957] by Demod 9889 with 8574 at 3
-Id : 382, {_}: least_upper_bound ?896 (least_upper_bound ?896 ?897) =>= least_upper_bound ?896 ?897 [897, 896] by Super 16 with 18 at 1,3
-Id : 383, {_}: least_upper_bound ?899 (least_upper_bound ?900 ?899) =>= least_upper_bound ?899 ?900 [900, 899] by Super 382 with 12 at 2,2
-Id : 9723, {_}: multiply ?3262 (least_upper_bound ?3263 identity) =<= least_upper_bound (multiply ?3262 ?3263) ?3262 [3263, 3262] by Demod 9722 with 2156 at 1,1,3
-Id : 9944, {_}: least_upper_bound ?12111 (multiply ?12111 ?12112) =>= multiply ?12111 (least_upper_bound ?12112 identity) [12112, 12111] by Super 12 with 9723 at 3
-Id : 9957, {_}: least_upper_bound (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Super 9944 with 2193 at 2,2
-Id : 10090, {_}: least_upper_bound identity (least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147))) =>= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 9957 with 16 at 2
-Id : 10091, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound (inverse ?12147) identity) [12147] by Demod 10090 with 8574 at 2
-Id : 10092, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =<= multiply (least_upper_bound identity ?12147) (least_upper_bound identity (inverse ?12147)) [12147] by Demod 10091 with 12 at 2,3
-Id : 50296, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound (inverse ?12147) (least_upper_bound identity ?12147) [12147] by Demod 10092 with 9890 at 3
-Id : 50343, {_}: least_upper_bound (least_upper_bound identity (inverse ?46312)) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Super 383 with 50296 at 2,2
-Id : 50540, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312))) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50343 with 16 at 2
-Id : 100, {_}: least_upper_bound ?287 (least_upper_bound ?287 ?288) =>= least_upper_bound ?287 ?288 [288, 287] by Super 16 with 18 at 1,3
-Id : 50541, {_}: least_upper_bound identity (least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312)) =>= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50540 with 100 at 2,2
-Id : 50542, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =<= least_upper_bound (least_upper_bound identity (inverse ?46312)) ?46312 [46312] by Demod 50541 with 8574 at 2
-Id : 50543, {_}: least_upper_bound (inverse ?46312) (least_upper_bound identity ?46312) =>= least_upper_bound identity (least_upper_bound (inverse ?46312) ?46312) [46312] by Demod 50542 with 16 at 3
-Id : 51165, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound identity (least_upper_bound (inverse ?11957) ?11957) [11957] by Demod 9890 with 50543 at 3
-Id : 51164, {_}: least_upper_bound ?12147 (least_upper_bound identity (inverse ?12147)) =?= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 50296 with 50543 at 3
-Id : 1772, {_}: multiply (multiply ?2886 (least_upper_bound identity (inverse ?2885))) ?2885 =>= multiply ?2886 (least_upper_bound identity ?2885) [2885, 2886] by Super 8 with 729 at 2,3
-Id : 2194, {_}: multiply (multiply ?3381 ?3380) (inverse ?3380) =>= ?3381 [3380, 3381] by Super 2130 with 2156 at 2,1,2
-Id : 2142, {_}: multiply ?3332 (inverse ?3332) =>= identity [3332] by Super 6 with 2108 at 2
-Id : 2212, {_}: multiply identity ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Super 8 with 2142 at 1,2
-Id : 2238, {_}: ?3416 =<= multiply ?3415 (multiply (inverse ?3415) ?3416) [3415, 3416] by Demod 2212 with 4 at 2
-Id : 4219, {_}: multiply ?5438 (inverse (multiply (inverse ?5439) ?5438)) =>= ?5439 [5439, 5438] by Super 2194 with 2238 at 1,2
-Id : 18113, {_}: inverse (multiply (inverse ?20071) (inverse ?20072)) =>= multiply ?20072 ?20071 [20072, 20071] by Super 2238 with 4219 at 2,3
-Id : 18209, {_}: inverse (multiply ?20210 ?20209) =<= multiply (inverse ?20209) (inverse ?20210) [20209, 20210] by Super 2156 with 18113 at 1,2
-Id : 18309, {_}: multiply (inverse (multiply ?20330 ?20331)) ?20330 =>= inverse ?20331 [20331, 20330] by Super 2130 with 18209 at 1,2
-Id : 20618, {_}: multiply (least_upper_bound identity (inverse (multiply ?22269 ?22270))) ?22269 =>= least_upper_bound ?22269 (inverse ?22270) [22270, 22269] by Super 235 with 18309 at 2,3
-Id : 379959, {_}: multiply (least_upper_bound ?332905 (inverse ?332906)) (inverse ?332905) =>= least_upper_bound identity (inverse (multiply ?332905 ?332906)) [332906, 332905] by Super 2194 with 20618 at 1,2
-Id : 243389, {_}: multiply (least_upper_bound identity (multiply ?228491 ?228492)) (inverse ?228492) =>= least_upper_bound (inverse ?228492) ?228491 [228492, 228491] by Super 235 with 2194 at 2,3
-Id : 177106, {_}: multiply (multiply ?175304 (least_upper_bound identity (inverse ?175305))) ?175305 =>= multiply ?175304 (least_upper_bound identity ?175305) [175305, 175304] by Super 8 with 729 at 2,3
-Id : 10132, {_}: multiply (inverse ?12250) (least_upper_bound ?12250 identity) =>= least_upper_bound identity (inverse ?12250) [12250] by Super 9764 with 6 at 1,3
-Id : 10133, {_}: multiply (inverse ?12252) (least_upper_bound identity ?12252) =>= least_upper_bound identity (inverse ?12252) [12252] by Super 10132 with 12 at 2,2
-Id : 10242, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound (least_upper_bound identity ?12325) (least_upper_bound identity (inverse ?12325)) [12325] by Super 235 with 10133 at 2,3
-Id : 10288, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =<= least_upper_bound identity (least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325))) [12325] by Demod 10242 with 16 at 3
-Id : 10289, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (least_upper_bound identity (inverse ?12325)) [12325] by Demod 10288 with 8574 at 3
-Id : 177160, {_}: multiply (least_upper_bound (inverse ?175487) (least_upper_bound identity (inverse (inverse ?175487)))) ?175487 =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Super 177106 with 10289 at 1,2
-Id : 236, {_}: multiply (least_upper_bound (inverse ?645) ?644) ?645 =>= least_upper_bound identity (multiply ?644 ?645) [644, 645] by Super 230 with 6 at 1,3
-Id : 177356, {_}: least_upper_bound identity (multiply (least_upper_bound identity (inverse (inverse ?175487))) ?175487) =>= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177160 with 236 at 2
-Id : 177357, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =<= multiply (least_upper_bound identity (inverse (inverse ?175487))) (least_upper_bound identity ?175487) [175487] by Demod 177356 with 2156 at 2,1,2,2
-Id : 177519, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175800) ?175800) =>= multiply (least_upper_bound identity ?175800) (least_upper_bound identity ?175800) [175800] by Demod 177357 with 2156 at 2,1,3
-Id : 177520, {_}: least_upper_bound identity (multiply (least_upper_bound ?175802 identity) ?175802) =>= multiply (least_upper_bound identity ?175802) (least_upper_bound identity ?175802) [175802] by Super 177519 with 12 at 1,2,2
-Id : 3515, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?4381) ?4382)) ?4381 =>= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4382, 4381] by Super 235 with 236 at 2,3
-Id : 1778, {_}: multiply (least_upper_bound (least_upper_bound identity (inverse ?2903)) ?2904) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Super 30 with 729 at 1,3
-Id : 1803, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (least_upper_bound identity ?2903) (multiply ?2904 ?2903) [2904, 2903] by Demod 1778 with 16 at 1,2
-Id : 1804, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound (multiply ?2904 ?2903) (least_upper_bound identity ?2903) [2904, 2903] by Demod 1803 with 12 at 3
-Id : 102, {_}: least_upper_bound ?294 ?293 =<= least_upper_bound (least_upper_bound ?294 ?293) ?293 [293, 294] by Super 16 with 18 at 2,2
-Id : 29053, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27543 ?27544) ?27545) =<= least_upper_bound (least_upper_bound ?27543 (least_upper_bound ?27544 identity)) ?27545 [27545, 27544, 27543] by Super 4634 with 16 at 1,3
-Id : 29054, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?27547 ?27548) ?27549) =<= least_upper_bound (least_upper_bound ?27547 (least_upper_bound identity ?27548)) ?27549 [27549, 27548, 27547] by Super 29053 with 12 at 2,1,3
-Id : 93172, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324)) [78324, 78323] by Super 102 with 29054 at 3
-Id : 93561, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =<= least_upper_bound (least_upper_bound ?78323 ?78324) (least_upper_bound identity ?78324) [78324, 78323] by Demod 93172 with 8574 at 3
-Id : 4534, {_}: least_upper_bound identity (least_upper_bound ?5822 ?5823) =<= least_upper_bound (least_upper_bound ?5822 identity) ?5823 [5823, 5822] by Demod 4487 with 2130 at 2
-Id : 27996, {_}: least_upper_bound ?26567 (least_upper_bound identity (least_upper_bound ?26568 ?26567)) =>= least_upper_bound ?26567 (least_upper_bound ?26568 identity) [26568, 26567] by Super 383 with 4534 at 2,2
-Id : 28002, {_}: least_upper_bound ?26586 (least_upper_bound identity ?26586) =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Super 27996 with 122 at 2,2,2
-Id : 28236, {_}: least_upper_bound ?26586 identity =<= least_upper_bound ?26586 (least_upper_bound (greatest_lower_bound ?26586 ?26585) identity) [26585, 26586] by Demod 28002 with 383 at 2
-Id : 8916, {_}: least_upper_bound identity (least_upper_bound ?11024 (least_upper_bound identity ?11025)) =>= least_upper_bound ?11024 (least_upper_bound identity ?11025) [11025, 11024] by Super 524 with 6477 at 1,2
-Id : 8917, {_}: least_upper_bound identity (least_upper_bound ?11027 (least_upper_bound ?11028 identity)) =>= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Super 8916 with 12 at 2,2,2
-Id : 4835, {_}: least_upper_bound identity (least_upper_bound (greatest_lower_bound ?6313 identity) ?6314) =>= least_upper_bound identity ?6314 [6314, 6313] by Super 4634 with 524 at 1,3
-Id : 4847, {_}: least_upper_bound identity (greatest_lower_bound ?6349 identity) =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Super 4835 with 22 at 2,2
-Id : 128, {_}: least_upper_bound ?356 (greatest_lower_bound ?357 ?356) =>= ?356 [357, 356] by Super 127 with 10 at 2,2
-Id : 4903, {_}: identity =<= least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?6349 identity) ?6348) [6348, 6349] by Demod 4847 with 128 at 2
-Id : 5840, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631) =>= greatest_lower_bound (greatest_lower_bound ?7630 identity) ?7631 [7631, 7630] by Super 606 with 4903 at 1,2
-Id : 5845, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7645) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Super 5840 with 606 at 1,2,2
-Id : 112, {_}: greatest_lower_bound ?313 (greatest_lower_bound ?313 ?314) =>= greatest_lower_bound ?313 ?314 [314, 313] by Super 14 with 20 at 1,3
-Id : 5908, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound ?7644 identity) identity) ?7645 [7644, 7645] by Demod 5845 with 112 at 2
-Id : 5909, {_}: greatest_lower_bound identity ?7645 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound ?7644 identity)) ?7645 [7644, 7645] by Demod 5908 with 10 at 1,3
-Id : 7862, {_}: greatest_lower_bound identity ?10013 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound ?10014 identity) ?10013) [10014, 10013] by Demod 5909 with 14 at 3
-Id : 146, {_}: greatest_lower_bound ?409 (least_upper_bound ?410 ?409) =>= ?409 [410, 409] by Super 145 with 12 at 2,2
-Id : 7879, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= greatest_lower_bound identity (least_upper_bound ?10064 identity) [10064, 10063] by Super 7862 with 146 at 2,3
-Id : 7984, {_}: greatest_lower_bound identity (least_upper_bound ?10063 (least_upper_bound ?10064 identity)) =>= identity [10064, 10063] by Demod 7879 with 146 at 3
-Id : 8758, {_}: least_upper_bound identity (least_upper_bound ?10813 (least_upper_bound ?10814 identity)) =>= least_upper_bound ?10813 (least_upper_bound ?10814 identity) [10814, 10813] by Super 524 with 7984 at 1,2
-Id : 9284, {_}: least_upper_bound ?11027 (least_upper_bound ?11028 identity) =?= least_upper_bound ?11027 (least_upper_bound identity ?11028) [11028, 11027] by Demod 8917 with 8758 at 2
-Id : 89245, {_}: least_upper_bound ?75550 identity =<= least_upper_bound ?75550 (least_upper_bound identity (greatest_lower_bound ?75550 ?75551)) [75551, 75550] by Demod 28236 with 9284 at 3
-Id : 89255, {_}: least_upper_bound (least_upper_bound ?75580 ?75581) identity =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Super 89245 with 606 at 2,2,3
-Id : 89821, {_}: least_upper_bound identity (least_upper_bound ?75580 ?75581) =<= least_upper_bound (least_upper_bound ?75580 ?75581) (least_upper_bound identity ?75581) [75581, 75580] by Demod 89255 with 12 at 2
-Id : 113848, {_}: least_upper_bound ?78323 (least_upper_bound identity ?78324) =?= least_upper_bound identity (least_upper_bound ?78323 ?78324) [78324, 78323] by Demod 93561 with 89821 at 3
-Id : 181989, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (least_upper_bound (multiply ?2904 ?2903) ?2903) [2904, 2903] by Demod 1804 with 113848 at 3
-Id : 181990, {_}: multiply (least_upper_bound identity (least_upper_bound (inverse ?2903) ?2904)) ?2903 =>= least_upper_bound identity (multiply (least_upper_bound ?2904 identity) ?2903) [2904, 2903] by Demod 181989 with 231 at 2,3
-Id : 230272, {_}: least_upper_bound identity (multiply (least_upper_bound ?4382 identity) ?4381) =?= least_upper_bound ?4381 (least_upper_bound identity (multiply ?4382 ?4381)) [4381, 4382] by Demod 3515 with 181990 at 2
-Id : 230301, {_}: least_upper_bound ?219571 (least_upper_bound identity (multiply ?219571 ?219571)) =>= multiply (least_upper_bound identity ?219571) (least_upper_bound identity ?219571) [219571] by Super 177520 with 230272 at 2
-Id : 232386, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (least_upper_bound ?221067 identity) (multiply ?221067 ?221067) [221067] by Super 16 with 230301 at 2
-Id : 233006, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound (multiply ?221067 ?221067) (least_upper_bound ?221067 identity) [221067] by Demod 232386 with 12 at 3
-Id : 4614, {_}: greatest_lower_bound ?5993 (least_upper_bound identity (least_upper_bound ?5992 ?5993)) =>= ?5993 [5992, 5993] by Super 146 with 4534 at 2,2
-Id : 27608, {_}: least_upper_bound ?26112 (least_upper_bound identity (least_upper_bound ?26113 ?26112)) =>= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Super 524 with 4614 at 1,2
-Id : 4631, {_}: least_upper_bound ?6045 (least_upper_bound identity (least_upper_bound ?6044 ?6045)) =>= least_upper_bound ?6045 (least_upper_bound ?6044 identity) [6044, 6045] by Super 383 with 4534 at 2,2
-Id : 83798, {_}: least_upper_bound ?26112 (least_upper_bound ?26113 identity) =?= least_upper_bound identity (least_upper_bound ?26113 ?26112) [26113, 26112] by Demod 27608 with 4631 at 2
-Id : 233007, {_}: multiply (least_upper_bound identity ?221067) (least_upper_bound identity ?221067) =<= least_upper_bound identity (least_upper_bound ?221067 (multiply ?221067 ?221067)) [221067] by Demod 233006 with 83798 at 3
-Id : 9743, {_}: least_upper_bound ?11859 (multiply ?11859 ?11860) =>= multiply ?11859 (least_upper_bound ?11860 identity) [11860, 11859] by Super 12 with 9723 at 3
-Id : 233595, {_}: multiply (least_upper_bound identity ?221617) (least_upper_bound identity ?221617) =<= least_upper_bound identity (multiply ?221617 (least_upper_bound ?221617 identity)) [221617] by Demod 233007 with 9743 at 2,3
-Id : 233596, {_}: multiply (least_upper_bound identity ?221619) (least_upper_bound identity ?221619) =<= least_upper_bound identity (multiply ?221619 (least_upper_bound identity ?221619)) [221619] by Super 233595 with 12 at 2,2,3
-Id : 243525, {_}: multiply (multiply (least_upper_bound identity ?228868) (least_upper_bound identity ?228868)) (inverse (least_upper_bound identity ?228868)) =>= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Super 243389 with 233596 at 1,2
-Id : 243950, {_}: least_upper_bound identity ?228868 =<= least_upper_bound (inverse (least_upper_bound identity ?228868)) ?228868 [228868] by Demod 243525 with 2194 at 2
-Id : 244049, {_}: least_upper_bound ?229075 (inverse (least_upper_bound identity ?229075)) =>= least_upper_bound identity ?229075 [229075] by Super 12 with 243950 at 3
-Id : 380052, {_}: multiply (least_upper_bound identity ?333235) (inverse ?333235) =<= least_upper_bound identity (inverse (multiply ?333235 (least_upper_bound identity ?333235))) [333235] by Super 379959 with 244049 at 1,2
-Id : 381402, {_}: least_upper_bound identity (inverse ?334503) =<= least_upper_bound identity (inverse (multiply ?334503 (least_upper_bound identity ?334503))) [334503] by Demod 380052 with 2193 at 2
-Id : 177358, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?175487) ?175487) =>= multiply (least_upper_bound identity ?175487) (least_upper_bound identity ?175487) [175487] by Demod 177357 with 2156 at 2,1,3
-Id : 177476, {_}: multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (multiply (least_upper_bound identity ?175688) (least_upper_bound identity ?175688)) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Super 10133 with 177358 at 2,2
-Id : 177670, {_}: multiply (multiply (inverse (multiply (least_upper_bound identity ?175688) ?175688)) (least_upper_bound identity ?175688)) (least_upper_bound identity ?175688) =>= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177476 with 8 at 2
-Id : 177671, {_}: multiply (inverse ?175688) (least_upper_bound identity ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177670 with 18309 at 1,2
-Id : 177672, {_}: least_upper_bound identity (inverse ?175688) =<= least_upper_bound identity (inverse (multiply (least_upper_bound identity ?175688) ?175688)) [175688] by Demod 177671 with 10133 at 2
-Id : 381492, {_}: least_upper_bound identity (inverse (inverse (multiply (least_upper_bound identity ?334735) ?334735))) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Super 381402 with 177672 at 2,1,2,3
-Id : 382266, {_}: least_upper_bound identity (multiply (least_upper_bound identity ?334735) ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 381492 with 2156 at 2,2
-Id : 382267, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (inverse (multiply (inverse (multiply (least_upper_bound identity ?334735) ?334735)) (least_upper_bound identity (inverse ?334735)))) [334735] by Demod 382266 with 177358 at 2
-Id : 18224, {_}: inverse (multiply (inverse ?20261) (inverse ?20262)) =>= multiply ?20262 ?20261 [20262, 20261] by Super 2238 with 4219 at 2,3
-Id : 18226, {_}: inverse (multiply (inverse ?20267) ?20266) =>= multiply (inverse ?20266) ?20267 [20266, 20267] by Super 18224 with 2156 at 2,1,2
-Id : 382268, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (inverse (least_upper_bound identity (inverse ?334735))) (multiply (least_upper_bound identity ?334735) ?334735)) [334735] by Demod 382267 with 18226 at 2,3
-Id : 382269, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =<= least_upper_bound identity (multiply (multiply (inverse (least_upper_bound identity (inverse ?334735))) (least_upper_bound identity ?334735)) ?334735) [334735] by Demod 382268 with 8 at 2,3
-Id : 18545, {_}: inverse (multiply ?20706 (inverse ?20707)) =>= multiply ?20707 (inverse ?20706) [20707, 20706] by Super 18224 with 2156 at 1,1,2
-Id : 18566, {_}: inverse (least_upper_bound identity (inverse ?20767)) =<= multiply ?20767 (inverse (least_upper_bound identity ?20767)) [20767] by Super 18545 with 2193 at 1,2
-Id : 19741, {_}: multiply (inverse (least_upper_bound identity (inverse ?21554))) (least_upper_bound identity ?21554) =>= ?21554 [21554] by Super 2130 with 18566 at 1,2
-Id : 382270, {_}: multiply (least_upper_bound identity ?334735) (least_upper_bound identity ?334735) =>= least_upper_bound identity (multiply ?334735 ?334735) [334735] by Demod 382269 with 19741 at 1,2,3
-Id : 382385, {_}: multiply (least_upper_bound identity (multiply (inverse ?334827) (inverse ?334827))) ?334827 =>= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Super 1772 with 382270 at 1,2
-Id : 2064, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 (multiply ?3201 identity) [3202, 3201] by Super 235 with 40 at 2,3
-Id : 223367, {_}: multiply (least_upper_bound identity (multiply ?3201 (inverse ?3202))) ?3202 =>= least_upper_bound ?3202 ?3201 [3202, 3201] by Demod 2064 with 2129 at 2,3
-Id : 382807, {_}: least_upper_bound ?334827 (inverse ?334827) =<= multiply (least_upper_bound identity (inverse ?334827)) (least_upper_bound identity ?334827) [334827] by Demod 382385 with 223367 at 2
-Id : 382808, {_}: least_upper_bound ?334827 (inverse ?334827) =<= least_upper_bound ?334827 (least_upper_bound identity (inverse ?334827)) [334827] by Demod 382807 with 10289 at 3
-Id : 383798, {_}: least_upper_bound ?12147 (inverse ?12147) =<= least_upper_bound identity (least_upper_bound (inverse ?12147) ?12147) [12147] by Demod 51164 with 382808 at 2
-Id : 383800, {_}: multiply (least_upper_bound identity ?11957) (least_upper_bound identity (inverse ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 51165 with 383798 at 3
-Id : 2115, {_}: multiply (inverse (inverse ?3274)) (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Super 28 with 2091 at 2,3
-Id : 10659, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply (inverse (inverse ?3274)) ?3275) ?3274 [3275, 3274] by Demod 2115 with 2156 at 1,2
-Id : 10660, {_}: multiply ?3274 (greatest_lower_bound ?3275 identity) =<= greatest_lower_bound (multiply ?3274 ?3275) ?3274 [3275, 3274] by Demod 10659 with 2156 at 1,1,3
-Id : 10678, {_}: greatest_lower_bound ?12834 (multiply ?12834 ?12835) =>= multiply ?12834 (greatest_lower_bound ?12835 identity) [12835, 12834] by Super 10 with 10660 at 3
-Id : 18328, {_}: greatest_lower_bound (inverse ?20397) (inverse (multiply ?20396 ?20397)) =>= multiply (inverse ?20397) (greatest_lower_bound (inverse ?20396) identity) [20396, 20397] by Super 10678 with 18209 at 2,2
-Id : 2116, {_}: multiply (inverse (inverse ?3277)) (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Super 28 with 2091 at 1,3
-Id : 11396, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply (inverse (inverse ?3277)) ?3278) [3278, 3277] by Demod 2116 with 2156 at 1,2
-Id : 11397, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =<= greatest_lower_bound ?3277 (multiply ?3277 ?3278) [3278, 3277] by Demod 11396 with 2156 at 1,2,3
-Id : 11398, {_}: multiply ?3277 (greatest_lower_bound identity ?3278) =?= multiply ?3277 (greatest_lower_bound ?3278 identity) [3278, 3277] by Demod 11397 with 10678 at 3
-Id : 78468, {_}: greatest_lower_bound (inverse ?65596) (inverse (multiply ?65597 ?65596)) =>= multiply (inverse ?65596) (greatest_lower_bound identity (inverse ?65597)) [65597, 65596] by Demod 18328 with 11398 at 3
-Id : 78507, {_}: greatest_lower_bound (inverse ?65693) (inverse (inverse ?65692)) =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Super 78468 with 18309 at 1,2,2
-Id : 78731, {_}: greatest_lower_bound (inverse ?65693) ?65692 =<= multiply (inverse ?65693) (greatest_lower_bound identity (inverse (inverse (multiply ?65693 ?65692)))) [65692, 65693] by Demod 78507 with 2156 at 2,2
-Id : 443714, {_}: greatest_lower_bound (inverse ?378148) ?378149 =<= multiply (inverse ?378148) (greatest_lower_bound identity (multiply ?378148 ?378149)) [378149, 378148] by Demod 78731 with 2156 at 2,2,3
-Id : 842, {_}: multiply (greatest_lower_bound ?1730 identity) ?1731 =<= greatest_lower_bound (multiply ?1730 ?1731) ?1731 [1731, 1730] by Super 265 with 4 at 2,3
-Id : 844, {_}: multiply (greatest_lower_bound (inverse ?1735) identity) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Super 842 with 6 at 1,3
-Id : 874, {_}: multiply (greatest_lower_bound identity (inverse ?1735)) ?1735 =>= greatest_lower_bound identity ?1735 [1735] by Demod 844 with 10 at 1,2
-Id : 2191, {_}: multiply (greatest_lower_bound identity ?3374) (inverse ?3374) =>= greatest_lower_bound identity (inverse ?3374) [3374] by Super 874 with 2156 at 2,1,2
-Id : 9776, {_}: multiply (greatest_lower_bound identity ?11955) (least_upper_bound (inverse ?11955) identity) =<= least_upper_bound (greatest_lower_bound identity (inverse ?11955)) (greatest_lower_bound identity ?11955) [11955] by Super 9764 with 2191 at 1,3
-Id : 47906, {_}: multiply (greatest_lower_bound identity ?45245) (least_upper_bound identity (inverse ?45245)) =<= least_upper_bound (greatest_lower_bound identity (inverse ?45245)) (greatest_lower_bound identity ?45245) [45245] by Demod 9776 with 12 at 2,2
-Id : 47957, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity (inverse (inverse ?45371))) =>= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Super 47906 with 2156 at 2,1,3
-Id : 48268, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =<= least_upper_bound (greatest_lower_bound identity ?45371) (greatest_lower_bound identity (inverse ?45371)) [45371] by Demod 47957 with 2156 at 2,2,2
-Id : 9956, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound (inverse ?12145) identity) [12145] by Super 9944 with 2191 at 2,2
-Id : 10089, {_}: least_upper_bound (greatest_lower_bound identity ?12145) (greatest_lower_bound identity (inverse ?12145)) =>= multiply (greatest_lower_bound identity ?12145) (least_upper_bound identity (inverse ?12145)) [12145] by Demod 9956 with 12 at 2,3
-Id : 105582, {_}: multiply (greatest_lower_bound identity (inverse ?45371)) (least_upper_bound identity ?45371) =?= multiply (greatest_lower_bound identity ?45371) (least_upper_bound identity (inverse ?45371)) [45371] by Demod 48268 with 10089 at 3
-Id : 443814, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?378412) (least_upper_bound identity (inverse ?378412)))) [378412] by Super 443714 with 105582 at 2,2,3
-Id : 5843, {_}: greatest_lower_bound identity (greatest_lower_bound identity ?7639) =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Super 5840 with 139 at 1,2,2
-Id : 5900, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound (least_upper_bound identity ?7638) identity) ?7639 [7638, 7639] by Demod 5843 with 112 at 2
-Id : 5901, {_}: greatest_lower_bound identity ?7639 =<= greatest_lower_bound (greatest_lower_bound identity (least_upper_bound identity ?7638)) ?7639 [7638, 7639] by Demod 5900 with 10 at 1,3
-Id : 7645, {_}: greatest_lower_bound identity ?9767 =<= greatest_lower_bound identity (greatest_lower_bound (least_upper_bound identity ?9768) ?9767) [9768, 9767] by Demod 5901 with 14 at 3
-Id : 270, {_}: multiply (greatest_lower_bound identity ?723) ?724 =<= greatest_lower_bound ?724 (multiply ?723 ?724) [724, 723] by Super 265 with 4 at 1,3
-Id : 7676, {_}: greatest_lower_bound identity (multiply ?9863 (least_upper_bound identity ?9864)) =<= greatest_lower_bound identity (multiply (greatest_lower_bound identity ?9863) (least_upper_bound identity ?9864)) [9864, 9863] by Super 7645 with 270 at 2,3
-Id : 444411, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (multiply ?378412 (least_upper_bound identity (inverse ?378412)))) [378412] by Demod 443814 with 7676 at 2,3
-Id : 2215, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound (multiply ?3422 ?3423) identity [3423, 3422] by Super 26 with 2142 at 2,3
-Id : 2235, {_}: multiply ?3422 (least_upper_bound ?3423 (inverse ?3422)) =>= least_upper_bound identity (multiply ?3422 ?3423) [3423, 3422] by Demod 2215 with 12 at 3
-Id : 444412, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =<= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?378412 identity))) [378412] by Demod 444411 with 2235 at 2,2,3
-Id : 444413, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= multiply (inverse (greatest_lower_bound identity (inverse ?378412))) identity [378412] by Demod 444412 with 24 at 2,3
-Id : 444414, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?378412))) (least_upper_bound identity ?378412) =>= inverse (greatest_lower_bound identity (inverse ?378412)) [378412] by Demod 444413 with 2129 at 3
-Id : 761747, {_}: least_upper_bound (least_upper_bound identity ?693163) (inverse (greatest_lower_bound identity (inverse ?693163))) =>= least_upper_bound identity ?693163 [693163] by Super 128 with 444414 at 2,2
-Id : 762288, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) (least_upper_bound identity ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 761747 with 12 at 2
-Id : 1150, {_}: least_upper_bound (least_upper_bound ?2078 ?2079) ?2078 =>= least_upper_bound ?2078 ?2079 [2079, 2078] by Super 12 with 100 at 3
-Id : 158742, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?149635 ?149636) ?149637) ?149635 =>= least_upper_bound ?149635 (least_upper_bound ?149636 ?149637) [149637, 149636, 149635] by Super 1150 with 16 at 1,2
-Id : 375, {_}: least_upper_bound (least_upper_bound ?872 ?873) ?872 =>= least_upper_bound ?872 ?873 [873, 872] by Super 12 with 100 at 3
-Id : 1142, {_}: least_upper_bound (least_upper_bound ?2051 ?2052) (least_upper_bound ?2051 ?2053) =>= least_upper_bound (least_upper_bound ?2051 ?2052) ?2053 [2053, 2052, 2051] by Super 16 with 375 at 1,3
-Id : 158880, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?150190 ?150191) ?150189) ?150190 =?= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Super 158742 with 1142 at 1,2
-Id : 1152, {_}: least_upper_bound (least_upper_bound (least_upper_bound ?2086 ?2084) ?2085) ?2086 =>= least_upper_bound ?2086 (least_upper_bound ?2084 ?2085) [2085, 2084, 2086] by Super 1150 with 16 at 1,2
-Id : 159604, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =<= least_upper_bound ?150190 (least_upper_bound ?150191 (least_upper_bound ?150190 ?150189)) [150189, 150191, 150190] by Demod 158880 with 1152 at 2
-Id : 126, {_}: least_upper_bound ?351 ?349 =<= least_upper_bound (least_upper_bound ?351 ?349) (greatest_lower_bound ?349 ?350) [350, 349, 351] by Super 16 with 22 at 2,2
-Id : 135029, {_}: least_upper_bound ?113864 ?113865 =<= least_upper_bound (greatest_lower_bound ?113865 ?113866) (least_upper_bound ?113864 ?113865) [113866, 113865, 113864] by Demod 126 with 12 at 3
-Id : 135153, {_}: least_upper_bound ?114345 (least_upper_bound ?114346 ?114344) =<= least_upper_bound ?114346 (least_upper_bound ?114345 (least_upper_bound ?114346 ?114344)) [114344, 114346, 114345] by Super 135029 with 139 at 1,3
-Id : 503059, {_}: least_upper_bound ?150190 (least_upper_bound ?150191 ?150189) =?= least_upper_bound ?150191 (least_upper_bound ?150190 ?150189) [150189, 150191, 150190] by Demod 159604 with 135153 at 3
-Id : 762289, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163) =>= least_upper_bound identity ?693163 [693163] by Demod 762288 with 503059 at 2
-Id : 2280, {_}: multiply (greatest_lower_bound identity ?3504) (inverse ?3504) =>= greatest_lower_bound identity (inverse ?3504) [3504] by Super 874 with 2156 at 2,1,2
-Id : 2286, {_}: multiply (greatest_lower_bound identity ?3514) (inverse (greatest_lower_bound identity ?3514)) =>= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Super 2280 with 112 at 1,2
-Id : 2335, {_}: identity =<= greatest_lower_bound identity (inverse (greatest_lower_bound identity ?3514)) [3514] by Demod 2286 with 2142 at 2
-Id : 2422, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity ?3608)) =>= inverse (greatest_lower_bound identity ?3608) [3608] by Super 524 with 2335 at 1,2
-Id : 2722, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827) =>= least_upper_bound (inverse (greatest_lower_bound identity ?3826)) ?3827 [3827, 3826] by Super 16 with 2422 at 1,3
-Id : 762290, {_}: least_upper_bound (inverse (greatest_lower_bound identity (inverse ?693163))) ?693163 =>= least_upper_bound identity ?693163 [693163] by Demod 762289 with 2722 at 2
-Id : 18327, {_}: multiply (inverse ?20394) (least_upper_bound (inverse ?20393) identity) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Super 9723 with 18209 at 1,3
-Id : 2112, {_}: multiply (inverse (inverse ?3265)) (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Super 26 with 2091 at 1,3
-Id : 10376, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply (inverse (inverse ?3265)) ?3266) [3266, 3265] by Demod 2112 with 2156 at 1,2
-Id : 10377, {_}: multiply ?3265 (least_upper_bound identity ?3266) =<= least_upper_bound ?3265 (multiply ?3265 ?3266) [3266, 3265] by Demod 10376 with 2156 at 1,2,3
-Id : 10378, {_}: multiply ?3265 (least_upper_bound identity ?3266) =?= multiply ?3265 (least_upper_bound ?3266 identity) [3266, 3265] by Demod 10377 with 9743 at 3
-Id : 18347, {_}: multiply (inverse ?20394) (least_upper_bound identity (inverse ?20393)) =<= least_upper_bound (inverse (multiply ?20393 ?20394)) (inverse ?20394) [20393, 20394] by Demod 18327 with 10378 at 2
-Id : 2048, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 (multiply ?3142 identity) [3143, 3142] by Super 270 with 40 at 2,3
-Id : 194485, {_}: multiply (greatest_lower_bound identity (multiply ?3142 (inverse ?3143))) ?3143 =>= greatest_lower_bound ?3143 ?3142 [3143, 3142] by Demod 2048 with 2129 at 2,3
-Id : 194529, {_}: multiply (inverse ?186266) (least_upper_bound identity (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Super 18347 with 194485 at 1,1,3
-Id : 194632, {_}: multiply (inverse ?186266) (inverse (greatest_lower_bound identity (multiply ?186265 (inverse ?186266)))) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186265, 186266] by Demod 194529 with 2422 at 2,2
-Id : 194633, {_}: inverse (multiply (greatest_lower_bound identity (multiply ?186265 (inverse ?186266))) ?186266) =>= least_upper_bound (inverse (greatest_lower_bound ?186266 ?186265)) (inverse ?186266) [186266, 186265] by Demod 194632 with 18209 at 2
-Id : 195668, {_}: inverse (greatest_lower_bound ?187604 ?187605) =<= least_upper_bound (inverse (greatest_lower_bound ?187604 ?187605)) (inverse ?187604) [187605, 187604] by Demod 194633 with 194485 at 1,2
-Id : 201008, {_}: inverse (greatest_lower_bound (inverse ?193412) ?193413) =<= least_upper_bound (inverse (greatest_lower_bound (inverse ?193412) ?193413)) ?193412 [193413, 193412] by Super 195668 with 2156 at 2,3
-Id : 201035, {_}: inverse (greatest_lower_bound (inverse ?193516) ?193517) =<= least_upper_bound (inverse (greatest_lower_bound ?193517 (inverse ?193516))) ?193516 [193517, 193516] by Super 201008 with 10 at 1,1,3
-Id : 762291, {_}: inverse (greatest_lower_bound (inverse ?693163) identity) =>= least_upper_bound identity ?693163 [693163] by Demod 762290 with 201035 at 2
-Id : 18116, {_}: multiply ?20080 (inverse (multiply (inverse ?20081) ?20080)) =>= ?20081 [20081, 20080] by Super 2194 with 2238 at 1,2
-Id : 20397, {_}: multiply ?22035 (inverse (multiply ?22036 ?22035)) =>= inverse ?22036 [22036, 22035] by Super 18116 with 2156 at 1,1,2,2
-Id : 267, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound (multiply ?710 ?711) identity [711, 710] by Super 265 with 6 at 2,3
-Id : 287, {_}: multiply (greatest_lower_bound ?710 (inverse ?711)) ?711 =>= greatest_lower_bound identity (multiply ?710 ?711) [711, 710] by Demod 267 with 10 at 3
-Id : 20404, {_}: multiply ?22056 (inverse (greatest_lower_bound identity (multiply ?22055 ?22056))) =>= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Super 20397 with 287 at 1,2,2
-Id : 271, {_}: multiply (greatest_lower_bound (inverse ?727) ?726) ?727 =>= greatest_lower_bound identity (multiply ?726 ?727) [726, 727] by Super 265 with 6 at 1,3
-Id : 20403, {_}: multiply ?22053 (inverse (greatest_lower_bound identity (multiply ?22052 ?22053))) =>= inverse (greatest_lower_bound (inverse ?22053) ?22052) [22052, 22053] by Super 20397 with 271 at 1,2,2
-Id : 354211, {_}: inverse (greatest_lower_bound (inverse ?22056) ?22055) =?= inverse (greatest_lower_bound ?22055 (inverse ?22056)) [22055, 22056] by Demod 20404 with 20403 at 2
-Id : 763705, {_}: inverse (greatest_lower_bound identity (inverse ?694794)) =>= least_upper_bound identity ?694794 [694794] by Demod 762291 with 354211 at 2
-Id : 763707, {_}: inverse (greatest_lower_bound identity ?694797) =<= least_upper_bound identity (inverse ?694797) [694797] by Super 763705 with 2156 at 2,1,2
-Id : 766509, {_}: multiply (least_upper_bound identity ?11957) (inverse (greatest_lower_bound identity ?11957)) =>= least_upper_bound ?11957 (inverse ?11957) [11957] by Demod 383800 with 763707 at 2,2
-Id : 383797, {_}: multiply (least_upper_bound identity (inverse ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 10289 with 382808 at 3
-Id : 766508, {_}: multiply (inverse (greatest_lower_bound identity ?12325)) (least_upper_bound identity ?12325) =>= least_upper_bound ?12325 (inverse ?12325) [12325] by Demod 383797 with 763707 at 1,2
-Id : 768092, {_}: least_upper_bound a (inverse a) === least_upper_bound a (inverse a) [] by Demod 768091 with 766508 at 3
-Id : 768091, {_}: least_upper_bound a (inverse a) =<= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 298 with 766509 at 2
-Id : 298, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound identity a) [] by Demod 297 with 12 at 2,3
-Id : 297, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound identity a)) (least_upper_bound a identity) [] by Demod 296 with 10 at 1,1,3
-Id : 296, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound identity a)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 295 with 10 at 1,2,2
-Id : 295, {_}: multiply (least_upper_bound identity a) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 2 with 12 at 1,2
-Id : 2, {_}: multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity)) =>= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by prove_p21x
-% SZS output end CNFRefutation for GRP184-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 88
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 91
- least_upper_bound is 94
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p22a_1 is 75
- p22a_2 is 74
- p22a_3 is 73
- prove_p22a is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p22a_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-Last chance: 1246130514.18
-Last chance: all is indexed 1246130534.19
-Last chance: failed over 100 goal 1246130534.19
-FAILURE in 0 iterations
-% SZS status Timeout for GRP185-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 93
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 90
- least_upper_bound is 94
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p22b is 92
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-Last chance: 1246130804.3
-Last chance: all is indexed 1246130824.31
-Last chance: failed over 100 goal 1246130824.31
-FAILURE in 0 iterations
-% SZS status Timeout for GRP185-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Found proof, 55.184694s
-% SZS status Unsatisfiable for GRP186-1.p
-% SZS output start CNFRefutation for GRP186-1.p
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 194, {_}: multiply ?539 (greatest_lower_bound ?540 ?541) =<= greatest_lower_bound (multiply ?539 ?540) (multiply ?539 ?541) [541, 540, 539] by monotony_glb1 ?539 ?540 ?541
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 125, {_}: least_upper_bound ?350 (greatest_lower_bound ?350 ?351) =>= ?350 [351, 350] by lub_absorbtion ?350 ?351
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 143, {_}: greatest_lower_bound ?403 (least_upper_bound ?403 ?404) =>= ?403 [404, 403] by glb_absorbtion ?403 ?404
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 228, {_}: multiply (least_upper_bound ?618 ?619) ?620 =<= least_upper_bound (multiply ?618 ?620) (multiply ?619 ?620) [620, 619, 618] by monotony_lub2 ?618 ?619 ?620
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 37, {_}: multiply (multiply ?58 ?59) ?60 =?= multiply ?58 (multiply ?59 ?60) [60, 59, 58] by associativity ?58 ?59 ?60
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 163, {_}: multiply ?463 (least_upper_bound ?464 ?465) =<= least_upper_bound (multiply ?463 ?464) (multiply ?463 ?465) [465, 464, 463] by monotony_lub1 ?463 ?464 ?465
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 1397, {_}: multiply (inverse ?2611) (least_upper_bound ?2611 ?2612) =>= least_upper_bound identity (multiply (inverse ?2611) ?2612) [2612, 2611] by Super 163 with 6 at 1,3
-Id : 120, {_}: least_upper_bound (greatest_lower_bound ?332 ?333) ?332 =>= ?332 [333, 332] by Super 12 with 22 at 3
-Id : 1403, {_}: multiply (inverse (greatest_lower_bound ?2630 ?2629)) ?2630 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2630 ?2629)) ?2630) [2629, 2630] by Super 1397 with 120 at 2,2
-Id : 137, {_}: greatest_lower_bound (least_upper_bound ?382 ?383) ?382 =>= ?382 [383, 382] by Super 10 with 24 at 3
-Id : 39, {_}: multiply (multiply ?65 (inverse ?66)) ?66 =>= multiply ?65 identity [66, 65] by Super 37 with 6 at 2,3
-Id : 1222, {_}: multiply (multiply ?2303 (inverse ?2304)) ?2304 =>= multiply ?2303 identity [2304, 2303] by Super 37 with 6 at 2,3
-Id : 1225, {_}: multiply identity ?2310 =<= multiply (inverse (inverse ?2310)) identity [2310] by Super 1222 with 6 at 1,2
-Id : 1240, {_}: ?2310 =<= multiply (inverse (inverse ?2310)) identity [2310] by Demod 1225 with 4 at 2
-Id : 38, {_}: multiply (multiply ?62 identity) ?63 =>= multiply ?62 ?63 [63, 62] by Super 37 with 4 at 2,3
-Id : 1245, {_}: multiply ?2332 ?2333 =<= multiply (inverse (inverse ?2332)) ?2333 [2333, 2332] by Super 38 with 1240 at 1,2
-Id : 1261, {_}: ?2310 =<= multiply ?2310 identity [2310] by Demod 1240 with 1245 at 3
-Id : 1262, {_}: multiply (multiply ?65 (inverse ?66)) ?66 =>= ?65 [66, 65] by Demod 39 with 1261 at 3
-Id : 234, {_}: multiply (least_upper_bound (inverse ?642) ?641) ?642 =>= least_upper_bound identity (multiply ?641 ?642) [641, 642] by Super 228 with 6 at 1,3
-Id : 1630, {_}: multiply (least_upper_bound identity (multiply ?2984 (inverse ?2985))) ?2985 =>= least_upper_bound (inverse (inverse ?2985)) ?2984 [2985, 2984] by Super 1262 with 234 at 1,2
-Id : 1277, {_}: inverse (inverse ?2419) =<= multiply ?2419 identity [2419] by Super 1261 with 1245 at 3
-Id : 1283, {_}: inverse (inverse ?2419) =>= ?2419 [2419] by Demod 1277 with 1261 at 3
-Id : 59624, {_}: multiply (least_upper_bound identity (multiply ?78799 (inverse ?78800))) ?78800 =>= least_upper_bound ?78800 ?78799 [78800, 78799] by Demod 1630 with 1283 at 1,3
-Id : 59667, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?78935) ?78934)) (inverse ?78935)) ?78935 =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Super 59624 with 1403 at 1,2
-Id : 59764, {_}: multiply (inverse (greatest_lower_bound (inverse ?78935) ?78934)) (multiply (inverse ?78935) ?78935) =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59667 with 8 at 2
-Id : 1311, {_}: multiply (multiply ?2436 ?2435) (inverse ?2435) =>= ?2436 [2435, 2436] by Super 1262 with 1283 at 2,1,2
-Id : 46, {_}: multiply identity ?93 =<= multiply (inverse ?92) (multiply ?92 ?93) [92, 93] by Super 37 with 6 at 1,2
-Id : 55, {_}: ?93 =<= multiply (inverse ?92) (multiply ?92 ?93) [92, 93] by Demod 46 with 4 at 2
-Id : 1907, {_}: inverse ?3391 =<= multiply (inverse (multiply ?3390 ?3391)) ?3390 [3390, 3391] by Super 55 with 1311 at 2,3
-Id : 2602, {_}: multiply (inverse ?4415) (inverse ?4416) =>= inverse (multiply ?4416 ?4415) [4416, 4415] by Super 1311 with 1907 at 1,2
-Id : 2683, {_}: multiply (inverse (multiply ?4589 ?4588)) ?4590 =<= multiply (inverse ?4588) (multiply (inverse ?4589) ?4590) [4590, 4588, 4589] by Super 8 with 2602 at 1,2
-Id : 59765, {_}: multiply (inverse (multiply ?78935 (greatest_lower_bound (inverse ?78935) ?78934))) ?78935 =>= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59764 with 2683 at 2
-Id : 59766, {_}: inverse (greatest_lower_bound (inverse ?78935) ?78934) =<= least_upper_bound ?78935 (inverse (greatest_lower_bound (inverse ?78935) ?78934)) [78934, 78935] by Demod 59765 with 1907 at 2
-Id : 75243, {_}: greatest_lower_bound (inverse (greatest_lower_bound (inverse ?90061) ?90062)) ?90061 =>= ?90061 [90062, 90061] by Super 137 with 59766 at 1,2
-Id : 75245, {_}: greatest_lower_bound (inverse (greatest_lower_bound ?90066 ?90067)) (inverse ?90066) =>= inverse ?90066 [90067, 90066] by Super 75243 with 1283 at 1,1,1,2
-Id : 90405, {_}: multiply (inverse (greatest_lower_bound (inverse (greatest_lower_bound ?103908 ?103909)) (inverse ?103908))) (inverse (greatest_lower_bound ?103908 ?103909)) =>= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Super 1403 with 75245 at 1,1,2,3
-Id : 90576, {_}: inverse (multiply (greatest_lower_bound ?103908 ?103909) (greatest_lower_bound (inverse (greatest_lower_bound ?103908 ?103909)) (inverse ?103908))) =>= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Demod 90405 with 2602 at 2
-Id : 1272, {_}: multiply ?2401 (inverse ?2401) =>= identity [2401] by Super 6 with 1245 at 2
-Id : 1323, {_}: multiply ?2456 (greatest_lower_bound (inverse ?2456) ?2457) =>= greatest_lower_bound identity (multiply ?2456 ?2457) [2457, 2456] by Super 28 with 1272 at 1,3
-Id : 90577, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound ?103908 ?103909) (inverse ?103908))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103909, 103908] by Demod 90576 with 1323 at 1,2
-Id : 1321, {_}: multiply (greatest_lower_bound ?2450 ?2451) (inverse ?2450) =>= greatest_lower_bound identity (multiply ?2451 (inverse ?2450)) [2451, 2450] by Super 32 with 1272 at 1,3
-Id : 90578, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply ?103909 (inverse ?103908)))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90577 with 1321 at 2,1,2
-Id : 110, {_}: greatest_lower_bound ?310 (greatest_lower_bound ?310 ?311) =>= greatest_lower_bound ?310 ?311 [311, 310] by Super 14 with 20 at 1,3
-Id : 90579, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (multiply (inverse (inverse ?103908)) (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90578 with 110 at 1,2
-Id : 90580, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound ?103908 ?103909) (inverse ?103908))) [103908, 103909] by Demod 90579 with 2602 at 2,3
-Id : 2693, {_}: multiply (inverse ?4622) (inverse ?4623) =>= inverse (multiply ?4623 ?4622) [4623, 4622] by Super 1311 with 1907 at 1,2
-Id : 2697, {_}: multiply ?4632 (inverse ?4633) =<= inverse (multiply ?4633 (inverse ?4632)) [4633, 4632] by Super 2693 with 1283 at 1,2
-Id : 90581, {_}: inverse (greatest_lower_bound identity (multiply ?103909 (inverse ?103908))) =<= least_upper_bound identity (multiply ?103908 (inverse (greatest_lower_bound ?103908 ?103909))) [103908, 103909] by Demod 90580 with 2697 at 2,3
-Id : 2159, {_}: multiply (least_upper_bound ?3809 ?3810) (inverse ?3809) =>= least_upper_bound identity (multiply ?3810 (inverse ?3809)) [3810, 3809] by Super 30 with 1272 at 1,3
-Id : 2167, {_}: multiply ?3833 (inverse (greatest_lower_bound ?3833 ?3832)) =<= least_upper_bound identity (multiply ?3833 (inverse (greatest_lower_bound ?3833 ?3832))) [3832, 3833] by Super 2159 with 120 at 1,2
-Id : 241130, {_}: inverse (greatest_lower_bound identity (multiply ?281248 (inverse ?281249))) =?= multiply ?281249 (inverse (greatest_lower_bound ?281249 ?281248)) [281249, 281248] by Demod 90581 with 2167 at 3
-Id : 241323, {_}: inverse (greatest_lower_bound identity (inverse (multiply ?281886 ?281885))) =<= multiply ?281886 (inverse (greatest_lower_bound ?281886 (inverse ?281885))) [281885, 281886] by Super 241130 with 2602 at 2,1,2
-Id : 1908, {_}: multiply (multiply ?3393 ?3394) (inverse ?3394) =>= ?3393 [3394, 3393] by Super 1262 with 1283 at 2,1,2
-Id : 1918, {_}: multiply (least_upper_bound identity (multiply ?3421 ?3422)) (inverse ?3422) =>= least_upper_bound (inverse ?3422) ?3421 [3422, 3421] by Super 1908 with 234 at 1,2
-Id : 169, {_}: multiply (inverse ?486) (least_upper_bound ?486 ?487) =>= least_upper_bound identity (multiply (inverse ?486) ?487) [487, 486] by Super 163 with 6 at 1,3
-Id : 1396, {_}: least_upper_bound ?2608 ?2609 =<= multiply (inverse (inverse ?2608)) (least_upper_bound identity (multiply (inverse ?2608) ?2609)) [2609, 2608] by Super 55 with 169 at 2,3
-Id : 1416, {_}: least_upper_bound ?2608 ?2609 =<= multiply ?2608 (least_upper_bound identity (multiply (inverse ?2608) ?2609)) [2609, 2608] by Demod 1396 with 1283 at 1,3
-Id : 512, {_}: least_upper_bound (greatest_lower_bound ?1197 ?1198) ?1197 =>= ?1197 [1198, 1197] by Super 12 with 22 at 3
-Id : 513, {_}: least_upper_bound (greatest_lower_bound ?1201 ?1200) ?1200 =>= ?1200 [1200, 1201] by Super 512 with 10 at 1,2
-Id : 1407, {_}: multiply (inverse (greatest_lower_bound ?2641 ?2642)) ?2642 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2641 ?2642)) ?2642) [2642, 2641] by Super 1397 with 513 at 2,2
-Id : 144, {_}: greatest_lower_bound ?406 (least_upper_bound ?407 ?406) =>= ?406 [407, 406] by Super 143 with 12 at 2,2
-Id : 12520, {_}: multiply (inverse (greatest_lower_bound ?25685 ?25686)) ?25685 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?25685 ?25686)) ?25685) [25686, 25685] by Super 1397 with 120 at 2,2
-Id : 12560, {_}: multiply (inverse (greatest_lower_bound identity ?25830)) identity =>= least_upper_bound identity (inverse (greatest_lower_bound identity ?25830)) [25830] by Super 12520 with 1261 at 2,3
-Id : 12795, {_}: inverse (greatest_lower_bound identity ?25965) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?25965)) [25965] by Demod 12560 with 1261 at 2
-Id : 12796, {_}: inverse (greatest_lower_bound identity ?25967) =<= least_upper_bound identity (inverse (greatest_lower_bound ?25967 identity)) [25967] by Super 12795 with 10 at 1,2,3
-Id : 20061, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound ?34946 identity)) ?34947) =>= least_upper_bound (inverse (greatest_lower_bound identity ?34946)) ?34947 [34947, 34946] by Super 16 with 12796 at 1,3
-Id : 20078, {_}: least_upper_bound identity (least_upper_bound ?35005 (inverse (greatest_lower_bound ?35004 identity))) =>= least_upper_bound (inverse (greatest_lower_bound identity ?35004)) ?35005 [35004, 35005] by Super 20061 with 12 at 2,2
-Id : 126, {_}: least_upper_bound ?353 (greatest_lower_bound ?354 ?353) =>= ?353 [354, 353] by Super 125 with 10 at 2,2
-Id : 547, {_}: least_upper_bound ?1258 ?1256 =<= least_upper_bound (least_upper_bound ?1258 ?1256) (greatest_lower_bound ?1257 ?1256) [1257, 1256, 1258] by Super 16 with 126 at 2,2
-Id : 570, {_}: least_upper_bound ?1258 ?1256 =<= least_upper_bound (greatest_lower_bound ?1257 ?1256) (least_upper_bound ?1258 ?1256) [1257, 1256, 1258] by Demod 547 with 12 at 3
-Id : 12745, {_}: inverse (greatest_lower_bound identity ?25830) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?25830)) [25830] by Demod 12560 with 1261 at 2
-Id : 12983, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound identity ?26133)) =>= identity [26133] by Super 24 with 12745 at 2,2
-Id : 12984, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound ?26135 identity)) =>= identity [26135] by Super 12983 with 10 at 1,2,2
-Id : 13334, {_}: least_upper_bound ?26447 (inverse (greatest_lower_bound ?26446 identity)) =<= least_upper_bound identity (least_upper_bound ?26447 (inverse (greatest_lower_bound ?26446 identity))) [26446, 26447] by Super 570 with 12984 at 1,3
-Id : 33938, {_}: least_upper_bound ?35005 (inverse (greatest_lower_bound ?35004 identity)) =?= least_upper_bound (inverse (greatest_lower_bound identity ?35004)) ?35005 [35004, 35005] by Demod 20078 with 13334 at 2
-Id : 59877, {_}: inverse (greatest_lower_bound (inverse ?79280) identity) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?79280))) ?79280 [79280] by Super 33938 with 59766 at 2
-Id : 13166, {_}: inverse (greatest_lower_bound identity ?26300) =<= least_upper_bound identity (inverse (greatest_lower_bound ?26300 identity)) [26300] by Super 12795 with 10 at 1,2,3
-Id : 588, {_}: greatest_lower_bound ?1337 ?1335 =<= greatest_lower_bound (greatest_lower_bound ?1337 (least_upper_bound ?1335 ?1336)) ?1335 [1336, 1335, 1337] by Super 14 with 137 at 2,2
-Id : 13179, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?26330 (least_upper_bound identity ?26331))) =>= least_upper_bound identity (inverse (greatest_lower_bound ?26330 identity)) [26331, 26330] by Super 13166 with 588 at 1,2,3
-Id : 13288, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?26330 (least_upper_bound identity ?26331))) =>= inverse (greatest_lower_bound identity ?26330) [26331, 26330] by Demod 13179 with 12796 at 3
-Id : 508, {_}: least_upper_bound ?1185 ?1183 =<= least_upper_bound (least_upper_bound ?1185 (greatest_lower_bound ?1183 ?1184)) ?1183 [1184, 1183, 1185] by Super 16 with 120 at 2,2
-Id : 139, {_}: greatest_lower_bound ?388 (greatest_lower_bound (least_upper_bound ?388 ?389) ?390) =>= greatest_lower_bound ?388 ?390 [390, 389, 388] by Super 14 with 24 at 1,3
-Id : 12760, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse (greatest_lower_bound identity ?25876)) ?25877) =>= greatest_lower_bound identity ?25877 [25877, 25876] by Super 139 with 12745 at 1,2,2
-Id : 13743, {_}: least_upper_bound ?26971 identity =<= least_upper_bound (least_upper_bound ?26971 (greatest_lower_bound identity ?26970)) identity [26970, 26971] by Super 508 with 12760 at 2,1,3
-Id : 13824, {_}: least_upper_bound ?26971 identity =<= least_upper_bound identity (least_upper_bound ?26971 (greatest_lower_bound identity ?26970)) [26970, 26971] by Demod 13743 with 12 at 3
-Id : 14000, {_}: greatest_lower_bound ?27303 identity =<= greatest_lower_bound (greatest_lower_bound ?27303 (least_upper_bound ?27301 identity)) identity [27301, 27303] by Super 588 with 13824 at 2,1,3
-Id : 15451, {_}: greatest_lower_bound ?29213 identity =<= greatest_lower_bound identity (greatest_lower_bound ?29213 (least_upper_bound ?29214 identity)) [29214, 29213] by Demod 14000 with 10 at 3
-Id : 15452, {_}: greatest_lower_bound ?29216 identity =<= greatest_lower_bound identity (greatest_lower_bound ?29216 (least_upper_bound identity ?29217)) [29217, 29216] by Super 15451 with 12 at 2,2,3
-Id : 21667, {_}: inverse (greatest_lower_bound ?26330 identity) =?= inverse (greatest_lower_bound identity ?26330) [26330] by Demod 13288 with 15452 at 1,2
-Id : 60032, {_}: inverse (greatest_lower_bound identity (inverse ?79280)) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?79280))) ?79280 [79280] by Demod 59877 with 21667 at 2
-Id : 61973, {_}: greatest_lower_bound ?80555 (inverse (greatest_lower_bound identity (inverse ?80555))) =>= ?80555 [80555] by Super 144 with 60032 at 2,2
-Id : 61975, {_}: greatest_lower_bound (inverse ?80558) (inverse (greatest_lower_bound identity ?80558)) =>= inverse ?80558 [80558] by Super 61973 with 1283 at 2,1,2,2
-Id : 64087, {_}: multiply (inverse (greatest_lower_bound (inverse ?81915) (inverse (greatest_lower_bound identity ?81915)))) (inverse (greatest_lower_bound identity ?81915)) =>= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Super 1407 with 61975 at 1,1,2,3
-Id : 64168, {_}: inverse (multiply (greatest_lower_bound identity ?81915) (greatest_lower_bound (inverse ?81915) (inverse (greatest_lower_bound identity ?81915)))) =>= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64087 with 2602 at 2
-Id : 1322, {_}: multiply ?2453 (greatest_lower_bound ?2454 (inverse ?2453)) =>= greatest_lower_bound (multiply ?2453 ?2454) identity [2454, 2453] by Super 28 with 1272 at 2,3
-Id : 1343, {_}: multiply ?2453 (greatest_lower_bound ?2454 (inverse ?2453)) =>= greatest_lower_bound identity (multiply ?2453 ?2454) [2454, 2453] by Demod 1322 with 10 at 3
-Id : 64169, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?81915) (inverse ?81915))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64168 with 1343 at 1,2
-Id : 1320, {_}: multiply (greatest_lower_bound ?2448 ?2447) (inverse ?2447) =>= greatest_lower_bound (multiply ?2448 (inverse ?2447)) identity [2447, 2448] by Super 32 with 1272 at 2,3
-Id : 1344, {_}: multiply (greatest_lower_bound ?2448 ?2447) (inverse ?2447) =>= greatest_lower_bound identity (multiply ?2448 (inverse ?2447)) [2447, 2448] by Demod 1320 with 10 at 3
-Id : 64170, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply identity (inverse ?81915)))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64169 with 1344 at 2,1,2
-Id : 64171, {_}: inverse (greatest_lower_bound identity (multiply identity (inverse ?81915))) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64170 with 110 at 1,2
-Id : 64172, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (multiply (inverse (inverse ?81915)) (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64171 with 4 at 2,1,2
-Id : 64173, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?81915) (inverse ?81915))) [81915] by Demod 64172 with 2602 at 2,3
-Id : 64174, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= least_upper_bound identity (multiply ?81915 (inverse (greatest_lower_bound identity ?81915))) [81915] by Demod 64173 with 2697 at 2,3
-Id : 1328, {_}: multiply ?2469 (least_upper_bound ?2470 (inverse ?2469)) =>= least_upper_bound (multiply ?2469 ?2470) identity [2470, 2469] by Super 26 with 1272 at 2,3
-Id : 1339, {_}: multiply ?2469 (least_upper_bound ?2470 (inverse ?2469)) =>= least_upper_bound identity (multiply ?2469 ?2470) [2470, 2469] by Demod 1328 with 12 at 3
-Id : 60418, {_}: multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661)))) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661))))) [79661] by Super 1339 with 60032 at 2,2
-Id : 60787, {_}: multiply ?79661 (inverse (greatest_lower_bound identity ?79661)) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity (inverse (inverse ?79661))))) [79661] by Demod 60418 with 1283 at 2,1,2,2
-Id : 60788, {_}: multiply ?79661 (inverse (greatest_lower_bound identity ?79661)) =<= least_upper_bound identity (multiply ?79661 (inverse (greatest_lower_bound identity ?79661))) [79661] by Demod 60787 with 1283 at 2,1,2,2,3
-Id : 79553, {_}: inverse (greatest_lower_bound identity (inverse ?81915)) =<= multiply ?81915 (inverse (greatest_lower_bound identity ?81915)) [81915] by Demod 64174 with 60788 at 3
-Id : 79566, {_}: multiply (inverse (greatest_lower_bound identity (inverse ?93969))) (greatest_lower_bound identity ?93969) =>= ?93969 [93969] by Super 1262 with 79553 at 1,2
-Id : 210019, {_}: least_upper_bound (greatest_lower_bound identity (inverse ?259211)) (greatest_lower_bound identity ?259211) =<= multiply (greatest_lower_bound identity (inverse ?259211)) (least_upper_bound identity ?259211) [259211] by Super 1416 with 79566 at 2,2,3
-Id : 210576, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound identity (inverse ?259634)) (greatest_lower_bound identity ?259634))) (inverse (least_upper_bound identity ?259634)) =>= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Super 1918 with 210019 at 2,1,2
-Id : 122, {_}: least_upper_bound ?338 (least_upper_bound (greatest_lower_bound ?338 ?339) ?340) =>= least_upper_bound ?338 ?340 [340, 339, 338] by Super 16 with 22 at 1,3
-Id : 210728, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity ?259634)) (inverse (least_upper_bound identity ?259634)) =>= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210576 with 122 at 1,2
-Id : 210729, {_}: multiply identity (inverse (least_upper_bound identity ?259634)) =<= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210728 with 22 at 1,2
-Id : 210730, {_}: inverse (least_upper_bound identity ?259634) =<= least_upper_bound (inverse (least_upper_bound identity ?259634)) (greatest_lower_bound identity (inverse ?259634)) [259634] by Demod 210729 with 4 at 2
-Id : 210731, {_}: inverse (least_upper_bound identity ?259634) =<= least_upper_bound (greatest_lower_bound identity (inverse ?259634)) (inverse (least_upper_bound identity ?259634)) [259634] by Demod 210730 with 12 at 3
-Id : 425033, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?443021)) (greatest_lower_bound identity (inverse ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Super 137 with 210731 at 1,2
-Id : 425426, {_}: greatest_lower_bound (greatest_lower_bound identity (inverse ?443021)) (inverse (least_upper_bound identity ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425033 with 10 at 2
-Id : 425427, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse ?443021) (inverse (least_upper_bound identity ?443021))) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425426 with 14 at 2
-Id : 441, {_}: greatest_lower_bound ?1042 (greatest_lower_bound ?1042 ?1043) =>= greatest_lower_bound ?1042 ?1043 [1043, 1042] by Super 14 with 20 at 1,3
-Id : 997, {_}: greatest_lower_bound ?1977 (greatest_lower_bound ?1978 ?1977) =>= greatest_lower_bound ?1977 ?1978 [1978, 1977] by Super 441 with 10 at 2,2
-Id : 1008, {_}: greatest_lower_bound ?2012 (greatest_lower_bound ?2010 (greatest_lower_bound ?2011 ?2012)) =>= greatest_lower_bound ?2012 (greatest_lower_bound ?2010 ?2011) [2011, 2010, 2012] by Super 997 with 14 at 2,2
-Id : 196, {_}: multiply (inverse ?547) (greatest_lower_bound ?546 ?547) =>= greatest_lower_bound (multiply (inverse ?547) ?546) identity [546, 547] by Super 194 with 6 at 2,3
-Id : 215, {_}: multiply (inverse ?547) (greatest_lower_bound ?546 ?547) =>= greatest_lower_bound identity (multiply (inverse ?547) ?546) [546, 547] by Demod 196 with 10 at 3
-Id : 145, {_}: greatest_lower_bound ?411 (least_upper_bound (least_upper_bound ?411 ?409) ?410) =>= ?411 [410, 409, 411] by Super 143 with 16 at 2,2
-Id : 13972, {_}: greatest_lower_bound identity (least_upper_bound (least_upper_bound ?27209 identity) ?27211) =>= identity [27211, 27209] by Super 145 with 13824 at 1,2,2
-Id : 14608, {_}: multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity =<= greatest_lower_bound identity (multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity) [27966, 27965] by Super 215 with 13972 at 2,2
-Id : 14746, {_}: inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966) =<= greatest_lower_bound identity (multiply (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) identity) [27966, 27965] by Demod 14608 with 1261 at 2
-Id : 14747, {_}: inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966) =<= greatest_lower_bound identity (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) [27966, 27965] by Demod 14746 with 1261 at 2,3
-Id : 14621, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound ?28005 identity) ?28006) =>= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Super 513 with 13972 at 1,2
-Id : 371, {_}: least_upper_bound ?890 (least_upper_bound ?890 ?891) =>= least_upper_bound ?890 ?891 [891, 890] by Super 16 with 18 at 1,3
-Id : 372, {_}: least_upper_bound ?893 (least_upper_bound ?894 ?893) =>= least_upper_bound ?893 ?894 [894, 893] by Super 371 with 12 at 2,2
-Id : 846, {_}: least_upper_bound ?1742 (least_upper_bound (least_upper_bound ?1743 ?1742) ?1744) =>= least_upper_bound (least_upper_bound ?1742 ?1743) ?1744 [1744, 1743, 1742] by Super 16 with 372 at 1,3
-Id : 14731, {_}: least_upper_bound (least_upper_bound identity ?28005) ?28006 =?= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Demod 14621 with 846 at 2
-Id : 14732, {_}: least_upper_bound identity (least_upper_bound ?28005 ?28006) =<= least_upper_bound (least_upper_bound ?28005 identity) ?28006 [28006, 28005] by Demod 14731 with 16 at 2
-Id : 26166, {_}: inverse (least_upper_bound identity (least_upper_bound ?27965 ?27966)) =<= greatest_lower_bound identity (inverse (least_upper_bound (least_upper_bound ?27965 identity) ?27966)) [27966, 27965] by Demod 14747 with 14732 at 1,2
-Id : 26240, {_}: inverse (least_upper_bound identity (least_upper_bound ?42502 ?42503)) =<= greatest_lower_bound identity (inverse (least_upper_bound identity (least_upper_bound ?42502 ?42503))) [42503, 42502] by Demod 26166 with 14732 at 1,2,3
-Id : 26243, {_}: inverse (least_upper_bound identity (least_upper_bound ?42512 ?42512)) =>= greatest_lower_bound identity (inverse (least_upper_bound identity ?42512)) [42512] by Super 26240 with 18 at 2,1,2,3
-Id : 26484, {_}: inverse (least_upper_bound identity ?42512) =<= greatest_lower_bound identity (inverse (least_upper_bound identity ?42512)) [42512] by Demod 26243 with 18 at 2,1,2
-Id : 26733, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) =>= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42902, 42901] by Super 1008 with 26484 at 2,2,2
-Id : 26831, {_}: greatest_lower_bound (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) (inverse (least_upper_bound identity ?42901)) =>= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42901, 42902] by Demod 26733 with 10 at 2
-Id : 112, {_}: greatest_lower_bound ?317 ?316 =<= greatest_lower_bound (greatest_lower_bound ?317 ?316) ?316 [316, 317] by Super 14 with 20 at 2,2
-Id : 26832, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound (inverse (least_upper_bound identity ?42901)) (greatest_lower_bound ?42902 identity) [42901, 42902] by Demod 26831 with 112 at 2
-Id : 26833, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound (greatest_lower_bound ?42902 identity) (inverse (least_upper_bound identity ?42901)) [42901, 42902] by Demod 26832 with 10 at 3
-Id : 594, {_}: greatest_lower_bound (least_upper_bound ?1355 ?1356) ?1355 =>= ?1355 [1356, 1355] by Super 10 with 24 at 3
-Id : 595, {_}: greatest_lower_bound (least_upper_bound ?1359 ?1358) ?1358 =>= ?1358 [1358, 1359] by Super 594 with 12 at 1,2
-Id : 14013, {_}: least_upper_bound ?27351 identity =<= least_upper_bound identity (least_upper_bound ?27351 (greatest_lower_bound identity ?27352)) [27352, 27351] by Demod 13743 with 12 at 3
-Id : 15143, {_}: least_upper_bound ?28845 identity =<= least_upper_bound identity (least_upper_bound ?28845 (greatest_lower_bound ?28846 identity)) [28846, 28845] by Super 14013 with 10 at 2,2,3
-Id : 15162, {_}: least_upper_bound (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) identity =>= least_upper_bound identity (greatest_lower_bound ?28908 identity) [28907, 28908] by Super 15143 with 120 at 2,3
-Id : 15331, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) =>= least_upper_bound identity (greatest_lower_bound ?28908 identity) [28907, 28908] by Demod 15162 with 12 at 2
-Id : 15332, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?28908 identity) ?28907) =>= identity [28907, 28908] by Demod 15331 with 126 at 3
-Id : 16566, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607) =>= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Super 595 with 15332 at 1,2
-Id : 442, {_}: greatest_lower_bound ?1045 (greatest_lower_bound ?1046 ?1045) =>= greatest_lower_bound ?1045 ?1046 [1046, 1045] by Super 441 with 10 at 2,2
-Id : 988, {_}: greatest_lower_bound ?1947 (greatest_lower_bound (greatest_lower_bound ?1948 ?1947) ?1949) =>= greatest_lower_bound (greatest_lower_bound ?1947 ?1948) ?1949 [1949, 1948, 1947] by Super 14 with 442 at 1,3
-Id : 16667, {_}: greatest_lower_bound (greatest_lower_bound identity ?30606) ?30607 =?= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Demod 16566 with 988 at 2
-Id : 16668, {_}: greatest_lower_bound identity (greatest_lower_bound ?30606 ?30607) =<= greatest_lower_bound (greatest_lower_bound ?30606 identity) ?30607 [30607, 30606] by Demod 16667 with 14 at 2
-Id : 26834, {_}: greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901)) =<= greatest_lower_bound identity (greatest_lower_bound ?42902 (inverse (least_upper_bound identity ?42901))) [42901, 42902] by Demod 26833 with 16668 at 3
-Id : 425428, {_}: greatest_lower_bound (inverse ?443021) (inverse (least_upper_bound identity ?443021)) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425427 with 26834 at 2
-Id : 100, {_}: least_upper_bound ?291 ?290 =<= least_upper_bound (least_upper_bound ?291 ?290) ?290 [290, 291] by Super 16 with 18 at 2,2
-Id : 1412, {_}: multiply (inverse (least_upper_bound ?2659 ?2660)) (least_upper_bound ?2659 ?2660) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2659 ?2660)) ?2660) [2660, 2659] by Super 1397 with 100 at 2,2
-Id : 1437, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2659 ?2660)) ?2660) [2660, 2659] by Demod 1412 with 6 at 2
-Id : 59670, {_}: multiply identity ?78944 =<= least_upper_bound ?78944 (inverse (least_upper_bound ?78943 (inverse ?78944))) [78943, 78944] by Super 59624 with 1437 at 1,2
-Id : 59771, {_}: ?78944 =<= least_upper_bound ?78944 (inverse (least_upper_bound ?78943 (inverse ?78944))) [78943, 78944] by Demod 59670 with 4 at 2
-Id : 89100, {_}: greatest_lower_bound ?102689 (inverse (least_upper_bound ?102690 (inverse ?102689))) =>= inverse (least_upper_bound ?102690 (inverse ?102689)) [102690, 102689] by Super 595 with 59771 at 1,2
-Id : 89102, {_}: greatest_lower_bound (inverse ?102694) (inverse (least_upper_bound ?102695 ?102694)) =>= inverse (least_upper_bound ?102695 (inverse (inverse ?102694))) [102695, 102694] by Super 89100 with 1283 at 2,1,2,2
-Id : 89528, {_}: greatest_lower_bound (inverse ?102694) (inverse (least_upper_bound ?102695 ?102694)) =>= inverse (least_upper_bound ?102695 ?102694) [102695, 102694] by Demod 89102 with 1283 at 2,1,3
-Id : 425429, {_}: inverse (least_upper_bound identity ?443021) =>= greatest_lower_bound identity (inverse ?443021) [443021] by Demod 425428 with 89528 at 2
-Id : 426630, {_}: inverse (greatest_lower_bound identity (inverse ?443891)) =>= least_upper_bound identity ?443891 [443891] by Super 1283 with 425429 at 1,2
-Id : 428479, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 243250 with 426630 at 3
-Id : 243250, {_}: least_upper_bound identity (multiply a b) =<= inverse (greatest_lower_bound identity (inverse (multiply a b))) [] by Demod 289 with 241323 at 3
-Id : 289, {_}: least_upper_bound identity (multiply a b) =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by Demod 2 with 12 at 2
-Id : 2, {_}: least_upper_bound (multiply a b) identity =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by prove_p23
-% SZS output end CNFRefutation for GRP186-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p23_1 is 75
- p23_2 is 74
- p23_3 is 73
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p23_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Found proof, 100.862668s
-% SZS status Unsatisfiable for GRP186-2.p
-% SZS output start CNFRefutation for GRP186-2.p
-Id : 131, {_}: least_upper_bound ?356 (greatest_lower_bound ?356 ?357) =>= ?356 [357, 356] by lub_absorbtion ?356 ?357
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 26, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 20, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 28, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p23_3 ?53 ?54
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 234, {_}: multiply (least_upper_bound ?624 ?625) ?626 =<= least_upper_bound (multiply ?624 ?626) (multiply ?625 ?626) [626, 625, 624] by monotony_lub2 ?624 ?625 ?626
-Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 34, {_}: inverse identity =>= identity [] by p23_1
-Id : 316, {_}: inverse (multiply ?814 ?815) =<= multiply (inverse ?815) (inverse ?814) [815, 814] by p23_3 ?814 ?815
-Id : 43, {_}: multiply (multiply ?64 ?65) ?66 =?= multiply ?64 (multiply ?65 ?66) [66, 65, 64] by associativity ?64 ?65 ?66
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 169, {_}: multiply ?469 (least_upper_bound ?470 ?471) =<= least_upper_bound (multiply ?469 ?470) (multiply ?469 ?471) [471, 470, 469] by monotony_lub1 ?469 ?470 ?471
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 1363, {_}: multiply (inverse ?2558) (least_upper_bound ?2558 ?2559) =>= least_upper_bound identity (multiply (inverse ?2558) ?2559) [2559, 2558] by Super 169 with 6 at 1,3
-Id : 650, {_}: least_upper_bound (greatest_lower_bound ?1395 ?1396) ?1395 =>= ?1395 [1396, 1395] by Super 12 with 22 at 3
-Id : 651, {_}: least_upper_bound (greatest_lower_bound ?1399 ?1398) ?1398 =>= ?1398 [1398, 1399] by Super 650 with 10 at 1,2
-Id : 1373, {_}: multiply (inverse (greatest_lower_bound ?2588 ?2589)) ?2589 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2588 ?2589)) ?2589) [2589, 2588] by Super 1363 with 651 at 2,2
-Id : 45, {_}: multiply (multiply ?71 (inverse ?72)) ?72 =>= multiply ?71 identity [72, 71] by Super 43 with 6 at 2,3
-Id : 317, {_}: inverse (multiply identity ?817) =<= multiply (inverse ?817) identity [817] by Super 316 with 34 at 2,3
-Id : 341, {_}: inverse ?863 =<= multiply (inverse ?863) identity [863] by Demod 317 with 4 at 1,2
-Id : 343, {_}: inverse (inverse ?866) =<= multiply ?866 identity [866] by Super 341 with 36 at 1,3
-Id : 354, {_}: ?866 =<= multiply ?866 identity [866] by Demod 343 with 36 at 2
-Id : 1260, {_}: multiply (multiply ?71 (inverse ?72)) ?72 =>= ?71 [72, 71] by Demod 45 with 354 at 3
-Id : 240, {_}: multiply (least_upper_bound (inverse ?648) ?647) ?648 =>= least_upper_bound identity (multiply ?647 ?648) [647, 648] by Super 234 with 6 at 1,3
-Id : 1623, {_}: multiply (least_upper_bound identity (multiply ?2972 (inverse ?2973))) ?2973 =>= least_upper_bound (inverse (inverse ?2973)) ?2972 [2973, 2972] by Super 1260 with 240 at 1,2
-Id : 139882, {_}: multiply (least_upper_bound identity (multiply ?153893 (inverse ?153894))) ?153894 =>= least_upper_bound ?153894 ?153893 [153894, 153893] by Demod 1623 with 36 at 1,3
-Id : 126, {_}: least_upper_bound (greatest_lower_bound ?338 ?339) ?338 =>= ?338 [339, 338] by Super 12 with 22 at 3
-Id : 1369, {_}: multiply (inverse (greatest_lower_bound ?2577 ?2576)) ?2577 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2577 ?2576)) ?2577) [2576, 2577] by Super 1363 with 126 at 2,2
-Id : 139933, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?154061) ?154060)) (inverse ?154061)) ?154061 =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Super 139882 with 1369 at 1,2
-Id : 140037, {_}: multiply (inverse (greatest_lower_bound (inverse ?154061) ?154060)) (multiply (inverse ?154061) ?154061) =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 139933 with 8 at 2
-Id : 311, {_}: multiply (inverse (multiply ?794 ?795)) ?796 =<= multiply (inverse ?795) (multiply (inverse ?794) ?796) [796, 795, 794] by Super 8 with 38 at 1,2
-Id : 140038, {_}: multiply (inverse (multiply ?154061 (greatest_lower_bound (inverse ?154061) ?154060))) ?154061 =>= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 140037 with 311 at 2
-Id : 1275, {_}: multiply (multiply ?2378 (inverse ?2379)) ?2379 =>= ?2378 [2379, 2378] by Demod 45 with 354 at 3
-Id : 1285, {_}: multiply (inverse (multiply ?2408 ?2407)) ?2408 =>= inverse ?2407 [2407, 2408] by Super 1275 with 38 at 1,2
-Id : 140039, {_}: inverse (greatest_lower_bound (inverse ?154061) ?154060) =<= least_upper_bound ?154061 (inverse (greatest_lower_bound (inverse ?154061) ?154060)) [154060, 154061] by Demod 140038 with 1285 at 2
-Id : 160759, {_}: greatest_lower_bound ?168171 (inverse (greatest_lower_bound (inverse ?168171) ?168172)) =>= ?168171 [168172, 168171] by Super 24 with 140039 at 2,2
-Id : 160761, {_}: greatest_lower_bound (inverse ?168176) (inverse (greatest_lower_bound ?168176 ?168177)) =>= inverse ?168176 [168177, 168176] by Super 160759 with 36 at 1,1,2,2
-Id : 178590, {_}: multiply (inverse (greatest_lower_bound (inverse ?184996) (inverse (greatest_lower_bound ?184996 ?184997)))) (inverse (greatest_lower_bound ?184996 ?184997)) =>= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Super 1373 with 160761 at 1,1,2,3
-Id : 178788, {_}: inverse (multiply (greatest_lower_bound ?184996 ?184997) (greatest_lower_bound (inverse ?184996) (inverse (greatest_lower_bound ?184996 ?184997)))) =>= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Demod 178590 with 38 at 2
-Id : 299, {_}: multiply ?763 (inverse ?763) =>= identity [763] by Super 6 with 36 at 1,2
-Id : 392, {_}: multiply ?921 (greatest_lower_bound ?922 (inverse ?921)) =>= greatest_lower_bound (multiply ?921 ?922) identity [922, 921] by Super 28 with 299 at 2,3
-Id : 417, {_}: multiply ?921 (greatest_lower_bound ?922 (inverse ?921)) =>= greatest_lower_bound identity (multiply ?921 ?922) [922, 921] by Demod 392 with 10 at 3
-Id : 178789, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound ?184996 ?184997) (inverse ?184996))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184997, 184996] by Demod 178788 with 417 at 1,2
-Id : 391, {_}: multiply (greatest_lower_bound ?918 ?919) (inverse ?918) =>= greatest_lower_bound identity (multiply ?919 (inverse ?918)) [919, 918] by Super 32 with 299 at 1,3
-Id : 178790, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply ?184997 (inverse ?184996)))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178789 with 391 at 2,1,2
-Id : 116, {_}: greatest_lower_bound ?316 (greatest_lower_bound ?316 ?317) =>= greatest_lower_bound ?316 ?317 [317, 316] by Super 14 with 20 at 1,3
-Id : 178791, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (multiply (inverse (inverse ?184996)) (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178790 with 116 at 1,2
-Id : 178792, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound ?184996 ?184997) (inverse ?184996))) [184996, 184997] by Demod 178791 with 38 at 2,3
-Id : 320, {_}: inverse (multiply ?825 (inverse ?824)) =>= multiply ?824 (inverse ?825) [824, 825] by Super 316 with 36 at 1,3
-Id : 178793, {_}: inverse (greatest_lower_bound identity (multiply ?184997 (inverse ?184996))) =<= least_upper_bound identity (multiply ?184996 (inverse (greatest_lower_bound ?184996 ?184997))) [184996, 184997] by Demod 178792 with 320 at 2,3
-Id : 2114, {_}: multiply (least_upper_bound ?3753 ?3754) (inverse ?3753) =>= least_upper_bound identity (multiply ?3754 (inverse ?3753)) [3754, 3753] by Super 30 with 299 at 1,3
-Id : 2124, {_}: multiply ?3785 (inverse (greatest_lower_bound ?3785 ?3784)) =<= least_upper_bound identity (multiply ?3785 (inverse (greatest_lower_bound ?3785 ?3784))) [3784, 3785] by Super 2114 with 126 at 1,2
-Id : 517036, {_}: inverse (greatest_lower_bound identity (multiply ?520378 (inverse ?520379))) =?= multiply ?520379 (inverse (greatest_lower_bound ?520379 ?520378)) [520379, 520378] by Demod 178793 with 2124 at 3
-Id : 517346, {_}: inverse (greatest_lower_bound identity (inverse (multiply ?521360 ?521359))) =<= multiply ?521360 (inverse (greatest_lower_bound ?521360 (inverse ?521359))) [521359, 521360] by Super 517036 with 38 at 2,1,2
-Id : 143, {_}: greatest_lower_bound (least_upper_bound ?388 ?389) ?388 =>= ?388 [389, 388] by Super 10 with 24 at 3
-Id : 394, {_}: multiply (multiply ?928 ?927) (inverse ?927) =>= multiply ?928 identity [927, 928] by Super 8 with 299 at 2,3
-Id : 2350, {_}: multiply (multiply ?4107 ?4108) (inverse ?4108) =>= ?4107 [4108, 4107] by Demod 394 with 354 at 3
-Id : 2362, {_}: multiply (least_upper_bound identity (multiply ?4143 ?4144)) (inverse ?4144) =>= least_upper_bound (inverse ?4144) ?4143 [4144, 4143] by Super 2350 with 240 at 1,2
-Id : 52, {_}: multiply identity ?99 =<= multiply (inverse ?98) (multiply ?98 ?99) [98, 99] by Super 43 with 6 at 1,2
-Id : 61, {_}: ?99 =<= multiply (inverse ?98) (multiply ?98 ?99) [98, 99] by Demod 52 with 4 at 2
-Id : 175, {_}: multiply (inverse ?492) (least_upper_bound ?492 ?493) =>= least_upper_bound identity (multiply (inverse ?492) ?493) [493, 492] by Super 169 with 6 at 1,3
-Id : 1362, {_}: least_upper_bound ?2555 ?2556 =<= multiply (inverse (inverse ?2555)) (least_upper_bound identity (multiply (inverse ?2555) ?2556)) [2556, 2555] by Super 61 with 175 at 2,3
-Id : 1384, {_}: least_upper_bound ?2555 ?2556 =<= multiply ?2555 (least_upper_bound identity (multiply (inverse ?2555) ?2556)) [2556, 2555] by Demod 1362 with 36 at 1,3
-Id : 327, {_}: inverse ?817 =<= multiply (inverse ?817) identity [817] by Demod 317 with 4 at 1,2
-Id : 338, {_}: multiply (inverse ?854) (least_upper_bound identity ?855) =<= least_upper_bound (inverse ?854) (multiply (inverse ?854) ?855) [855, 854] by Super 26 with 327 at 1,3
-Id : 332, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =<= greatest_lower_bound (multiply (inverse ?838) ?839) (inverse ?838) [839, 838] by Super 28 with 327 at 2,3
-Id : 350, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =<= greatest_lower_bound (inverse ?838) (multiply (inverse ?838) ?839) [839, 838] by Demod 332 with 10 at 3
-Id : 333, {_}: multiply (inverse ?841) (greatest_lower_bound identity ?842) =<= greatest_lower_bound (inverse ?841) (multiply (inverse ?841) ?842) [842, 841] by Super 28 with 327 at 1,3
-Id : 3646, {_}: multiply (inverse ?838) (greatest_lower_bound ?839 identity) =?= multiply (inverse ?838) (greatest_lower_bound identity ?839) [839, 838] by Demod 350 with 333 at 3
-Id : 3670, {_}: multiply (inverse (greatest_lower_bound ?5927 identity)) (greatest_lower_bound identity ?5927) =>= identity [5927] by Super 6 with 3646 at 2
-Id : 5362, {_}: multiply (inverse (greatest_lower_bound ?8279 identity)) (least_upper_bound identity (greatest_lower_bound identity ?8279)) =>= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Super 338 with 3670 at 2,3
-Id : 5430, {_}: multiply (inverse (greatest_lower_bound ?8279 identity)) identity =>= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Demod 5362 with 22 at 2,2
-Id : 5431, {_}: inverse (greatest_lower_bound ?8279 identity) =<= least_upper_bound (inverse (greatest_lower_bound ?8279 identity)) identity [8279] by Demod 5430 with 354 at 2
-Id : 5432, {_}: inverse (greatest_lower_bound ?8279 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound ?8279 identity)) [8279] by Demod 5431 with 12 at 3
-Id : 5579, {_}: least_upper_bound ?8466 (inverse (greatest_lower_bound ?8465 identity)) =<= least_upper_bound (least_upper_bound ?8466 identity) (inverse (greatest_lower_bound ?8465 identity)) [8465, 8466] by Super 16 with 5432 at 2,2
-Id : 5622, {_}: least_upper_bound ?8466 (inverse (greatest_lower_bound ?8465 identity)) =<= least_upper_bound (inverse (greatest_lower_bound ?8465 identity)) (least_upper_bound ?8466 identity) [8465, 8466] by Demod 5579 with 12 at 3
-Id : 400, {_}: multiply (least_upper_bound ?944 ?943) (inverse ?943) =>= least_upper_bound (multiply ?944 (inverse ?943)) identity [943, 944] by Super 30 with 299 at 2,3
-Id : 412, {_}: multiply (least_upper_bound ?944 ?943) (inverse ?943) =>= least_upper_bound identity (multiply ?944 (inverse ?943)) [943, 944] by Demod 400 with 12 at 3
-Id : 337, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =<= least_upper_bound (multiply (inverse ?851) ?852) (inverse ?851) [852, 851] by Super 26 with 327 at 2,3
-Id : 347, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =<= least_upper_bound (inverse ?851) (multiply (inverse ?851) ?852) [852, 851] by Demod 337 with 12 at 3
-Id : 3431, {_}: multiply (inverse ?851) (least_upper_bound ?852 identity) =?= multiply (inverse ?851) (least_upper_bound identity ?852) [852, 851] by Demod 347 with 338 at 3
-Id : 3454, {_}: multiply (inverse (least_upper_bound ?5686 identity)) (least_upper_bound identity ?5686) =>= identity [5686] by Super 6 with 3431 at 2
-Id : 4555, {_}: multiply (inverse (least_upper_bound ?7520 identity)) (least_upper_bound identity (least_upper_bound identity ?7520)) =>= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Super 338 with 3454 at 2,3
-Id : 104, {_}: least_upper_bound ?290 (least_upper_bound ?290 ?291) =>= least_upper_bound ?290 ?291 [291, 290] by Super 16 with 18 at 1,3
-Id : 4621, {_}: multiply (inverse (least_upper_bound ?7520 identity)) (least_upper_bound identity ?7520) =>= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Demod 4555 with 104 at 2,2
-Id : 4622, {_}: identity =<= least_upper_bound (inverse (least_upper_bound ?7520 identity)) identity [7520] by Demod 4621 with 3454 at 2
-Id : 4773, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?7713 identity)) [7713] by Demod 4622 with 12 at 3
-Id : 4780, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?7726 (least_upper_bound ?7727 identity))) [7727, 7726] by Super 4773 with 16 at 1,2,3
-Id : 6791, {_}: multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity)))) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Super 412 with 4780 at 1,2
-Id : 6824, {_}: inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Demod 6791 with 4 at 2
-Id : 6825, {_}: least_upper_bound ?9674 (least_upper_bound ?9675 identity) =<= least_upper_bound identity (multiply identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity))))) [9675, 9674] by Demod 6824 with 36 at 2
-Id : 6826, {_}: least_upper_bound ?9674 (least_upper_bound ?9675 identity) =<= least_upper_bound identity (inverse (inverse (least_upper_bound ?9674 (least_upper_bound ?9675 identity)))) [9675, 9674] by Demod 6825 with 4 at 2,3
-Id : 6913, {_}: least_upper_bound ?9827 (least_upper_bound ?9828 identity) =<= least_upper_bound identity (least_upper_bound ?9827 (least_upper_bound ?9828 identity)) [9828, 9827] by Demod 6826 with 36 at 2,3
-Id : 6922, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?9855 identity) ?9854) [9855, 9854] by Super 6913 with 12 at 2,3
-Id : 502, {_}: least_upper_bound (least_upper_bound ?1064 ?1065) ?1064 =>= least_upper_bound ?1064 ?1065 [1065, 1064] by Super 12 with 104 at 3
-Id : 6917, {_}: least_upper_bound ?9839 (least_upper_bound (least_upper_bound identity ?9838) identity) =?= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Super 6913 with 502 at 2,2,3
-Id : 6992, {_}: least_upper_bound ?9839 (least_upper_bound identity (least_upper_bound identity ?9838)) =?= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Demod 6917 with 12 at 2,2
-Id : 6993, {_}: least_upper_bound ?9839 (least_upper_bound identity ?9838) =<= least_upper_bound identity (least_upper_bound ?9839 (least_upper_bound identity ?9838)) [9838, 9839] by Demod 6992 with 104 at 2,2
-Id : 6914, {_}: least_upper_bound ?9830 (least_upper_bound ?9831 identity) =<= least_upper_bound identity (least_upper_bound ?9830 (least_upper_bound identity ?9831)) [9831, 9830] by Super 6913 with 12 at 2,2,3
-Id : 7479, {_}: least_upper_bound ?9839 (least_upper_bound identity ?9838) =?= least_upper_bound ?9839 (least_upper_bound ?9838 identity) [9838, 9839] by Demod 6993 with 6914 at 3
-Id : 7163, {_}: least_upper_bound ?10110 (least_upper_bound ?10111 identity) =<= least_upper_bound identity (least_upper_bound ?10110 (least_upper_bound identity ?10111)) [10111, 10110] by Super 6913 with 12 at 2,2,3
-Id : 7180, {_}: least_upper_bound ?10164 (least_upper_bound ?10165 identity) =<= least_upper_bound identity (least_upper_bound (least_upper_bound ?10164 identity) ?10165) [10165, 10164] by Super 7163 with 16 at 2,3
-Id : 8147, {_}: least_upper_bound ?11328 (least_upper_bound ?11329 identity) =?= least_upper_bound ?11329 (least_upper_bound ?11328 identity) [11329, 11328] by Demod 7180 with 6922 at 3
-Id : 8150, {_}: least_upper_bound (greatest_lower_bound identity ?11336) (least_upper_bound ?11337 identity) =>= least_upper_bound ?11337 identity [11337, 11336] by Super 8147 with 126 at 2,3
-Id : 8900, {_}: least_upper_bound (greatest_lower_bound identity ?11839) (least_upper_bound identity ?11840) =>= least_upper_bound ?11840 identity [11840, 11839] by Super 7479 with 8150 at 3
-Id : 10250, {_}: least_upper_bound (greatest_lower_bound identity ?13083) (least_upper_bound (least_upper_bound identity ?13084) ?13085) =>= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084, 13083] by Super 16 with 8900 at 1,3
-Id : 10334, {_}: least_upper_bound (greatest_lower_bound identity ?13083) (least_upper_bound identity (least_upper_bound ?13084 ?13085)) =>= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084, 13083] by Demod 10250 with 16 at 2,2
-Id : 10335, {_}: least_upper_bound (least_upper_bound ?13084 ?13085) identity =?= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084] by Demod 10334 with 8900 at 2
-Id : 10336, {_}: least_upper_bound identity (least_upper_bound ?13084 ?13085) =<= least_upper_bound (least_upper_bound ?13084 identity) ?13085 [13085, 13084] by Demod 10335 with 12 at 2
-Id : 10485, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =<= least_upper_bound identity (least_upper_bound identity (least_upper_bound ?9855 ?9854)) [9855, 9854] by Demod 6922 with 10336 at 2,3
-Id : 10492, {_}: least_upper_bound ?9854 (least_upper_bound ?9855 identity) =?= least_upper_bound identity (least_upper_bound ?9855 ?9854) [9855, 9854] by Demod 10485 with 104 at 3
-Id : 18158, {_}: least_upper_bound ?21052 (inverse (greatest_lower_bound ?21053 identity)) =<= least_upper_bound identity (least_upper_bound ?21052 (inverse (greatest_lower_bound ?21053 identity))) [21053, 21052] by Demod 5622 with 10492 at 3
-Id : 577, {_}: greatest_lower_bound (greatest_lower_bound ?1234 ?1235) ?1234 =>= greatest_lower_bound ?1234 ?1235 [1235, 1234] by Super 10 with 116 at 3
-Id : 18162, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound (greatest_lower_bound identity ?21063) identity)) =?= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Super 18158 with 577 at 1,2,2,3
-Id : 5589, {_}: inverse (greatest_lower_bound ?8486 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound ?8486 identity)) [8486] by Demod 5431 with 12 at 3
-Id : 5593, {_}: inverse (greatest_lower_bound (greatest_lower_bound identity ?8493) identity) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Super 5589 with 577 at 1,2,3
-Id : 5675, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity ?8493)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Demod 5593 with 10 at 1,2
-Id : 5676, {_}: inverse (greatest_lower_bound identity ?8493) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8493)) [8493] by Demod 5675 with 116 at 1,2
-Id : 5590, {_}: inverse (greatest_lower_bound ?8488 identity) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?8488)) [8488] by Super 5589 with 10 at 1,2,3
-Id : 5940, {_}: inverse (greatest_lower_bound identity ?8493) =?= inverse (greatest_lower_bound ?8493 identity) [8493] by Demod 5676 with 5590 at 3
-Id : 18288, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity (greatest_lower_bound identity ?21063))) =?= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Demod 18162 with 5940 at 2,2
-Id : 18289, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063)) =<= least_upper_bound identity (least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063))) [21063, 21064] by Demod 18288 with 116 at 1,2,2
-Id : 5804, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound (least_upper_bound ?8608 identity) (inverse (greatest_lower_bound identity ?8607)) [8607, 8608] by Super 16 with 5590 at 2,2
-Id : 5849, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound (inverse (greatest_lower_bound identity ?8607)) (least_upper_bound ?8608 identity) [8607, 8608] by Demod 5804 with 12 at 3
-Id : 19653, {_}: least_upper_bound ?8608 (inverse (greatest_lower_bound ?8607 identity)) =<= least_upper_bound identity (least_upper_bound ?8608 (inverse (greatest_lower_bound identity ?8607))) [8607, 8608] by Demod 5849 with 10492 at 3
-Id : 50221, {_}: least_upper_bound ?21064 (inverse (greatest_lower_bound identity ?21063)) =?= least_upper_bound ?21064 (inverse (greatest_lower_bound ?21063 identity)) [21063, 21064] by Demod 18289 with 19653 at 3
-Id : 140157, {_}: least_upper_bound ?154397 (inverse (greatest_lower_bound identity (inverse ?154397))) =>= inverse (greatest_lower_bound (inverse ?154397) identity) [154397] by Super 50221 with 140039 at 3
-Id : 140328, {_}: least_upper_bound ?154397 (inverse (greatest_lower_bound identity (inverse ?154397))) =>= inverse (greatest_lower_bound identity (inverse ?154397)) [154397] by Demod 140157 with 5940 at 3
-Id : 141908, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?155586))) ?155586 =>= ?155586 [155586] by Super 143 with 140328 at 1,2
-Id : 141910, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity ?155589)) (inverse ?155589) =>= inverse ?155589 [155589] by Super 141908 with 36 at 2,1,1,2
-Id : 144996, {_}: multiply (inverse (greatest_lower_bound (inverse (greatest_lower_bound identity ?157076)) (inverse ?157076))) (inverse (greatest_lower_bound identity ?157076)) =>= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Super 1369 with 141910 at 1,1,2,3
-Id : 145323, {_}: inverse (multiply (greatest_lower_bound identity ?157076) (greatest_lower_bound (inverse (greatest_lower_bound identity ?157076)) (inverse ?157076))) =>= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 144996 with 38 at 2
-Id : 393, {_}: multiply ?924 (greatest_lower_bound (inverse ?924) ?925) =>= greatest_lower_bound identity (multiply ?924 ?925) [925, 924] by Super 28 with 299 at 1,3
-Id : 145324, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?157076) (inverse ?157076))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145323 with 393 at 1,2
-Id : 390, {_}: multiply (greatest_lower_bound ?916 ?915) (inverse ?915) =>= greatest_lower_bound (multiply ?916 (inverse ?915)) identity [915, 916] by Super 32 with 299 at 2,3
-Id : 418, {_}: multiply (greatest_lower_bound ?916 ?915) (inverse ?915) =>= greatest_lower_bound identity (multiply ?916 (inverse ?915)) [915, 916] by Demod 390 with 10 at 3
-Id : 145325, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply identity (inverse ?157076)))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145324 with 418 at 2,1,2
-Id : 145326, {_}: inverse (greatest_lower_bound identity (multiply identity (inverse ?157076))) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145325 with 116 at 1,2
-Id : 145327, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (multiply (inverse (inverse ?157076)) (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145326 with 4 at 2,1,2
-Id : 145328, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?157076) (inverse ?157076))) [157076] by Demod 145327 with 38 at 2,3
-Id : 145329, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= least_upper_bound identity (multiply ?157076 (inverse (greatest_lower_bound identity ?157076))) [157076] by Demod 145328 with 320 at 2,3
-Id : 399, {_}: multiply ?940 (least_upper_bound (inverse ?940) ?941) =>= least_upper_bound identity (multiply ?940 ?941) [941, 940] by Super 26 with 299 at 1,3
-Id : 140842, {_}: multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994)))) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994))))) [154994] by Super 399 with 140328 at 2,2
-Id : 141158, {_}: multiply ?154994 (inverse (greatest_lower_bound identity ?154994)) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity (inverse (inverse ?154994))))) [154994] by Demod 140842 with 36 at 2,1,2,2
-Id : 141159, {_}: multiply ?154994 (inverse (greatest_lower_bound identity ?154994)) =<= least_upper_bound identity (multiply ?154994 (inverse (greatest_lower_bound identity ?154994))) [154994] by Demod 141158 with 36 at 2,1,2,2,3
-Id : 165997, {_}: inverse (greatest_lower_bound identity (inverse ?157076)) =<= multiply ?157076 (inverse (greatest_lower_bound identity ?157076)) [157076] by Demod 145329 with 141159 at 3
-Id : 166015, {_}: multiply (inverse (greatest_lower_bound identity (inverse ?173131))) (greatest_lower_bound identity ?173131) =>= ?173131 [173131] by Super 1260 with 165997 at 1,2
-Id : 396771, {_}: least_upper_bound (greatest_lower_bound identity (inverse ?441901)) (greatest_lower_bound identity ?441901) =<= multiply (greatest_lower_bound identity (inverse ?441901)) (least_upper_bound identity ?441901) [441901] by Super 1384 with 166015 at 2,2,3
-Id : 397621, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound identity (inverse ?442410)) (greatest_lower_bound identity ?442410))) (inverse (least_upper_bound identity ?442410)) =>= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Super 2362 with 396771 at 2,1,2
-Id : 128, {_}: least_upper_bound ?344 (least_upper_bound (greatest_lower_bound ?344 ?345) ?346) =>= least_upper_bound ?344 ?346 [346, 345, 344] by Super 16 with 22 at 1,3
-Id : 397861, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity ?442410)) (inverse (least_upper_bound identity ?442410)) =>= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397621 with 128 at 1,2
-Id : 397862, {_}: multiply identity (inverse (least_upper_bound identity ?442410)) =<= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397861 with 22 at 1,2
-Id : 397863, {_}: inverse (least_upper_bound identity ?442410) =<= least_upper_bound (inverse (least_upper_bound identity ?442410)) (greatest_lower_bound identity (inverse ?442410)) [442410] by Demod 397862 with 4 at 2
-Id : 397864, {_}: inverse (least_upper_bound identity ?442410) =<= least_upper_bound (greatest_lower_bound identity (inverse ?442410)) (inverse (least_upper_bound identity ?442410)) [442410] by Demod 397863 with 12 at 3
-Id : 697689, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?666285)) (greatest_lower_bound identity (inverse ?666285)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Super 143 with 397864 at 1,2
-Id : 698150, {_}: greatest_lower_bound (greatest_lower_bound identity (inverse ?666285)) (inverse (least_upper_bound identity ?666285)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 697689 with 10 at 2
-Id : 698151, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse ?666285) (inverse (least_upper_bound identity ?666285))) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698150 with 14 at 2
-Id : 4574, {_}: multiply (inverse (least_upper_bound ?7568 identity)) (greatest_lower_bound identity (least_upper_bound identity ?7568)) =>= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Super 333 with 3454 at 2,3
-Id : 4596, {_}: multiply (inverse (least_upper_bound ?7568 identity)) identity =>= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Demod 4574 with 24 at 2,2
-Id : 4597, {_}: inverse (least_upper_bound ?7568 identity) =<= greatest_lower_bound (inverse (least_upper_bound ?7568 identity)) identity [7568] by Demod 4596 with 354 at 2
-Id : 4680, {_}: inverse (least_upper_bound ?7650 identity) =<= greatest_lower_bound identity (inverse (least_upper_bound ?7650 identity)) [7650] by Demod 4597 with 10 at 3
-Id : 4681, {_}: inverse (least_upper_bound ?7652 identity) =<= greatest_lower_bound identity (inverse (least_upper_bound identity ?7652)) [7652] by Super 4680 with 12 at 1,2,3
-Id : 4945, {_}: greatest_lower_bound ?7822 (inverse (least_upper_bound ?7821 identity)) =<= greatest_lower_bound (greatest_lower_bound ?7822 identity) (inverse (least_upper_bound identity ?7821)) [7821, 7822] by Super 14 with 4681 at 2,2
-Id : 732, {_}: greatest_lower_bound (least_upper_bound ?1553 ?1554) ?1553 =>= ?1553 [1554, 1553] by Super 10 with 24 at 3
-Id : 733, {_}: greatest_lower_bound (least_upper_bound ?1557 ?1556) ?1556 =>= ?1556 [1556, 1557] by Super 732 with 12 at 1,2
-Id : 8152, {_}: least_upper_bound (greatest_lower_bound ?11342 identity) (least_upper_bound ?11343 identity) =>= least_upper_bound ?11343 identity [11343, 11342] by Super 8147 with 651 at 2,3
-Id : 9033, {_}: least_upper_bound ?11999 identity =<= least_upper_bound (least_upper_bound (greatest_lower_bound ?11998 identity) ?11999) identity [11998, 11999] by Super 16 with 8152 at 2
-Id : 11655, {_}: least_upper_bound ?14440 identity =<= least_upper_bound identity (least_upper_bound (greatest_lower_bound ?14441 identity) ?14440) [14441, 14440] by Demod 9033 with 12 at 3
-Id : 11666, {_}: least_upper_bound (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) identity =>= least_upper_bound identity (greatest_lower_bound ?14473 identity) [14472, 14473] by Super 11655 with 22 at 2,3
-Id : 11846, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) =>= least_upper_bound identity (greatest_lower_bound ?14473 identity) [14472, 14473] by Demod 11666 with 12 at 2
-Id : 132, {_}: least_upper_bound ?359 (greatest_lower_bound ?360 ?359) =>= ?359 [360, 359] by Super 131 with 10 at 2,2
-Id : 11847, {_}: least_upper_bound identity (greatest_lower_bound (greatest_lower_bound ?14473 identity) ?14472) =>= identity [14472, 14473] by Demod 11846 with 132 at 3
-Id : 13334, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound ?16294 identity) ?16295) =>= greatest_lower_bound (greatest_lower_bound ?16294 identity) ?16295 [16295, 16294] by Super 733 with 11847 at 1,2
-Id : 13335, {_}: greatest_lower_bound identity (greatest_lower_bound (greatest_lower_bound identity ?16297) ?16298) =>= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Super 13334 with 10 at 1,2,2
-Id : 13417, {_}: greatest_lower_bound identity (greatest_lower_bound identity (greatest_lower_bound ?16297 ?16298)) =>= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Demod 13335 with 14 at 2,2
-Id : 13418, {_}: greatest_lower_bound identity (greatest_lower_bound ?16297 ?16298) =<= greatest_lower_bound (greatest_lower_bound ?16297 identity) ?16298 [16298, 16297] by Demod 13417 with 116 at 2
-Id : 16433, {_}: greatest_lower_bound ?7822 (inverse (least_upper_bound ?7821 identity)) =<= greatest_lower_bound identity (greatest_lower_bound ?7822 (inverse (least_upper_bound identity ?7821))) [7821, 7822] by Demod 4945 with 13418 at 3
-Id : 698152, {_}: greatest_lower_bound (inverse ?666285) (inverse (least_upper_bound ?666285 identity)) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698151 with 16433 at 2
-Id : 1371, {_}: multiply (inverse (least_upper_bound ?2583 ?2582)) (least_upper_bound ?2583 ?2582) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2583 ?2582)) ?2583) [2582, 2583] by Super 1363 with 502 at 2,2
-Id : 1403, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2583 ?2582)) ?2583) [2582, 2583] by Demod 1371 with 6 at 2
-Id : 139935, {_}: multiply identity ?154067 =<= least_upper_bound ?154067 (inverse (least_upper_bound (inverse ?154067) ?154066)) [154066, 154067] by Super 139882 with 1403 at 1,2
-Id : 140043, {_}: ?154067 =<= least_upper_bound ?154067 (inverse (least_upper_bound (inverse ?154067) ?154066)) [154066, 154067] by Demod 139935 with 4 at 2
-Id : 171519, {_}: greatest_lower_bound ?178895 (inverse (least_upper_bound (inverse ?178895) ?178896)) =>= inverse (least_upper_bound (inverse ?178895) ?178896) [178896, 178895] by Super 733 with 140043 at 1,2
-Id : 171521, {_}: greatest_lower_bound (inverse ?178900) (inverse (least_upper_bound ?178900 ?178901)) =>= inverse (least_upper_bound (inverse (inverse ?178900)) ?178901) [178901, 178900] by Super 171519 with 36 at 1,1,2,2
-Id : 172001, {_}: greatest_lower_bound (inverse ?178900) (inverse (least_upper_bound ?178900 ?178901)) =>= inverse (least_upper_bound ?178900 ?178901) [178901, 178900] by Demod 171521 with 36 at 1,1,3
-Id : 698153, {_}: inverse (least_upper_bound ?666285 identity) =>= greatest_lower_bound identity (inverse ?666285) [666285] by Demod 698152 with 172001 at 2
-Id : 699473, {_}: inverse (greatest_lower_bound identity (inverse ?667289)) =>= least_upper_bound ?667289 identity [667289] by Super 36 with 698153 at 1,2
-Id : 702706, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 702705 with 12 at 3
-Id : 702705, {_}: least_upper_bound identity (multiply a b) =<= least_upper_bound (multiply a b) identity [] by Demod 520020 with 699473 at 3
-Id : 520020, {_}: least_upper_bound identity (multiply a b) =<= inverse (greatest_lower_bound identity (inverse (multiply a b))) [] by Demod 329 with 517346 at 3
-Id : 329, {_}: least_upper_bound identity (multiply a b) =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by Demod 2 with 12 at 2
-Id : 2, {_}: least_upper_bound (multiply a b) identity =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by prove_p23
-% SZS output end CNFRefutation for GRP186-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 94
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p33_1 is 75
- prove_p33 is 95
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_p33
-Last chance: 1246131250.76
-Last chance: all is indexed 1246131270.76
-Last chance: failed over 100 goal 1246131270.76
-FAILURE in 0 iterations
-% SZS status Timeout for GRP187-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 95
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang1 is 82
- multiply is 96
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang2 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-Last chance: 1246131544.05
-Last chance: all is indexed 1246131564.16
-Last chance: failed over 100 goal 1246131564.16
-FAILURE in 0 iterations
-% SZS status Timeout for GRP200-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang3 is 82
- multiply is 95
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang1 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-Last chance: 1246131837.06
-Last chance: all is indexed 1246131857.16
-Last chance: failed over 100 goal 1246131857.2
-FAILURE in 0 iterations
-% SZS status Timeout for GRP202-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Last chance: 1246132129.64
-Last chance: all is indexed 1246132149.64
-Last chance: failed over 100 goal 1246132149.65
-FAILURE in 0 iterations
-% SZS status Timeout for GRP404-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 218.239700s
-% SZS status Unsatisfiable for GRP405-1.p
-% SZS output start CNFRefutation for GRP405-1.p
-Id : 4, {_}: multiply ?2 (inverse (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) =>= ?4 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: multiply ?6 (inverse (multiply (inverse (multiply (inverse (multiply ?6 ?7)) ?8)) (inverse (multiply ?7 (multiply (inverse ?7) ?7))))) =>= ?8 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 7, {_}: multiply ?17 (inverse (multiply (inverse ?16) (inverse (multiply ?18 (multiply (inverse ?18) ?18))))) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16)) (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) [15, 18, 16, 17] by Super 5 with 4 at 1,1,1,2,2
-Id : 40, {_}: multiply (inverse (multiply ?213 ?214)) (multiply ?213 (inverse (multiply (inverse ?215) (inverse (multiply ?214 (multiply (inverse ?214) ?214)))))) =>= ?215 [215, 214, 213] by Super 4 with 7 at 2,2
-Id : 64, {_}: multiply (inverse (multiply ?350 ?351)) (multiply ?350 (multiply ?352 (inverse (multiply (inverse ?353) (inverse (multiply ?354 (multiply (inverse ?354) ?354))))))) =>= multiply (inverse (multiply (inverse (multiply ?352 ?354)) ?351)) ?353 [354, 353, 352, 351, 350] by Super 40 with 7 at 2,2,2
-Id : 124, {_}: multiply (inverse (multiply ?685 ?686)) (multiply ?685 ?687) =?= multiply (inverse (multiply (inverse (multiply ?688 ?689)) ?686)) (multiply (inverse (multiply ?688 ?689)) ?687) [689, 688, 687, 686, 685] by Super 64 with 4 at 2,2,2
-Id : 70, {_}: multiply (inverse (multiply ?400 ?401)) (multiply ?400 ?399) =?= multiply (inverse (multiply (inverse (multiply ?402 ?403)) ?401)) (multiply (inverse (multiply ?402 ?403)) ?399) [403, 402, 399, 401, 400] by Super 64 with 4 at 2,2,2
-Id : 155, {_}: multiply (inverse (multiply ?925 ?926)) (multiply ?925 ?927) =?= multiply (inverse (multiply ?924 ?926)) (multiply ?924 ?927) [924, 927, 926, 925] by Super 124 with 70 at 3
-Id : 113, {_}: multiply ?598 (inverse (multiply (inverse (multiply (inverse (multiply ?598 ?599)) ?597)) (inverse (multiply ?599 (multiply (inverse ?599) ?599))))) =?= inverse (multiply (inverse (multiply (inverse (multiply ?595 ?596)) (multiply ?595 ?597))) (inverse (multiply ?596 (multiply (inverse ?596) ?596)))) [596, 595, 597, 599, 598] by Super 7 with 70 at 1,1,1,3
-Id : 176, {_}: ?597 =<= inverse (multiply (inverse (multiply (inverse (multiply ?595 ?596)) (multiply ?595 ?597))) (inverse (multiply ?596 (multiply (inverse ?596) ?596)))) [596, 595, 597] by Demod 113 with 4 at 2
-Id : 9637, {_}: multiply (inverse (multiply ?67788 (inverse (multiply ?67789 (multiply (inverse ?67789) ?67789))))) (multiply ?67788 ?67790) =?= multiply ?67791 (multiply (inverse (multiply (inverse (multiply ?67792 ?67789)) (multiply ?67792 ?67791))) ?67790) [67792, 67791, 67790, 67789, 67788] by Super 155 with 176 at 1,3
-Id : 10194, {_}: multiply ?72717 (multiply (inverse (multiply (inverse (multiply ?72718 ?72719)) (multiply ?72718 ?72717))) ?72720) =?= multiply ?72721 (multiply (inverse (multiply (inverse (multiply ?72722 ?72719)) (multiply ?72722 ?72721))) ?72720) [72722, 72721, 72720, 72719, 72718, 72717] by Super 9637 with 176 at 1,2
-Id : 10232, {_}: multiply ?73113 (multiply (inverse (multiply (inverse (multiply ?73114 (inverse (multiply (inverse (multiply (inverse (multiply ?73117 ?73111)) ?73112)) (inverse (multiply ?73111 (multiply (inverse ?73111) ?73111))))))) (multiply ?73114 ?73113))) ?73115) =?= multiply ?73116 (multiply (inverse (multiply (inverse ?73112) (multiply ?73117 ?73116))) ?73115) [73116, 73115, 73112, 73111, 73117, 73114, 73113] by Super 10194 with 4 at 1,1,1,1,2,3
-Id : 227, {_}: multiply (inverse (multiply ?1261 ?1262)) (multiply ?1261 ?1263) =?= multiply (inverse (multiply ?1264 ?1262)) (multiply ?1264 ?1263) [1264, 1263, 1262, 1261] by Super 124 with 70 at 3
-Id : 234, {_}: multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply (inverse (multiply ?1311 ?1307)) ?1308)) (inverse (multiply ?1307 (multiply (inverse ?1307) ?1307))))))) (multiply ?1309 ?1310) =>= multiply (inverse ?1308) (multiply ?1311 ?1310) [1310, 1308, 1307, 1311, 1309] by Super 227 with 4 at 1,1,3
-Id : 10841, {_}: multiply ?78382 (multiply (inverse (multiply (inverse ?78383) (multiply ?78384 ?78382))) ?78385) =?= multiply ?78386 (multiply (inverse (multiply (inverse ?78383) (multiply ?78384 ?78386))) ?78385) [78386, 78385, 78384, 78383, 78382] by Demod 10232 with 234 at 1,1,2,2
-Id : 10882, {_}: multiply ?78768 (multiply (inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?78766 ?78767)) (multiply ?78766 ?78765))) (inverse (multiply ?78767 (multiply (inverse ?78767) ?78767))))) (multiply ?78769 ?78768))) ?78770) =?= multiply ?78771 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78771))) ?78770) [78771, 78770, 78769, 78765, 78767, 78766, 78768] by Super 10841 with 176 at 1,1,1,2,3
-Id : 11114, {_}: multiply ?78768 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78768))) ?78770) =?= multiply ?78771 (multiply (inverse (multiply ?78765 (multiply ?78769 ?78771))) ?78770) [78771, 78770, 78769, 78765, 78768] by Demod 10882 with 176 at 1,1,1,2,2
-Id : 11923, {_}: multiply ?86959 (inverse (multiply (inverse (multiply ?86960 (multiply (inverse (multiply ?86961 (multiply ?86962 ?86960))) ?86963))) (inverse (multiply ?86964 (multiply (inverse ?86964) ?86964))))) =>= multiply (inverse (multiply ?86961 (multiply ?86962 (inverse (multiply ?86959 ?86964))))) ?86963 [86964, 86963, 86962, 86961, 86960, 86959] by Super 4 with 11114 at 1,1,1,2,2
-Id : 31525, {_}: multiply ?228038 (multiply ?228039 (inverse (multiply (inverse (multiply (inverse (multiply ?228040 (multiply ?228041 (inverse (multiply (inverse (multiply ?228039 ?228042)) ?228043))))) ?228044)) (inverse (multiply ?228042 (multiply (inverse ?228042) ?228042)))))) =>= multiply (inverse (multiply ?228040 (multiply ?228041 (inverse (multiply ?228038 ?228043))))) ?228044 [228044, 228043, 228042, 228041, 228040, 228039, 228038] by Super 11923 with 7 at 2,2
-Id : 31856, {_}: multiply ?231713 (multiply ?231714 (inverse (multiply (inverse (multiply (inverse (multiply ?231714 ?231716)) ?231717)) (inverse (multiply ?231716 (multiply (inverse ?231716) ?231716)))))) =?= multiply (inverse (multiply (inverse (multiply ?231715 ?231712)) (multiply ?231715 (inverse (multiply ?231713 ?231717))))) (inverse (multiply ?231712 (multiply (inverse ?231712) ?231712))) [231712, 231715, 231717, 231716, 231714, 231713] by Super 31525 with 176 at 1,1,2,2,2
-Id : 32694, {_}: multiply ?234105 ?234106 =<= multiply (inverse (multiply (inverse (multiply ?234107 ?234108)) (multiply ?234107 (inverse (multiply ?234105 ?234106))))) (inverse (multiply ?234108 (multiply (inverse ?234108) ?234108))) [234108, 234107, 234106, 234105] by Demod 31856 with 4 at 2,2
-Id : 32770, {_}: multiply ?234751 (inverse (multiply (inverse (multiply (inverse (multiply ?234751 ?234749)) ?234750)) (inverse (multiply ?234749 (multiply (inverse ?234749) ?234749))))) =?= multiply (inverse (multiply (inverse (multiply ?234752 ?234753)) (multiply ?234752 (inverse ?234750)))) (inverse (multiply ?234753 (multiply (inverse ?234753) ?234753))) [234753, 234752, 234750, 234749, 234751] by Super 32694 with 4 at 1,2,2,1,1,3
-Id : 33040, {_}: ?234750 =<= multiply (inverse (multiply (inverse (multiply ?234752 ?234753)) (multiply ?234752 (inverse ?234750)))) (inverse (multiply ?234753 (multiply (inverse ?234753) ?234753))) [234753, 234752, 234750] by Demod 32770 with 4 at 2
-Id : 15, {_}: multiply (inverse (multiply ?60 ?62)) (multiply ?60 (inverse (multiply (inverse ?61) (inverse (multiply ?62 (multiply (inverse ?62) ?62)))))) =>= ?61 [61, 62, 60] by Super 4 with 7 at 2,2
-Id : 11333, {_}: multiply ?82186 (inverse (multiply (inverse (multiply ?82185 (multiply (inverse (multiply ?82182 (multiply ?82183 ?82185))) ?82184))) (inverse (multiply ?82187 (multiply (inverse ?82187) ?82187))))) =>= multiply (inverse (multiply ?82182 (multiply ?82183 (inverse (multiply ?82186 ?82187))))) ?82184 [82187, 82184, 82183, 82182, 82185, 82186] by Super 4 with 11114 at 1,1,1,2,2
-Id : 33373, {_}: multiply ?237625 (inverse (multiply (inverse (multiply (inverse ?237622) ?237622)) (inverse (multiply ?237626 (multiply (inverse ?237626) ?237626))))) =?= multiply (inverse (multiply (inverse (multiply ?237623 ?237624)) (multiply ?237623 (inverse (multiply ?237625 ?237626))))) (inverse (multiply ?237624 (multiply (inverse ?237624) ?237624))) [237624, 237623, 237626, 237622, 237625] by Super 11333 with 33040 at 2,1,1,1,2,2
-Id : 33632, {_}: multiply ?237625 (inverse (multiply (inverse (multiply (inverse ?237622) ?237622)) (inverse (multiply ?237626 (multiply (inverse ?237626) ?237626))))) =>= multiply ?237625 ?237626 [237626, 237622, 237625] by Demod 33373 with 33040 at 3
-Id : 33860, {_}: multiply (inverse (multiply ?240296 ?240298)) (multiply ?240296 ?240298) =?= multiply (inverse ?240297) ?240297 [240297, 240298, 240296] by Super 15 with 33632 at 2,2
-Id : 40668, {_}: ?278603 =<= multiply (inverse (multiply (inverse ?278604) ?278604)) (inverse (multiply (inverse ?278603) (multiply (inverse (inverse ?278603)) (inverse ?278603)))) [278604, 278603] by Super 33040 with 33860 at 1,1,3
-Id : 35324, {_}: multiply (inverse (multiply ?248214 ?248215)) (multiply ?248214 ?248215) =?= multiply (inverse ?248216) ?248216 [248216, 248215, 248214] by Super 15 with 33632 at 2,2
-Id : 35547, {_}: multiply (inverse ?249874) ?249874 =?= multiply (inverse ?249877) ?249877 [249877, 249874] by Super 35324 with 33860 at 2
-Id : 40715, {_}: ?278907 =<= multiply (inverse (multiply (inverse ?278908) ?278908)) (inverse (multiply (inverse ?278907) (multiply (inverse ?278906) ?278906))) [278906, 278908, 278907] by Super 40668 with 35547 at 2,1,2,3
-Id : 300, {_}: ?1622 =<= inverse (multiply (inverse (multiply (inverse (multiply ?1623 ?1624)) (multiply ?1623 ?1622))) (inverse (multiply ?1624 (multiply (inverse ?1624) ?1624)))) [1624, 1623, 1622] by Demod 113 with 4 at 2
-Id : 305, {_}: ?1655 =<= inverse (multiply (inverse (multiply (inverse (multiply ?1656 (multiply ?1652 ?1653))) (multiply ?1656 ?1655))) (inverse (multiply (multiply ?1652 ?1653) (multiply (inverse (multiply ?1654 ?1653)) (multiply ?1654 ?1653))))) [1654, 1653, 1652, 1656, 1655] by Super 300 with 155 at 2,1,2,1,3
-Id : 11337, {_}: multiply (inverse (multiply ?82211 (multiply ?82212 ?82210))) ?82213 =<= inverse (multiply (inverse (multiply (inverse (multiply ?82210 ?82215)) (multiply ?82214 (multiply (inverse (multiply ?82211 (multiply ?82212 ?82214))) ?82213)))) (inverse (multiply ?82215 (multiply (inverse ?82215) ?82215)))) [82214, 82215, 82213, 82210, 82212, 82211] by Super 176 with 11114 at 2,1,1,1,3
-Id : 14547, {_}: multiply ?104639 (multiply (inverse (multiply ?104634 (multiply ?104635 ?104636))) ?104637) =<= multiply (inverse (multiply ?104640 (multiply ?104641 (inverse (multiply ?104639 ?104638))))) (multiply (inverse (multiply ?104634 (multiply ?104635 (inverse (multiply ?104640 (multiply ?104641 (inverse (multiply ?104636 ?104638)))))))) ?104637) [104638, 104641, 104640, 104637, 104636, 104635, 104634, 104639] by Super 11333 with 11337 at 2,2
-Id : 368, {_}: multiply (inverse (multiply ?1959 (multiply ?1960 (inverse (multiply (inverse ?1961) (inverse (multiply ?1962 (multiply (inverse ?1962) ?1962)))))))) (multiply ?1959 ?1963) =>= multiply (inverse ?1961) (multiply (inverse (multiply ?1960 ?1962)) ?1963) [1963, 1962, 1961, 1960, 1959] by Super 124 with 15 at 1,1,3
-Id : 384, {_}: multiply (inverse (multiply ?2092 (multiply ?2093 (inverse (multiply ?2089 (inverse (multiply ?2094 (multiply (inverse ?2094) ?2094)))))))) (multiply ?2092 ?2095) =?= multiply (inverse (multiply (inverse (multiply (inverse (multiply ?2090 ?2091)) (multiply ?2090 ?2089))) (inverse (multiply ?2091 (multiply (inverse ?2091) ?2091))))) (multiply (inverse (multiply ?2093 ?2094)) ?2095) [2091, 2090, 2095, 2094, 2089, 2093, 2092] by Super 368 with 176 at 1,1,2,2,1,1,2
-Id : 409, {_}: multiply (inverse (multiply ?2092 (multiply ?2093 (inverse (multiply ?2089 (inverse (multiply ?2094 (multiply (inverse ?2094) ?2094)))))))) (multiply ?2092 ?2095) =>= multiply ?2089 (multiply (inverse (multiply ?2093 ?2094)) ?2095) [2095, 2094, 2089, 2093, 2092] by Demod 384 with 176 at 1,3
-Id : 11831, {_}: multiply (inverse (multiply ?86031 (multiply ?86037 (inverse (multiply ?86038 (inverse (multiply ?86039 (multiply (inverse ?86039) ?86039)))))))) (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply ?86031 ?86036))))) ?86035) =?= multiply ?86038 (multiply (inverse (multiply ?86037 ?86039)) (inverse (multiply (inverse (multiply ?86032 (multiply (inverse (multiply ?86033 (multiply ?86034 ?86032))) ?86035))) (inverse (multiply ?86036 (multiply (inverse ?86036) ?86036)))))) [86032, 86035, 86036, 86034, 86033, 86039, 86038, 86037, 86031] by Super 409 with 11333 at 2,2
-Id : 12202, {_}: multiply (inverse (multiply ?86031 (multiply ?86037 (inverse (multiply ?86038 (inverse (multiply ?86039 (multiply (inverse ?86039) ?86039)))))))) (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply ?86031 ?86036))))) ?86035) =>= multiply ?86038 (multiply (inverse (multiply ?86033 (multiply ?86034 (inverse (multiply (inverse (multiply ?86037 ?86039)) ?86036))))) ?86035) [86035, 86036, 86034, 86033, 86039, 86038, 86037, 86031] by Demod 11831 with 11333 at 2,3
-Id : 18076, {_}: multiply ?132847 (multiply (inverse (multiply ?132848 (multiply ?132849 ?132850))) ?132851) =<= multiply ?132847 (multiply (inverse (multiply ?132848 (multiply ?132849 (inverse (multiply (inverse (multiply ?132853 ?132846)) (multiply ?132853 (inverse (multiply ?132850 (inverse (multiply ?132846 (multiply (inverse ?132846) ?132846))))))))))) ?132851) [132846, 132853, 132851, 132850, 132849, 132848, 132847] by Super 14547 with 12202 at 3
-Id : 21064, {_}: multiply ?157169 (inverse (multiply (inverse (multiply (inverse (multiply ?157169 ?157170)) (multiply (inverse (multiply ?157163 (multiply ?157164 ?157165))) ?157166))) (inverse (multiply ?157170 (multiply (inverse ?157170) ?157170))))) =?= multiply (inverse (multiply ?157163 (multiply ?157164 (inverse (multiply (inverse (multiply ?157167 ?157168)) (multiply ?157167 (inverse (multiply ?157165 (inverse (multiply ?157168 (multiply (inverse ?157168) ?157168))))))))))) ?157166 [157168, 157167, 157166, 157165, 157164, 157163, 157170, 157169] by Super 4 with 18076 at 1,1,1,2,2
-Id : 21742, {_}: multiply (inverse (multiply ?157163 (multiply ?157164 ?157165))) ?157166 =<= multiply (inverse (multiply ?157163 (multiply ?157164 (inverse (multiply (inverse (multiply ?157167 ?157168)) (multiply ?157167 (inverse (multiply ?157165 (inverse (multiply ?157168 (multiply (inverse ?157168) ?157168))))))))))) ?157166 [157168, 157167, 157166, 157165, 157164, 157163] by Demod 21064 with 4 at 2
-Id : 22341, {_}: inverse (multiply (inverse (multiply ?165075 ?165076)) (multiply ?165075 (inverse (multiply ?165074 (inverse (multiply ?165076 (multiply (inverse ?165076) ?165076))))))) =?= inverse (multiply (inverse (multiply (inverse (multiply ?165073 (multiply ?165077 ?165078))) (multiply ?165073 ?165074))) (inverse (multiply (multiply ?165077 ?165078) (multiply (inverse (multiply ?165079 ?165078)) (multiply ?165079 ?165078))))) [165079, 165078, 165077, 165073, 165074, 165076, 165075] by Super 305 with 21742 at 1,3
-Id : 22802, {_}: inverse (multiply (inverse (multiply ?165075 ?165076)) (multiply ?165075 (inverse (multiply ?165074 (inverse (multiply ?165076 (multiply (inverse ?165076) ?165076))))))) =>= ?165074 [165074, 165076, 165075] by Demod 22341 with 305 at 3
-Id : 38026, {_}: inverse (multiply (inverse (multiply ?263789 ?263790)) (multiply ?263789 ?263790)) =?= inverse (multiply (inverse ?263791) ?263791) [263791, 263790, 263789] by Super 22802 with 33632 at 2,1,2
-Id : 38262, {_}: inverse (multiply (inverse ?265529) ?265529) =?= inverse (multiply (inverse ?265532) ?265532) [265532, 265529] by Super 38026 with 35547 at 1,2
-Id : 38507, {_}: multiply (inverse ?265709) ?265709 =?= multiply (inverse (multiply (inverse ?265708) ?265708)) (multiply (inverse ?265707) ?265707) [265707, 265708, 265709] by Super 35547 with 38262 at 1,3
-Id : 40747, {_}: multiply (inverse ?279111) ?279111 =?= multiply (inverse (multiply (inverse ?279112) ?279112)) (inverse (multiply (inverse ?279110) ?279110)) [279110, 279112, 279111] by Super 40668 with 38507 at 1,2,3
-Id : 41831, {_}: multiply (inverse ?285057) (inverse (multiply (inverse (multiply (inverse ?285056) ?285056)) (inverse (multiply ?285057 (multiply (inverse ?285057) ?285057))))) =?= inverse (multiply (inverse ?285058) ?285058) [285058, 285056, 285057] by Super 4 with 40747 at 1,1,1,2,2
-Id : 33864, {_}: multiply ?240317 (inverse (multiply (inverse (multiply (inverse (multiply ?240317 ?240318)) ?240316)) (inverse (multiply ?240318 (multiply (inverse ?240318) ?240318))))) =?= inverse (multiply (inverse (multiply (inverse ?240315) ?240315)) (inverse (multiply ?240316 (multiply (inverse ?240316) ?240316)))) [240315, 240316, 240318, 240317] by Super 4 with 33632 at 1,1,1,2,2
-Id : 36969, {_}: ?257201 =<= inverse (multiply (inverse (multiply (inverse ?257202) ?257202)) (inverse (multiply ?257201 (multiply (inverse ?257201) ?257201)))) [257202, 257201] by Demod 33864 with 4 at 2
-Id : 37018, {_}: ?257524 =<= inverse (multiply (inverse (multiply (inverse ?257525) ?257525)) (inverse (multiply ?257524 (multiply (inverse ?257523) ?257523)))) [257523, 257525, 257524] by Super 36969 with 35547 at 2,1,2,1,3
-Id : 42424, {_}: multiply (inverse ?285057) ?285057 =?= inverse (multiply (inverse ?285058) ?285058) [285058, 285057] by Demod 41831 with 37018 at 2,2
-Id : 59456, {_}: ?377115 =<= multiply (inverse (inverse (multiply (inverse ?377116) ?377116))) (inverse (multiply (inverse ?377115) (multiply (inverse ?377117) ?377117))) [377117, 377116, 377115] by Super 40715 with 42424 at 1,1,3
-Id : 59618, {_}: multiply (inverse ?378144) ?378141 =<= multiply (inverse (inverse (multiply (inverse ?378143) ?378143))) (inverse (multiply (inverse (multiply ?378142 ?378141)) (multiply ?378142 ?378144))) [378142, 378143, 378141, 378144] by Super 59456 with 155 at 1,2,3
-Id : 293, {_}: multiply ?1577 ?1574 =<= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?1577 ?1576)) ?1578)) (multiply (inverse (multiply ?1575 ?1576)) (multiply ?1575 ?1574)))) (inverse (multiply ?1578 (multiply (inverse ?1578) ?1578)))) [1575, 1578, 1576, 1574, 1577] by Super 7 with 176 at 2,2
-Id : 49313, {_}: ?325983 =<= multiply (multiply (inverse ?325984) ?325984) (inverse (multiply (inverse ?325983) (multiply (inverse ?325985) ?325985))) [325985, 325984, 325983] by Super 40715 with 42424 at 1,3
-Id : 70497, {_}: multiply (inverse ?433725) ?433726 =<= multiply (multiply (inverse ?433727) ?433727) (inverse (multiply (inverse (multiply ?433728 ?433726)) (multiply ?433728 ?433725))) [433728, 433727, 433726, 433725] by Super 49313 with 155 at 1,2,3
-Id : 104522, {_}: multiply (inverse ?611346) ?611347 =<= multiply (multiply (inverse ?611348) ?611348) (inverse (multiply (multiply (inverse ?611349) ?611349) (multiply (inverse ?611347) ?611346))) [611349, 611348, 611347, 611346] by Super 70497 with 42424 at 1,1,2,3
-Id : 104531, {_}: multiply (inverse ?611424) (multiply (inverse ?611422) ?611422) =?= multiply (multiply (inverse ?611425) ?611425) (inverse (multiply (multiply (inverse ?611426) ?611426) (multiply (inverse (multiply (inverse ?611423) ?611423)) ?611424))) [611423, 611426, 611425, 611422, 611424] by Super 104522 with 38262 at 1,2,1,2,3
-Id : 70690, {_}: multiply (inverse ?435205) ?435206 =<= multiply (multiply (inverse ?435207) ?435207) (inverse (multiply (multiply (inverse ?435204) ?435204) (multiply (inverse ?435206) ?435205))) [435204, 435207, 435206, 435205] by Super 70497 with 42424 at 1,1,2,3
-Id : 105085, {_}: multiply (inverse ?611424) (multiply (inverse ?611422) ?611422) =?= multiply (inverse ?611424) (multiply (inverse ?611423) ?611423) [611423, 611422, 611424] by Demod 104531 with 70690 at 3
-Id : 105821, {_}: multiply ?618521 (multiply (inverse ?618519) ?618519) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?618521 ?618522)) ?618523)) (multiply (inverse (multiply (inverse ?618518) ?618522)) (multiply (inverse ?618518) (multiply (inverse ?618520) ?618520))))) (inverse (multiply ?618523 (multiply (inverse ?618523) ?618523)))) [618520, 618518, 618523, 618522, 618519, 618521] by Super 293 with 105085 at 2,2,1,1,1,3
-Id : 108557, {_}: multiply ?634262 (multiply (inverse ?634263) ?634263) =?= multiply ?634262 (multiply (inverse ?634264) ?634264) [634264, 634263, 634262] by Demod 105821 with 293 at 3
-Id : 108677, {_}: multiply ?635011 (multiply (inverse ?635012) ?635012) =?= multiply ?635011 (inverse (multiply (inverse ?635010) ?635010)) [635010, 635012, 635011] by Super 108557 with 42424 at 2,3
-Id : 41162, {_}: ?281232 =<= multiply (inverse (multiply (inverse ?281233) ?281233)) (inverse (multiply (inverse ?281232) (multiply (inverse ?281234) ?281234))) [281234, 281233, 281232] by Super 40668 with 35547 at 2,1,2,3
-Id : 41252, {_}: multiply (inverse ?281896) ?281893 =<= multiply (inverse (multiply (inverse ?281895) ?281895)) (inverse (multiply (inverse (multiply ?281894 ?281893)) (multiply ?281894 ?281896))) [281894, 281895, 281893, 281896] by Super 41162 with 155 at 1,2,3
-Id : 104693, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?612594 ?612592)) (multiply ?612594 ?612591)))) (multiply (inverse ?612593) ?612593) =?= multiply (multiply (inverse ?612595) ?612595) (inverse (multiply (multiply (inverse ?612596) ?612596) (multiply (inverse ?612591) ?612592))) [612596, 612595, 612593, 612591, 612592, 612594] by Super 104522 with 41252 at 2,1,2,3
-Id : 105218, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?612594 ?612592)) (multiply ?612594 ?612591)))) (multiply (inverse ?612593) ?612593) =>= multiply (inverse ?612592) ?612591 [612593, 612591, 612592, 612594] by Demod 104693 with 70690 at 3
-Id : 118665, {_}: multiply (inverse ?687026) ?687027 =<= multiply (inverse (inverse (multiply (inverse (multiply ?687025 ?687026)) (multiply ?687025 ?687027)))) (inverse (multiply (inverse ?687029) ?687029)) [687029, 687025, 687027, 687026] by Super 108677 with 105218 at 2
-Id : 118666, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?687031 ?687032)) (multiply ?687031 ?687033)))) (multiply (inverse ?687034) ?687034) =>= multiply (inverse ?687032) ?687033 [687034, 687033, 687032, 687031] by Demod 104693 with 70690 at 3
-Id : 202978, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1106072) ?1106072) (multiply (inverse ?1106073) ?1106074)))) (multiply (inverse ?1106075) ?1106075) =>= multiply (inverse ?1106073) ?1106074 [1106075, 1106074, 1106073, 1106072] by Super 118666 with 42424 at 1,1,1,1,2
-Id : 203337, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1108543) ?1108543) ?1108542))) (multiply (inverse ?1108545) ?1108545) =?= multiply (inverse ?1108544) (inverse (multiply (inverse (multiply (inverse (multiply (inverse ?1108544) ?1108541)) ?1108542)) (inverse (multiply ?1108541 (multiply (inverse ?1108541) ?1108541))))) [1108541, 1108544, 1108545, 1108542, 1108543] by Super 202978 with 4 at 2,1,1,1,2
-Id : 203960, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1108543) ?1108543) ?1108542))) (multiply (inverse ?1108545) ?1108545) =>= ?1108542 [1108545, 1108542, 1108543] by Demod 203337 with 4 at 3
-Id : 204499, {_}: ?1113563 =<= multiply (inverse (inverse (multiply (multiply (inverse ?1113562) ?1113562) ?1113563))) (inverse (multiply (inverse ?1113565) ?1113565)) [1113565, 1113562, 1113563] by Super 108677 with 203960 at 2
-Id : 42548, {_}: ?289376 =<= multiply (multiply (inverse ?289374) ?289374) (inverse (multiply (inverse ?289376) (multiply (inverse ?289377) ?289377))) [289377, 289374, 289376] by Super 40715 with 42424 at 1,3
-Id : 204490, {_}: inverse (multiply (multiply (inverse ?1113513) ?1113513) ?1113514) =?= multiply (multiply (inverse ?1113516) ?1113516) (inverse ?1113514) [1113516, 1113514, 1113513] by Super 42548 with 203960 at 1,2,3
-Id : 209225, {_}: ?1138104 =<= multiply (inverse (multiply (multiply (inverse ?1138103) ?1138103) (inverse ?1138104))) (inverse (multiply (inverse ?1138106) ?1138106)) [1138106, 1138103, 1138104] by Super 204499 with 204490 at 1,1,3
-Id : 232, {_}: multiply (inverse (multiply ?1297 ?1298)) (multiply ?1297 (multiply ?1293 ?1295)) =?= multiply (inverse (multiply (inverse (multiply ?1293 ?1294)) ?1298)) (multiply (inverse (multiply ?1296 ?1294)) (multiply ?1296 ?1295)) [1296, 1294, 1295, 1293, 1298, 1297] by Super 227 with 155 at 2,3
-Id : 210415, {_}: multiply (inverse (multiply (multiply (inverse ?1144394) ?1144394) (inverse ?1144395))) (multiply (inverse ?1144396) ?1144396) =>= ?1144395 [1144396, 1144395, 1144394] by Super 203960 with 204490 at 1,1,2
-Id : 210932, {_}: multiply (inverse (multiply (inverse (multiply (inverse ?1147471) ?1147471)) (inverse ?1147473))) (multiply (inverse ?1147474) ?1147474) =>= ?1147473 [1147474, 1147473, 1147471] by Super 210415 with 42424 at 1,1,1,2
-Id : 224465, {_}: multiply (inverse (multiply ?1210775 (inverse ?1210776))) (multiply ?1210775 (multiply (inverse ?1210777) ?1210777)) =>= ?1210776 [1210777, 1210776, 1210775] by Super 232 with 210932 at 3
-Id : 224626, {_}: multiply (inverse (multiply ?1211759 (inverse ?1211760))) (multiply ?1211759 (inverse (multiply (inverse ?1211758) ?1211758))) =>= ?1211760 [1211758, 1211760, 1211759] by Super 224465 with 42424 at 2,2,2
-Id : 227024, {_}: ?1221988 =<= inverse (multiply (inverse ?1221988) (multiply (inverse (inverse ?1221988)) (inverse ?1221988))) [1221988] by Super 15 with 224626 at 2
-Id : 228909, {_}: ?1228455 =<= multiply (multiply (inverse ?1228456) ?1228456) ?1228455 [1228456, 1228455] by Super 42548 with 227024 at 2,3
-Id : 230161, {_}: ?1138104 =<= multiply (inverse (inverse ?1138104)) (inverse (multiply (inverse ?1138106) ?1138106)) [1138106, 1138104] by Demod 209225 with 228909 at 1,1,3
-Id : 230162, {_}: multiply (inverse ?687026) ?687027 =<= multiply (inverse (multiply ?687025 ?687026)) (multiply ?687025 ?687027) [687025, 687027, 687026] by Demod 118665 with 230161 at 3
-Id : 230229, {_}: multiply (inverse ?378144) ?378141 =<= multiply (inverse (inverse (multiply (inverse ?378143) ?378143))) (inverse (multiply (inverse ?378141) ?378144)) [378143, 378141, 378144] by Demod 59618 with 230162 at 1,2,3
-Id : 70571, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =?= multiply (multiply (inverse ?434318) ?434318) (inverse (multiply (inverse (multiply (inverse (multiply (inverse ?434315) ?434315)) ?434317)) (multiply (inverse ?434314) ?434314))) [434314, 434315, 434318, 434317, 434316] by Super 70497 with 40747 at 2,1,2,3
-Id : 70940, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =?= multiply (inverse (multiply (inverse ?434315) ?434315)) ?434317 [434315, 434317, 434316] by Demod 70571 with 42548 at 3
-Id : 204504, {_}: multiply (inverse (inverse (multiply (multiply (inverse ?1113587) ?1113587) ?1113588))) (multiply (inverse ?1113589) ?1113589) =>= ?1113588 [1113589, 1113588, 1113587] by Demod 203337 with 4 at 3
-Id : 204894, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?1115926) ?1115926)) ?1115928))) (multiply (inverse ?1115929) ?1115929) =>= ?1115928 [1115929, 1115928, 1115926] by Super 204504 with 42424 at 1,1,1,1,2
-Id : 222906, {_}: multiply (inverse (multiply ?1203249 (inverse ?1203248))) (multiply ?1203249 (multiply (inverse ?1203247) ?1203247)) =>= ?1203248 [1203247, 1203248, 1203249] by Super 232 with 210932 at 3
-Id : 230230, {_}: multiply (inverse (inverse ?1203248)) (multiply (inverse ?1203247) ?1203247) =>= ?1203248 [1203247, 1203248] by Demod 222906 with 230162 at 2
-Id : 230233, {_}: multiply (inverse (multiply (inverse ?1115926) ?1115926)) ?1115928 =>= ?1115928 [1115928, 1115926] by Demod 204894 with 230230 at 2
-Id : 230259, {_}: multiply (inverse (inverse (multiply (inverse ?434316) ?434316))) ?434317 =>= ?434317 [434317, 434316] by Demod 70940 with 230233 at 3
-Id : 230302, {_}: multiply (inverse ?378144) ?378141 =<= inverse (multiply (inverse ?378141) ?378144) [378141, 378144] by Demod 230229 with 230259 at 3
-Id : 230467, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= inverse (multiply (inverse (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16)) (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) [15, 16, 18, 17] by Demod 7 with 230302 at 2,2
-Id : 230468, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (inverse (multiply (inverse (multiply ?17 ?18)) ?15)) ?16) [15, 16, 18, 17] by Demod 230467 with 230302 at 3
-Id : 230469, {_}: multiply ?17 (multiply (inverse (inverse (multiply ?18 (multiply (inverse ?18) ?18)))) ?16) =?= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230468 with 230302 at 1,2,3
-Id : 43162, {_}: ?293590 =<= inverse (multiply (inverse (inverse (multiply (inverse ?293589) ?293589))) (inverse (multiply ?293590 (multiply (inverse ?293591) ?293591)))) [293591, 293589, 293590] by Super 37018 with 42424 at 1,1,1,3
-Id : 230270, {_}: ?293590 =<= inverse (inverse (multiply ?293590 (multiply (inverse ?293591) ?293591))) [293591, 293590] by Demod 43162 with 230259 at 1,3
-Id : 230643, {_}: multiply ?17 (multiply ?18 ?16) =<= multiply (inverse (inverse (multiply ?15 (multiply (inverse ?15) ?15)))) (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230469 with 230270 at 1,2,2
-Id : 230644, {_}: multiply ?17 (multiply ?18 ?16) =<= multiply ?15 (multiply (multiply (inverse ?15) (multiply ?17 ?18)) ?16) [15, 16, 18, 17] by Demod 230643 with 230270 at 1,3
-Id : 298, {_}: multiply (inverse (multiply ?1613 (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612))))) (multiply ?1613 ?1614) =?= multiply ?1610 (multiply (inverse (multiply (inverse (multiply ?1611 ?1612)) (multiply ?1611 ?1610))) ?1614) [1611, 1610, 1614, 1612, 1613] by Super 155 with 176 at 1,3
-Id : 230219, {_}: multiply (inverse (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612)))) ?1614 =?= multiply ?1610 (multiply (inverse (multiply (inverse (multiply ?1611 ?1612)) (multiply ?1611 ?1610))) ?1614) [1611, 1610, 1614, 1612] by Demod 298 with 230162 at 2
-Id : 230220, {_}: multiply (inverse (inverse (multiply ?1612 (multiply (inverse ?1612) ?1612)))) ?1614 =?= multiply ?1610 (multiply (inverse (multiply (inverse ?1612) ?1610)) ?1614) [1610, 1614, 1612] by Demod 230219 with 230162 at 1,1,2,3
-Id : 230678, {_}: multiply ?1612 ?1614 =<= multiply ?1610 (multiply (inverse (multiply (inverse ?1612) ?1610)) ?1614) [1610, 1614, 1612] by Demod 230220 with 230270 at 1,2
-Id : 230679, {_}: multiply ?1612 ?1614 =<= multiply ?1610 (multiply (multiply (inverse ?1610) ?1612) ?1614) [1610, 1614, 1612] by Demod 230678 with 230302 at 1,2,3
-Id : 230680, {_}: multiply ?17 (multiply ?18 ?16) =?= multiply (multiply ?17 ?18) ?16 [16, 18, 17] by Demod 230644 with 230679 at 3
-Id : 231308, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 230680 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP405-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 13.415244s
-% SZS status Unsatisfiable for GRP422-1.p
-% SZS output start CNFRefutation for GRP422-1.p
-Id : 5, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (multiply (inverse ?8) (inverse (multiply (inverse ?8) ?8))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 4, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (multiply (inverse ?4) (inverse (multiply (inverse ?4) ?4))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 20, {_}: inverse (multiply (inverse (multiply ?72 ?73)) (multiply ?72 ?74)) =?= multiply (inverse ?74) (inverse (multiply (inverse ?73) (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse ?74) ?74))))))) [74, 73, 72] by Super 5 with 4 at 2,1,1,1,2
-Id : 9, {_}: inverse (multiply (inverse (multiply ?29 ?28)) (multiply ?29 ?30)) =?= multiply (inverse ?30) (inverse (multiply (inverse ?28) (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse ?30) ?30))))))) [30, 28, 29] by Super 5 with 4 at 2,1,1,1,2
-Id : 35, {_}: inverse (multiply (inverse (multiply ?156 ?157)) (multiply ?156 ?158)) =?= inverse (multiply (inverse (multiply ?155 ?157)) (multiply ?155 ?158)) [155, 158, 157, 156] by Super 20 with 9 at 3
-Id : 59, {_}: inverse (multiply (inverse (multiply ?228 (inverse (multiply (inverse (multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226))) (multiply (inverse ?229) (inverse (multiply (inverse ?229) ?229))))))) (multiply ?228 ?229)) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 229, 226, 225, 227, 228] by Super 4 with 35 at 1,1,2,1,1,1,2
-Id : 156, {_}: multiply (inverse (multiply ?725 ?726)) (multiply ?725 ?727) =?= multiply (inverse (multiply ?728 ?726)) (multiply ?728 ?727) [728, 727, 726, 725] by Demod 59 with 4 at 2
-Id : 163, {_}: multiply (inverse (multiply ?773 (multiply ?770 ?772))) (multiply ?773 ?774) =?= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770, 773] by Super 156 with 4 at 1,3
-Id : 55, {_}: inverse (multiply (inverse (multiply ?201 (inverse (multiply (inverse ?202) (multiply (inverse (multiply ?198 ?199)) (inverse (multiply (inverse (multiply ?200 ?199)) (multiply ?200 ?199)))))))) (multiply ?201 (multiply ?198 ?199))) =>= ?202 [200, 199, 198, 202, 201] by Super 4 with 35 at 2,2,1,2,1,1,1,2
-Id : 3142, {_}: inverse (multiply (inverse (multiply ?22079 (inverse (multiply (inverse (multiply ?22076 (multiply ?22077 ?22078))) (multiply ?22076 (inverse (multiply (inverse (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))))))))) (multiply ?22079 (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078)))))))) =>= ?22080 [22080, 22081, 22078, 22077, 22076, 22079] by Super 55 with 163 at 1,2,1,1,1,2
-Id : 290, {_}: inverse (multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply ?1310 ?1311)) (multiply ?1310 (inverse (multiply (inverse ?1312) ?1312))))))) (multiply ?1309 ?1312)) =>= multiply (inverse ?1312) ?1311 [1312, 1311, 1310, 1309] by Super 4 with 35 at 2,1,1,1,2
-Id : 110, {_}: multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 226, 225, 227] by Demod 59 with 4 at 2
-Id : 300, {_}: inverse (multiply (inverse (multiply ?1382 (inverse (multiply (inverse (multiply ?1383 ?1384)) (multiply ?1383 (inverse (multiply (inverse (multiply ?1381 ?1380)) (multiply ?1381 ?1380)))))))) (multiply ?1382 (multiply ?1379 ?1380))) =>= multiply (inverse (multiply ?1379 ?1380)) ?1384 [1379, 1380, 1381, 1384, 1383, 1382] by Super 290 with 110 at 1,2,2,1,2,1,1,1,2
-Id : 3323, {_}: multiply (inverse (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22077 ?22078) =>= ?22080 [22078, 22080, 22077] by Demod 3142 with 300 at 2
-Id : 3887, {_}: multiply (inverse (multiply ?27309 (multiply ?27310 ?27311))) (multiply ?27309 (multiply ?27310 ?27311)) =?= multiply (inverse ?27312) ?27312 [27312, 27311, 27310, 27309] by Super 163 with 3323 at 2,3
-Id : 3460, {_}: multiply (inverse (multiply ?24443 (multiply ?24440 ?24442))) (multiply ?24443 (multiply ?24440 ?24442)) =?= multiply (inverse ?24441) ?24441 [24441, 24442, 24440, 24443] by Super 163 with 3323 at 2,3
-Id : 3992, {_}: multiply (inverse ?28111) ?28111 =?= multiply (inverse ?28115) ?28115 [28115, 28111] by Super 3887 with 3460 at 2
-Id : 157, {_}: multiply (inverse (multiply ?734 ?735)) (multiply ?734 (multiply ?730 ?732)) =?= multiply (inverse (multiply (inverse (multiply ?730 ?731)) ?735)) (multiply (inverse (multiply ?733 ?731)) (multiply ?733 ?732)) [733, 731, 732, 730, 735, 734] by Super 156 with 110 at 2,3
-Id : 160, {_}: multiply (inverse (multiply ?754 (multiply ?750 ?752))) (multiply ?754 ?755) =?= multiply (inverse (multiply (inverse (multiply ?753 ?751)) (multiply ?753 ?752))) (multiply (inverse (multiply ?750 ?751)) ?755) [751, 753, 755, 752, 750, 754] by Super 156 with 110 at 1,1,3
-Id : 587, {_}: multiply (inverse (multiply ?3234 (multiply ?3232 ?3231))) (multiply ?3234 (multiply ?3232 ?3235)) =?= multiply (inverse (multiply ?3229 (multiply ?3230 ?3231))) (multiply ?3229 (multiply ?3230 ?3235)) [3230, 3229, 3235, 3231, 3232, 3234] by Super 157 with 160 at 3
-Id : 61, {_}: inverse (multiply (inverse (multiply ?240 (inverse (multiply (inverse (multiply ?239 ?238)) (multiply ?239 (inverse (multiply (inverse ?241) ?241))))))) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 239, 240] by Super 4 with 35 at 2,1,1,1,2
-Id : 4188, {_}: multiply (inverse (multiply ?29120 ?29121)) (multiply ?29120 ?29118) =?= multiply (inverse (multiply (inverse ?29118) ?29121)) (multiply (inverse ?29119) ?29119) [29119, 29118, 29121, 29120] by Super 110 with 3992 at 2,3
-Id : 10540, {_}: inverse (multiply (inverse (multiply ?66148 (inverse (multiply (inverse (multiply (inverse (multiply ?66144 ?66145)) (multiply ?66144 ?66146))) (multiply (inverse (multiply (inverse ?66146) ?66145)) (inverse (multiply (inverse ?66149) ?66149))))))) (multiply ?66148 ?66149)) =?= multiply (inverse ?66149) (multiply (inverse ?66147) ?66147) [66147, 66149, 66146, 66145, 66144, 66148] by Super 61 with 4188 at 1,1,1,2,1,1,1,2
-Id : 306, {_}: inverse (multiply (inverse (multiply ?1422 (inverse (multiply (inverse (multiply (inverse (multiply ?1421 ?1419)) (multiply ?1421 ?1420))) (multiply (inverse (multiply ?1418 ?1419)) (inverse (multiply (inverse ?1423) ?1423))))))) (multiply ?1422 ?1423)) =>= multiply (inverse ?1423) (multiply ?1418 ?1420) [1423, 1418, 1420, 1419, 1421, 1422] by Super 290 with 110 at 1,1,1,2,1,1,1,2
-Id : 10986, {_}: multiply (inverse ?66149) (multiply (inverse ?66146) ?66146) =?= multiply (inverse ?66149) (multiply (inverse ?66147) ?66147) [66147, 66146, 66149] by Demod 10540 with 306 at 2
-Id : 18, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?64 ?65)) (multiply ?64 ?66)))) (multiply (inverse ?66) (inverse (multiply (inverse ?66) ?66)))) =>= ?65 [66, 65, 64] by Super 4 with 9 at 1,1,1,2
-Id : 20513, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?122739 ?122740)) (multiply ?122739 ?122741)))) (multiply (inverse ?122741) (inverse (multiply (inverse ?122742) ?122742)))) =>= ?122740 [122742, 122741, 122740, 122739] by Super 18 with 3992 at 1,2,2,1,2
-Id : 23232, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?138627 ?138628)) (multiply ?138627 (inverse (multiply (inverse ?138629) ?138629)))))) (multiply (inverse ?138630) ?138630)) =>= ?138628 [138630, 138629, 138628, 138627] by Super 20513 with 3992 at 2,1,2
-Id : 20104, {_}: multiply (inverse (multiply ?120500 (inverse (multiply (inverse (inverse ?120501)) (multiply (inverse ?120502) (inverse (multiply (inverse ?120503) ?120503))))))) (multiply ?120500 ?120502) =>= ?120501 [120503, 120502, 120501, 120500] by Super 3323 with 3992 at 1,2,2,1,2,1,1,2
-Id : 20225, {_}: multiply (inverse (multiply ?121420 (inverse (multiply (inverse (inverse ?121421)) (multiply (inverse ?121419) ?121419))))) (multiply ?121420 (inverse (multiply (inverse ?121422) ?121422))) =>= ?121421 [121422, 121419, 121421, 121420] by Super 20104 with 3992 at 2,1,2,1,1,2
-Id : 23426, {_}: inverse (multiply (inverse (inverse ?140049)) (multiply (inverse ?140053) ?140053)) =?= inverse (multiply (inverse (inverse ?140049)) (multiply (inverse ?140050) ?140050)) [140050, 140053, 140049] by Super 23232 with 20225 at 1,1,1,1,2
-Id : 4770, {_}: inverse (multiply (inverse (multiply ?32594 ?32595)) (multiply ?32594 ?32595)) =?= inverse (multiply (inverse ?32596) ?32596) [32596, 32595, 32594] by Super 35 with 3992 at 1,3
-Id : 4818, {_}: inverse (multiply (inverse (multiply (inverse ?32938) ?32938)) (multiply (inverse ?32937) ?32937)) =?= inverse (multiply (inverse ?32939) ?32939) [32939, 32937, 32938] by Super 4770 with 3992 at 2,1,2
-Id : 21029, {_}: inverse (multiply (inverse (multiply ?125759 (inverse (multiply (inverse ?125760) (multiply (inverse ?125761) (inverse (multiply (inverse ?125762) ?125762))))))) (multiply ?125759 ?125761)) =>= ?125760 [125762, 125761, 125760, 125759] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 21146, {_}: inverse (multiply (inverse (multiply ?126647 (inverse (multiply (inverse ?126648) (multiply (inverse ?126646) ?126646))))) (multiply ?126647 (inverse (multiply (inverse ?126649) ?126649)))) =>= ?126648 [126649, 126646, 126648, 126647] by Super 21029 with 3992 at 2,1,2,1,1,1,2
-Id : 26499, {_}: multiply (inverse ?155764) ?155764 =?= inverse (multiply (inverse ?155765) ?155765) [155765, 155764] by Super 4818 with 21146 at 2
-Id : 4144, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?28920 ?28921)) (multiply ?28920 ?28918)))) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28918, 28921, 28920] by Super 18 with 3992 at 1,2,2,1,2
-Id : 27501, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?161353) ?161353))) (multiply (inverse (inverse (multiply (inverse ?161354) (multiply (inverse ?161355) ?161355)))) (inverse (multiply (inverse ?161356) ?161356)))) =>= ?161354 [161356, 161355, 161354, 161353] by Super 21146 with 26499 at 1,1,1,2
-Id : 5969, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?38946) ?38946))) (multiply (inverse ?38947) (inverse (multiply (inverse ?38947) ?38947)))) =>= ?38947 [38947, 38946] by Super 18 with 3992 at 1,1,1,1,2
-Id : 5995, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?39112) ?39112))) (multiply (inverse ?39113) (inverse (multiply (inverse ?39111) ?39111)))) =>= ?39113 [39111, 39113, 39112] by Super 5969 with 3992 at 1,2,2,1,2
-Id : 27636, {_}: inverse (multiply (inverse ?161354) (multiply (inverse ?161355) ?161355)) =>= ?161354 [161355, 161354] by Demod 27501 with 5995 at 2
-Id : 28099, {_}: inverse (multiply (inverse (multiply ?126647 ?126648)) (multiply ?126647 (inverse (multiply (inverse ?126649) ?126649)))) =>= ?126648 [126649, 126648, 126647] by Demod 21146 with 27636 at 2,1,1,1,2
-Id : 28101, {_}: inverse (multiply (inverse (multiply ?240 ?238)) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 240] by Demod 61 with 28099 at 2,1,1,1,2
-Id : 28103, {_}: inverse (multiply (inverse (multiply (inverse ?28918) ?28921)) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28921, 28918] by Demod 4144 with 28101 at 1,1,1,2
-Id : 28104, {_}: multiply (inverse (inverse (multiply (inverse ?28919) ?28919))) ?28921 =>= ?28921 [28921, 28919] by Demod 28103 with 28101 at 2
-Id : 28383, {_}: a2 === a2 [] by Demod 27989 with 28104 at 2
-Id : 27989, {_}: multiply (inverse (inverse (multiply (inverse ?163408) ?163408))) a2 =>= a2 [163408] by Super 27714 with 26499 at 1,1,2
-Id : 27714, {_}: multiply (inverse (multiply (inverse ?162124) ?162124)) a2 =>= a2 [162124] by Super 24198 with 26499 at 1,2
-Id : 24198, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?143636)) (multiply (inverse ?143638) ?143638))) (multiply (inverse (inverse ?143636)) (multiply (inverse ?143639) ?143639))) a2 =>= a2 [143639, 143638, 143636] by Super 11949 with 23426 at 1,1,2
-Id : 11949, {_}: multiply (multiply (inverse (multiply (inverse ?73741) (multiply (inverse ?73744) ?73744))) (multiply (inverse ?73741) (multiply (inverse ?73743) ?73743))) a2 =>= a2 [73743, 73744, 73741] by Super 5806 with 10986 at 2,1,2
-Id : 5806, {_}: multiply (multiply (inverse (multiply ?38037 (multiply (inverse ?38038) ?38038))) (multiply ?38037 (multiply (inverse ?38036) ?38036))) a2 =>= a2 [38036, 38038, 38037] by Super 4426 with 3992 at 2,2,1,2
-Id : 4426, {_}: multiply (multiply (inverse (multiply ?30432 (multiply ?30433 ?30431))) (multiply ?30432 (multiply ?30433 ?30431))) a2 =>= a2 [30431, 30433, 30432] by Super 4403 with 587 at 1,2
-Id : 4403, {_}: multiply (multiply (inverse ?30303) ?30303) a2 =>= a2 [30303] by Super 2 with 3992 at 1,2
-Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP422-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 11.150294s
-% SZS status Unsatisfiable for GRP423-1.p
-% SZS output start CNFRefutation for GRP423-1.p
-Id : 5, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (multiply (inverse ?8) (inverse (multiply (inverse ?8) ?8))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 4, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (multiply (inverse ?4) (inverse (multiply (inverse ?4) ?4))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 20, {_}: inverse (multiply (inverse (multiply ?72 ?73)) (multiply ?72 ?74)) =?= multiply (inverse ?74) (inverse (multiply (inverse ?73) (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse (inverse (multiply (inverse ?74) ?74))) (inverse (multiply (inverse ?74) ?74))))))) [74, 73, 72] by Super 5 with 4 at 2,1,1,1,2
-Id : 9, {_}: inverse (multiply (inverse (multiply ?29 ?28)) (multiply ?29 ?30)) =?= multiply (inverse ?30) (inverse (multiply (inverse ?28) (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse (inverse (multiply (inverse ?30) ?30))) (inverse (multiply (inverse ?30) ?30))))))) [30, 28, 29] by Super 5 with 4 at 2,1,1,1,2
-Id : 35, {_}: inverse (multiply (inverse (multiply ?156 ?157)) (multiply ?156 ?158)) =?= inverse (multiply (inverse (multiply ?155 ?157)) (multiply ?155 ?158)) [155, 158, 157, 156] by Super 20 with 9 at 3
-Id : 59, {_}: inverse (multiply (inverse (multiply ?228 (inverse (multiply (inverse (multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226))) (multiply (inverse ?229) (inverse (multiply (inverse ?229) ?229))))))) (multiply ?228 ?229)) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 229, 226, 225, 227, 228] by Super 4 with 35 at 1,1,2,1,1,1,2
-Id : 156, {_}: multiply (inverse (multiply ?725 ?726)) (multiply ?725 ?727) =?= multiply (inverse (multiply ?728 ?726)) (multiply ?728 ?727) [728, 727, 726, 725] by Demod 59 with 4 at 2
-Id : 163, {_}: multiply (inverse (multiply ?773 (multiply ?770 ?772))) (multiply ?773 ?774) =?= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770, 773] by Super 156 with 4 at 1,3
-Id : 110, {_}: multiply (inverse (multiply ?227 ?225)) (multiply ?227 ?226) =?= multiply (inverse (multiply ?224 ?225)) (multiply ?224 ?226) [224, 226, 225, 227] by Demod 59 with 4 at 2
-Id : 55, {_}: inverse (multiply (inverse (multiply ?201 (inverse (multiply (inverse ?202) (multiply (inverse (multiply ?198 ?199)) (inverse (multiply (inverse (multiply ?200 ?199)) (multiply ?200 ?199)))))))) (multiply ?201 (multiply ?198 ?199))) =>= ?202 [200, 199, 198, 202, 201] by Super 4 with 35 at 2,2,1,2,1,1,1,2
-Id : 3142, {_}: inverse (multiply (inverse (multiply ?22079 (inverse (multiply (inverse (multiply ?22076 (multiply ?22077 ?22078))) (multiply ?22076 (inverse (multiply (inverse (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22081 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))))))))) (multiply ?22079 (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078)))))))) =>= ?22080 [22080, 22081, 22078, 22077, 22076, 22079] by Super 55 with 163 at 1,2,1,1,1,2
-Id : 290, {_}: inverse (multiply (inverse (multiply ?1309 (inverse (multiply (inverse (multiply ?1310 ?1311)) (multiply ?1310 (inverse (multiply (inverse ?1312) ?1312))))))) (multiply ?1309 ?1312)) =>= multiply (inverse ?1312) ?1311 [1312, 1311, 1310, 1309] by Super 4 with 35 at 2,1,1,1,2
-Id : 300, {_}: inverse (multiply (inverse (multiply ?1382 (inverse (multiply (inverse (multiply ?1383 ?1384)) (multiply ?1383 (inverse (multiply (inverse (multiply ?1381 ?1380)) (multiply ?1381 ?1380)))))))) (multiply ?1382 (multiply ?1379 ?1380))) =>= multiply (inverse (multiply ?1379 ?1380)) ?1384 [1379, 1380, 1381, 1384, 1383, 1382] by Super 290 with 110 at 1,2,2,1,2,1,1,1,2
-Id : 3323, {_}: multiply (inverse (multiply ?22077 (inverse (multiply (inverse (inverse ?22080)) (multiply (inverse ?22078) (inverse (multiply (inverse ?22078) ?22078))))))) (multiply ?22077 ?22078) =>= ?22080 [22078, 22080, 22077] by Demod 3142 with 300 at 2
-Id : 3887, {_}: multiply (inverse (multiply ?27309 (multiply ?27310 ?27311))) (multiply ?27309 (multiply ?27310 ?27311)) =?= multiply (inverse ?27312) ?27312 [27312, 27311, 27310, 27309] by Super 163 with 3323 at 2,3
-Id : 3460, {_}: multiply (inverse (multiply ?24443 (multiply ?24440 ?24442))) (multiply ?24443 (multiply ?24440 ?24442)) =?= multiply (inverse ?24441) ?24441 [24441, 24442, 24440, 24443] by Super 163 with 3323 at 2,3
-Id : 3992, {_}: multiply (inverse ?28111) ?28111 =?= multiply (inverse ?28115) ?28115 [28115, 28111] by Super 3887 with 3460 at 2
-Id : 4190, {_}: multiply (inverse (multiply ?29130 ?29128)) (multiply ?29130 ?29131) =?= multiply (inverse (multiply (inverse ?29129) ?29129)) (multiply (inverse ?29128) ?29131) [29129, 29131, 29128, 29130] by Super 110 with 3992 at 1,1,3
-Id : 18, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?64 ?65)) (multiply ?64 ?66)))) (multiply (inverse ?66) (inverse (multiply (inverse ?66) ?66)))) =>= ?65 [66, 65, 64] by Super 4 with 9 at 1,1,1,2
-Id : 4144, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?28920 ?28921)) (multiply ?28920 ?28918)))) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28918, 28921, 28920] by Super 18 with 3992 at 1,2,2,1,2
-Id : 61, {_}: inverse (multiply (inverse (multiply ?240 (inverse (multiply (inverse (multiply ?239 ?238)) (multiply ?239 (inverse (multiply (inverse ?241) ?241))))))) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 239, 240] by Super 4 with 35 at 2,1,1,1,2
-Id : 14797, {_}: inverse (multiply (inverse (multiply ?88631 (inverse (multiply (inverse ?88632) (multiply (inverse ?88633) (inverse (multiply (inverse ?88634) ?88634))))))) (multiply ?88631 ?88633)) =>= ?88632 [88634, 88633, 88632, 88631] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 14914, {_}: inverse (multiply (inverse (multiply ?89519 (inverse (multiply (inverse ?89520) (multiply (inverse ?89518) ?89518))))) (multiply ?89519 (inverse (multiply (inverse ?89521) ?89521)))) =>= ?89520 [89521, 89518, 89520, 89519] by Super 14797 with 3992 at 2,1,2,1,1,1,2
-Id : 4605, {_}: inverse (multiply (inverse (multiply ?31655 ?31656)) (multiply ?31655 ?31656)) =?= inverse (multiply (inverse ?31657) ?31657) [31657, 31656, 31655] by Super 35 with 3992 at 1,3
-Id : 4653, {_}: inverse (multiply (inverse (multiply (inverse ?31999) ?31999)) (multiply (inverse ?31998) ?31998)) =?= inverse (multiply (inverse ?32000) ?32000) [32000, 31998, 31999] by Super 4605 with 3992 at 2,1,2
-Id : 18958, {_}: multiply (inverse ?111309) ?111309 =?= inverse (multiply (inverse ?111310) ?111310) [111310, 111309] by Super 4653 with 14914 at 2
-Id : 19832, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?116164) ?116164))) (multiply (inverse (inverse (multiply (inverse ?116165) (multiply (inverse ?116166) ?116166)))) (inverse (multiply (inverse ?116167) ?116167)))) =>= ?116165 [116167, 116166, 116165, 116164] by Super 14914 with 18958 at 1,1,1,2
-Id : 5672, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?37316) ?37316))) (multiply (inverse ?37317) (inverse (multiply (inverse ?37317) ?37317)))) =>= ?37317 [37317, 37316] by Super 18 with 3992 at 1,1,1,1,2
-Id : 5698, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?37482) ?37482))) (multiply (inverse ?37483) (inverse (multiply (inverse ?37481) ?37481)))) =>= ?37483 [37481, 37483, 37482] by Super 5672 with 3992 at 1,2,2,1,2
-Id : 19967, {_}: inverse (multiply (inverse ?116165) (multiply (inverse ?116166) ?116166)) =>= ?116165 [116166, 116165] by Demod 19832 with 5698 at 2
-Id : 20043, {_}: inverse (multiply (inverse (multiply ?89519 ?89520)) (multiply ?89519 (inverse (multiply (inverse ?89521) ?89521)))) =>= ?89520 [89521, 89520, 89519] by Demod 14914 with 19967 at 2,1,1,1,2
-Id : 20045, {_}: inverse (multiply (inverse (multiply ?240 ?238)) (multiply ?240 ?241)) =>= multiply (inverse ?241) ?238 [241, 238, 240] by Demod 61 with 20043 at 2,1,1,1,2
-Id : 20047, {_}: inverse (multiply (inverse (multiply (inverse ?28918) ?28921)) (multiply (inverse ?28918) (inverse (multiply (inverse ?28919) ?28919)))) =>= ?28921 [28919, 28921, 28918] by Demod 4144 with 20045 at 1,1,1,2
-Id : 20048, {_}: multiply (inverse (inverse (multiply (inverse ?28919) ?28919))) ?28921 =>= ?28921 [28921, 28919] by Demod 20047 with 20045 at 2
-Id : 20166, {_}: multiply (inverse (multiply (inverse ?117322) ?117322)) ?117323 =>= ?117323 [117323, 117322] by Super 20048 with 19967 at 1,1,2
-Id : 20329, {_}: multiply (inverse (multiply ?29130 ?29128)) (multiply ?29130 ?29131) =>= multiply (inverse ?29128) ?29131 [29131, 29128, 29130] by Demod 4190 with 20166 at 3
-Id : 20341, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (inverse (multiply (inverse ?771) (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772))))))) ?774) [771, 774, 772, 770] by Demod 163 with 20329 at 2
-Id : 20330, {_}: inverse (multiply (inverse ?238) ?241) =>= multiply (inverse ?241) ?238 [241, 238] by Demod 20045 with 20329 at 1,2
-Id : 20355, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (inverse (multiply (inverse ?772) (inverse (multiply (inverse ?772) ?772)))) ?771))) ?774) [771, 774, 772, 770] by Demod 20341 with 20330 at 2,1,1,2,3
-Id : 20356, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (inverse (inverse (multiply (inverse ?772) ?772))) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20355 with 20330 at 1,2,1,1,2,3
-Id : 20357, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (inverse (multiply (inverse ?772) ?772)) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20356 with 20330 at 1,1,1,2,1,1,2,3
-Id : 20358, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply (multiply (multiply (inverse ?772) ?772) ?772) ?771))) ?774) [771, 774, 772, 770] by Demod 20357 with 20330 at 1,1,2,1,1,2,3
-Id : 20377, {_}: multiply (multiply (inverse ?117322) ?117322) ?117323 =>= ?117323 [117323, 117322] by Demod 20166 with 20330 at 1,2
-Id : 20385, {_}: multiply (inverse (multiply ?770 ?772)) ?774 =<= multiply ?771 (multiply (inverse (multiply ?770 (multiply ?772 ?771))) ?774) [771, 774, 772, 770] by Demod 20358 with 20377 at 1,2,1,1,2,3
-Id : 20405, {_}: multiply (inverse (multiply (multiply (inverse ?117787) ?117787) ?117788)) ?117789 =?= multiply ?117790 (multiply (inverse (multiply ?117788 ?117790)) ?117789) [117790, 117789, 117788, 117787] by Super 20385 with 20377 at 1,1,2,3
-Id : 20523, {_}: multiply (inverse ?118011) ?118012 =<= multiply ?118013 (multiply (inverse (multiply ?118011 ?118013)) ?118012) [118013, 118012, 118011] by Demod 20405 with 20377 at 1,1,2
-Id : 20527, {_}: multiply (inverse (inverse (multiply ?118030 ?118031))) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (inverse (multiply (inverse ?118031) ?118032)) ?118033) [118032, 118033, 118031, 118030] by Super 20523 with 20329 at 1,1,2,3
-Id : 20587, {_}: multiply (inverse (inverse (multiply ?118030 ?118031))) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (multiply (inverse ?118032) ?118031) ?118033) [118032, 118033, 118031, 118030] by Demod 20527 with 20330 at 1,2,3
-Id : 3464, {_}: multiply (inverse (multiply ?24465 (inverse (multiply (inverse (inverse ?24466)) (multiply (inverse ?24467) (inverse (multiply (inverse ?24467) ?24467))))))) (multiply ?24465 ?24467) =>= ?24466 [24467, 24466, 24465] by Demod 3142 with 300 at 2
-Id : 12890, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?78617 (inverse ?78618))) (multiply ?78617 ?78619)))) (multiply (inverse ?78619) (inverse (multiply (inverse ?78619) ?78619))) =>= ?78618 [78619, 78618, 78617] by Super 3464 with 9 at 1,1,2
-Id : 13250, {_}: multiply (inverse (inverse (multiply (inverse ?80376) ?80376))) (multiply (inverse (inverse ?80377)) (inverse (multiply (inverse (inverse ?80377)) (inverse ?80377)))) =>= ?80377 [80377, 80376] by Super 12890 with 3992 at 1,1,1,2
-Id : 13299, {_}: multiply (inverse (inverse (multiply (inverse ?80682) ?80682))) (multiply (inverse (inverse ?80683)) (inverse (multiply (inverse ?80681) ?80681))) =>= ?80683 [80681, 80683, 80682] by Super 13250 with 3992 at 1,2,2,2
-Id : 209, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?973 ?974)) (multiply ?973 ?975)))) (multiply (inverse ?975) (inverse (multiply (inverse ?975) ?975)))) =>= ?974 [975, 974, 973] by Super 4 with 9 at 1,1,1,2
-Id : 228, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse (multiply ?1090 ?1088)) (multiply ?1090 ?1089))) (multiply (inverse (multiply ?1087 ?1088)) ?1091)))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1091, 1087, 1089, 1088, 1090] by Super 209 with 110 at 1,1,1,1,1,1,2
-Id : 20052, {_}: inverse (multiply (inverse (inverse (multiply (multiply (inverse ?1089) ?1088) (multiply (inverse (multiply ?1087 ?1088)) ?1091)))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1091, 1087, 1088, 1089] by Demod 228 with 20045 at 1,1,1,1,1,2
-Id : 87, {_}: inverse (multiply (inverse (multiply ?396 ?397)) (multiply ?396 ?398)) =?= inverse (multiply (inverse (multiply ?399 ?397)) (multiply ?399 ?398)) [399, 398, 397, 396] by Super 20 with 9 at 3
-Id : 92, {_}: inverse (multiply (inverse (multiply ?429 (multiply ?425 ?427))) (multiply ?429 ?430)) =?= inverse (multiply (inverse (multiply (inverse (multiply ?428 ?426)) (multiply ?428 ?427))) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 428, 430, 427, 425, 429] by Super 87 with 35 at 1,1,3
-Id : 20057, {_}: multiply (inverse ?430) (multiply ?425 ?427) =<= inverse (multiply (inverse (multiply (inverse (multiply ?428 ?426)) (multiply ?428 ?427))) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 428, 427, 425, 430] by Demod 92 with 20045 at 2
-Id : 20058, {_}: multiply (inverse ?430) (multiply ?425 ?427) =<= inverse (multiply (multiply (inverse ?427) ?426) (multiply (inverse (multiply ?425 ?426)) ?430)) [426, 427, 425, 430] by Demod 20057 with 20045 at 1,1,3
-Id : 20064, {_}: inverse (multiply (inverse (multiply (inverse ?1091) (multiply ?1087 ?1089))) (multiply (inverse ?1091) (inverse (multiply (inverse ?1091) ?1091)))) =>= multiply ?1087 ?1089 [1089, 1087, 1091] by Demod 20052 with 20058 at 1,1,1,2
-Id : 20065, {_}: multiply (inverse (inverse (multiply (inverse ?1091) ?1091))) (multiply ?1087 ?1089) =>= multiply ?1087 ?1089 [1089, 1087, 1091] by Demod 20064 with 20045 at 2
-Id : 20068, {_}: multiply (inverse (inverse ?80683)) (inverse (multiply (inverse ?80681) ?80681)) =>= ?80683 [80681, 80683] by Demod 13299 with 20065 at 2
-Id : 20372, {_}: multiply (inverse (inverse ?80683)) (multiply (inverse ?80681) ?80681) =>= ?80683 [80681, 80683] by Demod 20068 with 20330 at 2,2
-Id : 20427, {_}: multiply (inverse ?117788) ?117789 =<= multiply ?117790 (multiply (inverse (multiply ?117788 ?117790)) ?117789) [117790, 117789, 117788] by Demod 20405 with 20377 at 1,1,2
-Id : 20499, {_}: multiply (inverse ?117898) (multiply ?117898 (inverse (inverse ?117899))) =>= ?117899 [117899, 117898] by Super 20372 with 20427 at 2
-Id : 4166, {_}: inverse (multiply (inverse (multiply ?29022 (inverse (multiply (inverse ?29023) (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021))))))) (multiply ?29022 ?29020)) =>= ?29023 [29021, 29020, 29023, 29022] by Super 4 with 3992 at 1,2,2,1,2,1,1,1,2
-Id : 20061, {_}: multiply (inverse ?29020) (inverse (multiply (inverse ?29023) (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021))))) =>= ?29023 [29021, 29023, 29020] by Demod 4166 with 20045 at 2
-Id : 20368, {_}: multiply (inverse ?29020) (multiply (inverse (multiply (inverse ?29020) (inverse (multiply (inverse ?29021) ?29021)))) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20061 with 20330 at 2,2
-Id : 20369, {_}: multiply (inverse ?29020) (multiply (multiply (inverse (inverse (multiply (inverse ?29021) ?29021))) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20368 with 20330 at 1,2,2
-Id : 20370, {_}: multiply (inverse ?29020) (multiply (multiply (inverse (multiply (inverse ?29021) ?29021)) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20369 with 20330 at 1,1,1,2,2
-Id : 20371, {_}: multiply (inverse ?29020) (multiply (multiply (multiply (inverse ?29021) ?29021) ?29020) ?29023) =>= ?29023 [29023, 29021, 29020] by Demod 20370 with 20330 at 1,1,2,2
-Id : 20379, {_}: multiply (inverse ?29020) (multiply ?29020 ?29023) =>= ?29023 [29023, 29020] by Demod 20371 with 20377 at 1,2,2
-Id : 20582, {_}: inverse (inverse ?117899) =>= ?117899 [117899] by Demod 20499 with 20379 at 2
-Id : 32543, {_}: multiply (multiply ?118030 ?118031) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (multiply (inverse ?118032) ?118031) ?118033) [118032, 118033, 118031, 118030] by Demod 20587 with 20582 at 1,2
-Id : 20530, {_}: multiply (inverse (multiply (inverse ?118044) ?118044)) ?118045 =?= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045, 118044] by Super 20523 with 20377 at 1,1,2,3
-Id : 20593, {_}: multiply (multiply (inverse ?118044) ?118044) ?118045 =?= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045, 118044] by Demod 20530 with 20330 at 1,2
-Id : 20594, {_}: ?118045 =<= multiply ?118046 (multiply (inverse ?118046) ?118045) [118046, 118045] by Demod 20593 with 20377 at 2
-Id : 20765, {_}: multiply (inverse ?118471) (multiply ?118472 ?118473) =<= multiply (inverse (multiply (inverse ?118472) ?118471)) ?118473 [118473, 118472, 118471] by Super 20329 with 20594 at 1,1,2
-Id : 20804, {_}: multiply (inverse ?118471) (multiply ?118472 ?118473) =<= multiply (multiply (inverse ?118471) ?118472) ?118473 [118473, 118472, 118471] by Demod 20765 with 20330 at 1,3
-Id : 32544, {_}: multiply (multiply ?118030 ?118031) ?118033 =<= multiply (multiply ?118030 ?118032) (multiply (inverse ?118032) (multiply ?118031 ?118033)) [118032, 118033, 118031, 118030] by Demod 32543 with 20804 at 2,3
-Id : 20531, {_}: multiply (inverse (inverse ?118048)) ?118050 =<= multiply (multiply ?118048 ?118049) (multiply (inverse ?118049) ?118050) [118049, 118050, 118048] by Super 20523 with 20379 at 1,1,2,3
-Id : 22088, {_}: multiply ?118048 ?118050 =<= multiply (multiply ?118048 ?118049) (multiply (inverse ?118049) ?118050) [118049, 118050, 118048] by Demod 20531 with 20582 at 1,2
-Id : 32545, {_}: multiply (multiply ?118030 ?118031) ?118033 =?= multiply ?118030 (multiply ?118031 ?118033) [118033, 118031, 118030] by Demod 32544 with 22088 at 3
-Id : 33073, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 32545 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP423-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 19.948413s
-% SZS status Unsatisfiable for GRP444-1.p
-% SZS output start CNFRefutation for GRP444-1.p
-Id : 5, {_}: inverse (multiply ?7 (multiply ?8 (multiply (multiply ?9 (inverse ?9)) (inverse (multiply ?10 (multiply ?7 ?8)))))) =>= ?10 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (multiply ?2 (multiply ?3 (multiply (multiply ?4 (inverse ?4)) (inverse (multiply ?5 (multiply ?2 ?3)))))) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 6, {_}: inverse (multiply ?14 (multiply (multiply (multiply ?12 (inverse ?12)) (inverse (multiply ?13 (multiply ?16 ?14)))) (multiply (multiply ?15 (inverse ?15)) ?13))) =>= ?16 [15, 16, 13, 12, 14] by Super 5 with 4 at 2,2,2,1,2
-Id : 9, {_}: inverse (multiply (multiply (multiply ?32 (inverse ?32)) (inverse (multiply ?33 (multiply ?34 ?31)))) (multiply (multiply (multiply ?35 (inverse ?35)) ?33) (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 35, 31, 34, 33, 32] by Super 4 with 6 at 2,2,2,1,2
-Id : 11, {_}: inverse (multiply ?47 (multiply (multiply (multiply ?48 (inverse ?48)) (inverse (multiply ?49 (multiply ?50 ?47)))) (multiply (multiply ?51 (inverse ?51)) ?49))) =>= ?50 [51, 50, 49, 48, 47] by Super 5 with 4 at 2,2,2,1,2
-Id : 15, {_}: inverse (multiply (multiply (multiply ?82 (inverse ?82)) ?80) (multiply (multiply (multiply ?83 (inverse ?83)) ?81) (multiply (multiply ?85 (inverse ?85)) ?84))) =?= multiply (multiply ?79 (inverse ?79)) (inverse (multiply ?80 (multiply ?81 ?84))) [79, 84, 85, 81, 83, 80, 82] by Super 11 with 6 at 2,1,2,1,2
-Id : 70, {_}: multiply (multiply ?656 (inverse ?656)) (inverse (multiply (inverse (multiply ?653 (multiply ?655 ?657))) (multiply ?653 ?655))) =>= ?657 [657, 655, 653, 656] by Super 9 with 15 at 2
-Id : 7, {_}: inverse (multiply ?22 (multiply ?23 (multiply (multiply (multiply ?18 (multiply ?19 (multiply (multiply ?20 (inverse ?20)) (inverse (multiply ?21 (multiply ?18 ?19)))))) ?21) (inverse (multiply ?24 (multiply ?22 ?23)))))) =>= ?24 [24, 21, 20, 19, 18, 23, 22] by Super 5 with 4 at 2,1,2,2,1,2
-Id : 141, {_}: multiply (multiply ?1411 (inverse ?1411)) (inverse (multiply (inverse (multiply ?1412 (multiply ?1413 ?1414))) (multiply ?1412 ?1413))) =>= ?1414 [1414, 1413, 1412, 1411] by Super 9 with 15 at 2
-Id : 147, {_}: multiply (multiply ?1460 (inverse ?1460)) (inverse (multiply ?1458 (multiply ?1461 (multiply (multiply ?1456 (inverse ?1456)) (inverse (multiply ?1457 (multiply ?1458 ?1461))))))) =?= multiply (multiply ?1459 (inverse ?1459)) ?1457 [1459, 1457, 1456, 1461, 1458, 1460] by Super 141 with 6 at 1,1,2,2
-Id : 163, {_}: multiply (multiply ?1460 (inverse ?1460)) ?1457 =?= multiply (multiply ?1459 (inverse ?1459)) ?1457 [1459, 1457, 1460] by Demod 147 with 4 at 2,2
-Id : 237, {_}: inverse (multiply ?2095 (multiply ?2096 (multiply (multiply (multiply ?2097 (multiply ?2098 (multiply (multiply ?2099 (inverse ?2099)) (inverse (multiply ?2100 (multiply ?2097 ?2098)))))) ?2100) (inverse (multiply (multiply ?2094 (inverse ?2094)) (multiply ?2095 ?2096)))))) =?= multiply ?2093 (inverse ?2093) [2093, 2094, 2100, 2099, 2098, 2097, 2096, 2095] by Super 7 with 163 at 1,2,2,2,1,2
-Id : 290, {_}: multiply ?2094 (inverse ?2094) =?= multiply ?2093 (inverse ?2093) [2093, 2094] by Demod 237 with 7 at 2
-Id : 326, {_}: multiply (multiply ?2479 (inverse ?2479)) (inverse (multiply (inverse (multiply ?2477 (multiply (inverse ?2477) ?2480))) (multiply ?2478 (inverse ?2478)))) =>= ?2480 [2478, 2480, 2477, 2479] by Super 70 with 290 at 2,1,2,2
-Id : 328, {_}: multiply (multiply ?2489 (inverse ?2489)) (inverse (multiply (inverse (multiply ?2490 (multiply ?2488 (inverse ?2488)))) (multiply ?2490 ?2487))) =>= inverse ?2487 [2487, 2488, 2490, 2489] by Super 70 with 290 at 2,1,1,1,2,2
-Id : 604, {_}: inverse (multiply ?3845 (multiply ?3847 (inverse ?3847))) =?= inverse (multiply ?3845 (multiply ?3846 (inverse ?3846))) [3846, 3847, 3845] by Super 4 with 328 at 2,2,1,2
-Id : 792, {_}: inverse (multiply ?4988 (multiply (inverse ?4988) ?4987)) =?= inverse (multiply ?4986 (multiply (inverse ?4986) ?4987)) [4986, 4987, 4988] by Super 4 with 326 at 2,2,1,2
-Id : 870, {_}: inverse (multiply ?5461 (multiply ?5463 (inverse ?5463))) =?= inverse (multiply ?5462 (multiply (inverse ?5462) (inverse (inverse ?5461)))) [5462, 5463, 5461] by Super 604 with 792 at 3
-Id : 2786, {_}: inverse (multiply (inverse ?15453) (multiply ?15454 (multiply (multiply ?15455 (inverse ?15455)) (inverse (multiply ?15456 (multiply (inverse ?15456) ?15454)))))) =>= ?15453 [15456, 15455, 15454, 15453] by Super 6 with 326 at 1,2,1,2
-Id : 2859, {_}: inverse (multiply (inverse ?15956) (multiply (inverse (inverse (inverse (multiply ?15954 (multiply (inverse ?15954) ?15955))))) ?15955)) =>= ?15956 [15955, 15954, 15956] by Super 2786 with 326 at 2,2,1,2
-Id : 3662, {_}: inverse (multiply (inverse (inverse (inverse (multiply ?19641 (multiply (inverse ?19641) ?19642))))) (multiply ?19642 (multiply (multiply ?19643 (inverse ?19643)) ?19640))) =>= inverse ?19640 [19640, 19643, 19642, 19641] by Super 4 with 2859 at 2,2,2,1,2
-Id : 13794, {_}: inverse (inverse (multiply ?72764 (multiply (inverse (inverse (inverse (multiply ?72761 (multiply (inverse ?72761) ?72762))))) ?72762))) =>= ?72764 [72762, 72761, 72764] by Super 4 with 3662 at 2
-Id : 3676, {_}: multiply (multiply ?19736 (inverse ?19736)) (multiply (inverse (inverse (inverse (multiply ?19734 (multiply (inverse ?19734) ?19735))))) (multiply ?19737 (inverse ?19737))) =>= inverse ?19735 [19737, 19735, 19734, 19736] by Super 328 with 2859 at 2,2
-Id : 16741, {_}: inverse (inverse (inverse (multiply ?88187 (inverse ?88187)))) =?= multiply ?88186 (inverse ?88186) [88186, 88187] by Super 13794 with 3676 at 1,1,2
-Id : 17199, {_}: inverse (multiply ?90662 (multiply ?90661 (inverse ?90661))) =?= inverse (multiply ?90662 (inverse (inverse (inverse (multiply ?90660 (inverse ?90660)))))) [90660, 90661, 90662] by Super 870 with 16741 at 2,1,3
-Id : 3671, {_}: multiply (multiply ?19707 (inverse ?19707)) (multiply (inverse (inverse (inverse (multiply ?19705 (multiply (inverse ?19705) ?19706))))) (multiply ?19706 ?19708)) =>= ?19708 [19708, 19706, 19705, 19707] by Super 70 with 2859 at 2,2
-Id : 2874, {_}: inverse (multiply (inverse (multiply ?16071 (multiply (inverse ?16071) (inverse (inverse ?16069))))) (multiply ?16072 (multiply (multiply ?16073 (inverse ?16073)) (inverse (multiply ?16074 (multiply (inverse ?16074) ?16072)))))) =?= multiply ?16069 (multiply ?16070 (inverse ?16070)) [16070, 16074, 16073, 16072, 16069, 16071] by Super 2786 with 870 at 1,1,2
-Id : 790, {_}: inverse (multiply (inverse ?4975) (multiply ?4974 (multiply (multiply ?4976 (inverse ?4976)) (inverse (multiply ?4973 (multiply (inverse ?4973) ?4974)))))) =>= ?4975 [4973, 4976, 4974, 4975] by Super 6 with 326 at 1,2,1,2
-Id : 2903, {_}: multiply ?16071 (multiply (inverse ?16071) (inverse (inverse ?16069))) =?= multiply ?16069 (multiply ?16070 (inverse ?16070)) [16070, 16069, 16071] by Demod 2874 with 790 at 2
-Id : 17213, {_}: multiply ?90740 (inverse ?90740) =?= multiply (inverse (inverse (multiply ?90738 (inverse ?90738)))) (multiply ?90739 (inverse ?90739)) [90739, 90738, 90740] by Super 290 with 16741 at 2,3
-Id : 20625, {_}: multiply ?106744 (multiply (inverse ?106744) (inverse (inverse (inverse (inverse (multiply ?106742 (inverse ?106742))))))) =?= multiply ?106741 (inverse ?106741) [106741, 106742, 106744] by Super 2903 with 17213 at 3
-Id : 31961, {_}: multiply (multiply ?163343 (inverse ?163343)) (multiply (inverse (inverse (inverse (multiply ?163344 (multiply (inverse ?163344) ?163340))))) (multiply ?163342 (inverse ?163342))) =?= multiply (inverse ?163340) (inverse (inverse (inverse (inverse (multiply ?163341 (inverse ?163341)))))) [163341, 163342, 163340, 163344, 163343] by Super 3671 with 20625 at 2,2,2
-Id : 32420, {_}: inverse ?163340 =<= multiply (inverse ?163340) (inverse (inverse (inverse (inverse (multiply ?163341 (inverse ?163341)))))) [163341, 163340] by Demod 31961 with 3676 at 2
-Id : 32623, {_}: inverse (multiply (inverse ?166463) (multiply (inverse (inverse (inverse (multiply ?166461 (inverse ?166461))))) (inverse (inverse (inverse (inverse (multiply ?166462 (inverse ?166462)))))))) =>= ?166463 [166462, 166461, 166463] by Super 2859 with 32420 at 2,1,1,1,1,2,1,2
-Id : 32947, {_}: inverse (multiply (inverse ?166463) (inverse (inverse (inverse (multiply ?166461 (inverse ?166461)))))) =>= ?166463 [166461, 166463] by Demod 32623 with 32420 at 2,1,2
-Id : 34867, {_}: inverse (multiply (inverse ?172645) (multiply ?172647 (inverse ?172647))) =>= ?172645 [172647, 172645] by Super 17199 with 32947 at 3
-Id : 35297, {_}: multiply (multiply ?2479 (inverse ?2479)) (multiply ?2477 (multiply (inverse ?2477) ?2480)) =>= ?2480 [2480, 2477, 2479] by Demod 326 with 34867 at 2,2
-Id : 35489, {_}: inverse (multiply (inverse ?174505) (multiply ?174506 (inverse ?174506))) =>= ?174505 [174506, 174505] by Super 17199 with 32947 at 3
-Id : 616, {_}: multiply (multiply ?3943 (inverse ?3943)) (inverse (multiply (inverse (multiply ?3944 (multiply ?3945 (inverse ?3945)))) (multiply ?3944 ?3946))) =>= inverse ?3946 [3946, 3945, 3944, 3943] by Super 70 with 290 at 2,1,1,1,2,2
-Id : 619, {_}: multiply (multiply ?3962 (inverse ?3962)) (inverse (multiply (inverse (multiply ?3963 (multiply ?3964 (inverse ?3964)))) (multiply ?3961 (inverse ?3961)))) =>= inverse (inverse ?3963) [3961, 3964, 3963, 3962] by Super 616 with 290 at 2,1,2,2
-Id : 35296, {_}: multiply (multiply ?3962 (inverse ?3962)) (multiply ?3963 (multiply ?3964 (inverse ?3964))) =>= inverse (inverse ?3963) [3964, 3963, 3962] by Demod 619 with 34867 at 2,2
-Id : 35298, {_}: inverse (inverse (inverse (inverse (inverse (multiply ?19734 (multiply (inverse ?19734) ?19735)))))) =>= inverse ?19735 [19735, 19734] by Demod 3676 with 35296 at 2
-Id : 35615, {_}: inverse (multiply (inverse ?175100) (multiply ?175101 (inverse ?175101))) =?= inverse (inverse (inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))))) [175099, 175101, 175100] by Super 35489 with 35298 at 1,1,2
-Id : 35759, {_}: ?175100 =<= inverse (inverse (inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))))) [175099, 175100] by Demod 35615 with 34867 at 2
-Id : 14284, {_}: inverse (inverse (multiply ?75692 (multiply (inverse (inverse (inverse (multiply ?75693 (multiply (inverse ?75693) ?75694))))) ?75694))) =>= ?75692 [75694, 75693, 75692] by Super 4 with 3662 at 2
-Id : 14330, {_}: inverse (inverse (multiply ?75974 (multiply (inverse (inverse (inverse (multiply ?75975 (multiply ?75973 (inverse ?75973)))))) (inverse (inverse ?75975))))) =>= ?75974 [75973, 75975, 75974] by Super 14284 with 290 at 2,1,1,1,1,2,1,1,2
-Id : 36610, {_}: inverse (inverse (multiply ?177975 (multiply (inverse (inverse (inverse (multiply (inverse (inverse (inverse (multiply ?177974 (multiply (inverse ?177974) ?177973))))) (multiply ?177976 (inverse ?177976)))))) (inverse ?177973)))) =>= ?177975 [177976, 177973, 177974, 177975] by Super 14330 with 35759 at 1,2,2,1,1,2
-Id : 36795, {_}: inverse (inverse (multiply ?177975 (multiply (inverse (inverse (inverse (inverse (multiply ?177974 (multiply (inverse ?177974) ?177973)))))) (inverse ?177973)))) =>= ?177975 [177973, 177974, 177975] by Demod 36610 with 34867 at 1,1,1,2,1,1,2
-Id : 37525, {_}: inverse (inverse (multiply ?181200 (multiply ?181201 (inverse ?181201)))) =>= ?181200 [181201, 181200] by Demod 36795 with 35759 at 1,2,1,1,2
-Id : 37547, {_}: inverse (inverse (multiply ?181321 (multiply (inverse (inverse (multiply ?181319 (inverse ?181319)))) (multiply ?181320 (inverse ?181320))))) =>= ?181321 [181320, 181319, 181321] by Super 37525 with 16741 at 2,2,1,1,2
-Id : 36638, {_}: ?178102 =<= inverse (inverse (inverse (inverse (multiply ?178103 (multiply (inverse ?178103) ?178102))))) [178103, 178102] by Demod 35615 with 34867 at 2
-Id : 36754, {_}: multiply (inverse (inverse (multiply ?178614 (inverse ?178614)))) ?178615 =>= inverse (inverse (inverse (inverse ?178615))) [178615, 178614] by Super 36638 with 35297 at 1,1,1,1,3
-Id : 37663, {_}: inverse (inverse (multiply ?181321 (inverse (inverse (inverse (inverse (multiply ?181320 (inverse ?181320)))))))) =>= ?181321 [181320, 181321] by Demod 37547 with 36754 at 2,1,1,2
-Id : 32690, {_}: inverse ?166743 =<= multiply (inverse ?166743) (inverse (inverse (inverse (inverse (multiply ?166744 (inverse ?166744)))))) [166744, 166743] by Demod 31961 with 3676 at 2
-Id : 32829, {_}: inverse (multiply ?167379 (multiply ?167380 (multiply (multiply ?167381 (inverse ?167381)) (inverse (multiply ?167382 (multiply ?167379 ?167380)))))) =?= multiply ?167382 (inverse (inverse (inverse (inverse (multiply ?167383 (inverse ?167383)))))) [167383, 167382, 167381, 167380, 167379] by Super 32690 with 4 at 1,3
-Id : 33031, {_}: ?167382 =<= multiply ?167382 (inverse (inverse (inverse (inverse (multiply ?167383 (inverse ?167383)))))) [167383, 167382] by Demod 32829 with 4 at 2
-Id : 37664, {_}: inverse (inverse ?181321) =>= ?181321 [181321] by Demod 37663 with 33031 at 1,1,2
-Id : 37819, {_}: ?175100 =<= inverse (inverse (multiply ?175099 (multiply (inverse ?175099) ?175100))) [175099, 175100] by Demod 35759 with 37664 at 3
-Id : 37820, {_}: ?175100 =<= multiply ?175099 (multiply (inverse ?175099) ?175100) [175099, 175100] by Demod 37819 with 37664 at 3
-Id : 37837, {_}: multiply (multiply ?2479 (inverse ?2479)) ?2480 =>= ?2480 [2480, 2479] by Demod 35297 with 37820 at 2,2
-Id : 37843, {_}: inverse (multiply ?2 (multiply ?3 (inverse (multiply ?5 (multiply ?2 ?3))))) =>= ?5 [5, 3, 2] by Demod 4 with 37837 at 2,2,1,2
-Id : 37841, {_}: inverse (multiply ?14 (multiply (inverse (multiply ?13 (multiply ?16 ?14))) (multiply (multiply ?15 (inverse ?15)) ?13))) =>= ?16 [15, 16, 13, 14] by Demod 6 with 37837 at 1,2,1,2
-Id : 37842, {_}: inverse (multiply ?14 (multiply (inverse (multiply ?13 (multiply ?16 ?14))) ?13)) =>= ?16 [16, 13, 14] by Demod 37841 with 37837 at 2,2,1,2
-Id : 13762, {_}: inverse (multiply (inverse ?72514) (multiply ?72515 (multiply (multiply ?72516 (inverse ?72516)) (inverse (multiply ?72517 (multiply (inverse ?72517) ?72515)))))) =?= multiply (inverse (inverse (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72517, 72516, 72515, 72514] by Super 790 with 3662 at 1,1,2
-Id : 14092, {_}: ?72514 =<= multiply (inverse (inverse (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72514] by Demod 13762 with 790 at 2
-Id : 37791, {_}: ?72514 =<= multiply (inverse (multiply ?72511 (multiply (inverse ?72511) ?72512))) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72511, 72514] by Demod 14092 with 37664 at 1,3
-Id : 37888, {_}: ?72514 =<= multiply (inverse ?72512) (multiply ?72512 (multiply (multiply ?72513 (inverse ?72513)) ?72514)) [72513, 72512, 72514] by Demod 37791 with 37820 at 1,1,3
-Id : 37889, {_}: ?72514 =<= multiply (inverse ?72512) (multiply ?72512 ?72514) [72512, 72514] by Demod 37888 with 37837 at 2,2,3
-Id : 37945, {_}: multiply (multiply (inverse ?181731) ?181731) ?181732 =>= ?181732 [181732, 181731] by Super 37837 with 37664 at 2,1,2
-Id : 37993, {_}: inverse (multiply (multiply (inverse ?181852) ?181852) (multiply ?181853 (inverse (multiply ?181854 ?181853)))) =>= ?181854 [181854, 181853, 181852] by Super 37843 with 37945 at 2,1,2,2,1,2
-Id : 38039, {_}: inverse (multiply ?181853 (inverse (multiply ?181854 ?181853))) =>= ?181854 [181854, 181853] by Demod 37993 with 37945 at 1,2
-Id : 38275, {_}: inverse ?182456 =<= multiply ?182455 (inverse (multiply ?182456 ?182455)) [182455, 182456] by Super 37664 with 38039 at 1,2
-Id : 38457, {_}: inverse (multiply ?182870 ?182871) =<= multiply (inverse ?182871) (inverse ?182870) [182871, 182870] by Super 37889 with 38275 at 2,3
-Id : 38459, {_}: inverse (multiply (inverse ?182877) ?182878) =>= multiply (inverse ?182878) ?182877 [182878, 182877] by Super 38457 with 37664 at 2,3
-Id : 38608, {_}: multiply (inverse (multiply (inverse (multiply ?183123 (multiply ?183124 (inverse ?183122)))) ?183123)) ?183122 =>= ?183124 [183122, 183124, 183123] by Super 37842 with 38459 at 2
-Id : 38646, {_}: multiply (multiply (inverse ?183123) (multiply ?183123 (multiply ?183124 (inverse ?183122)))) ?183122 =>= ?183124 [183122, 183124, 183123] by Demod 38608 with 38459 at 1,2
-Id : 38647, {_}: multiply (multiply ?183124 (inverse ?183122)) ?183122 =>= ?183124 [183122, 183124] by Demod 38646 with 37889 at 1,2
-Id : 39562, {_}: inverse (multiply ?184856 (multiply ?184857 (inverse ?184858))) =>= multiply ?184858 (inverse (multiply ?184856 ?184857)) [184858, 184857, 184856] by Super 37843 with 38647 at 1,2,2,1,2
-Id : 39573, {_}: inverse (multiply ?184910 (inverse ?184909)) =<= multiply (multiply ?184909 ?184911) (inverse (multiply ?184910 ?184911)) [184911, 184909, 184910] by Super 39562 with 38275 at 2,1,2
-Id : 38360, {_}: inverse (multiply ?182630 (inverse ?182631)) =>= multiply ?182631 (inverse ?182630) [182631, 182630] by Super 37820 with 38275 at 2,3
-Id : 40719, {_}: multiply ?186598 (inverse ?186599) =<= multiply (multiply ?186598 ?186600) (inverse (multiply ?186599 ?186600)) [186600, 186599, 186598] by Demod 39573 with 38360 at 2
-Id : 37844, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply (multiply (multiply ?35 (inverse ?35)) ?33) (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 35, 31, 34, 33] by Demod 9 with 37837 at 1,1,2
-Id : 37845, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply ?33 (multiply (multiply ?36 (inverse ?36)) ?34))) =>= ?31 [36, 31, 34, 33] by Demod 37844 with 37837 at 1,2,1,2
-Id : 37846, {_}: inverse (multiply (inverse (multiply ?33 (multiply ?34 ?31))) (multiply ?33 ?34)) =>= ?31 [31, 34, 33] by Demod 37845 with 37837 at 2,2,1,2
-Id : 38597, {_}: multiply (inverse (multiply ?33 ?34)) (multiply ?33 (multiply ?34 ?31)) =>= ?31 [31, 34, 33] by Demod 37846 with 38459 at 2
-Id : 40727, {_}: multiply ?186633 (inverse (inverse (multiply ?186630 ?186631))) =<= multiply (multiply ?186633 (multiply ?186630 (multiply ?186631 ?186632))) (inverse ?186632) [186632, 186631, 186630, 186633] by Super 40719 with 38597 at 1,2,3
-Id : 40827, {_}: multiply ?186633 (multiply ?186630 ?186631) =<= multiply (multiply ?186633 (multiply ?186630 (multiply ?186631 ?186632))) (inverse ?186632) [186632, 186631, 186630, 186633] by Demod 40727 with 37664 at 2,2
-Id : 38369, {_}: inverse ?182667 =<= multiply ?182668 (inverse (multiply ?182667 ?182668)) [182668, 182667] by Super 37664 with 38039 at 1,2
-Id : 38383, {_}: inverse ?182710 =<= multiply (inverse (multiply ?182709 ?182710)) (inverse (inverse ?182709)) [182709, 182710] by Super 38369 with 38275 at 1,2,3
-Id : 38416, {_}: inverse ?182710 =<= multiply (inverse (multiply ?182709 ?182710)) ?182709 [182709, 182710] by Demod 38383 with 37664 at 2,3
-Id : 38850, {_}: inverse (multiply ?183591 (multiply ?183592 (inverse ?183590))) =>= multiply ?183590 (inverse (multiply ?183591 ?183592)) [183590, 183592, 183591] by Super 37843 with 38647 at 1,2,2,1,2
-Id : 39557, {_}: inverse (multiply ?184829 (inverse ?184830)) =<= multiply (multiply ?184830 (inverse (multiply ?184828 ?184829))) ?184828 [184828, 184830, 184829] by Super 38416 with 38850 at 1,3
-Id : 40495, {_}: multiply ?186270 (inverse ?186271) =<= multiply (multiply ?186270 (inverse (multiply ?186272 ?186271))) ?186272 [186272, 186271, 186270] by Demod 39557 with 38360 at 2
-Id : 38758, {_}: inverse ?183471 =<= multiply (inverse (multiply ?183472 ?183471)) ?183472 [183472, 183471] by Demod 38383 with 37664 at 2,3
-Id : 38773, {_}: inverse (multiply ?183521 (inverse (multiply ?183522 (multiply ?183523 ?183521)))) =>= multiply ?183522 ?183523 [183523, 183522, 183521] by Super 38758 with 37843 at 1,3
-Id : 38833, {_}: multiply (multiply ?183522 (multiply ?183523 ?183521)) (inverse ?183521) =>= multiply ?183522 ?183523 [183521, 183523, 183522] by Demod 38773 with 38360 at 2
-Id : 40530, {_}: multiply (multiply ?186419 (multiply ?186420 (multiply ?186422 ?186421))) (inverse ?186421) =>= multiply (multiply ?186419 ?186420) ?186422 [186421, 186422, 186420, 186419] by Super 40495 with 38833 at 1,3
-Id : 56629, {_}: multiply ?186633 (multiply ?186630 ?186631) =?= multiply (multiply ?186633 ?186630) ?186631 [186631, 186630, 186633] by Demod 40827 with 40530 at 3
-Id : 57301, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 56629 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP444-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- divide is 93
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 0.102216s
-% SZS status Unsatisfiable for GRP452-1.p
-% SZS output start CNFRefutation for GRP452-1.p
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
-Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 265, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 269, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 265 with 33 at 2,1,1,3
-Id : 285, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 269 with 33 at 2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 270, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 265 with 40 at 2,1,1,3
-Id : 286, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 270 with 8 at 1,1,2
-Id : 306, {_}: divide (divide (inverse (inverse ?778)) ?779) (inverse ?779) =>= ?778 [779, 778] by Super 63 with 286 at 1,2
-Id : 319, {_}: multiply (divide (inverse (inverse ?778)) ?779) ?779 =>= ?778 [779, 778] by Demod 306 with 33 at 2
-Id : 743, {_}: ?1513 =<= inverse (inverse (inverse (inverse ?1513))) [1513] by Super 36 with 319 at 2
-Id : 138, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 1751, {_}: multiply ?3407 (divide (inverse ?3408) ?3409) =<= inverse (inverse (divide (inverse (divide ?3408 ?3407)) ?3409)) [3409, 3408, 3407] by Super 743 with 138 at 1,1,3
-Id : 1830, {_}: multiply ?3532 (divide (inverse ?3532) ?3533) =>= inverse (inverse (inverse ?3533)) [3533, 3532] by Super 1751 with 40 at 1,1,3
-Id : 682, {_}: ?1380 =<= inverse (inverse (inverse (inverse ?1380))) [1380] by Super 36 with 319 at 2
-Id : 735, {_}: multiply ?1490 (inverse (inverse (inverse ?1489))) =>= divide ?1490 ?1489 [1489, 1490] by Super 33 with 682 at 2,3
-Id : 742, {_}: multiply (divide ?1510 ?1511) ?1511 =>= inverse (inverse ?1510) [1511, 1510] by Super 319 with 682 at 1,1,2
-Id : 868, {_}: inverse (inverse ?1672) =<= divide (divide ?1672 (inverse (inverse (inverse ?1673)))) ?1673 [1673, 1672] by Super 735 with 742 at 2
-Id : 1203, {_}: inverse (inverse ?2233) =<= divide (multiply ?2233 (inverse (inverse ?2234))) ?2234 [2234, 2233] by Demod 868 with 33 at 1,3
-Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
-Id : 1217, {_}: inverse (inverse (inverse (inverse (divide ?2285 ?2285)))) =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Super 1203 with 55 at 1,3
-Id : 1250, {_}: divide ?2285 ?2285 =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Demod 1217 with 682 at 2
-Id : 1251, {_}: divide ?2285 ?2285 =?= divide ?2286 ?2286 [2286, 2285] by Demod 1250 with 682 at 1,3
-Id : 1840, {_}: multiply ?3573 (divide ?3572 ?3572) =?= inverse (inverse (inverse (inverse ?3573))) [3572, 3573] by Super 1830 with 1251 at 2,2
-Id : 1879, {_}: multiply ?3573 (divide ?3572 ?3572) =>= ?3573 [3572, 3573] by Demod 1840 with 682 at 3
-Id : 1919, {_}: multiply (inverse (divide ?3678 ?3679)) (divide ?3677 ?3677) =>= inverse (inverse (multiply ?3679 (inverse ?3678))) [3677, 3679, 3678] by Super 285 with 1879 at 2,1,1,3
-Id : 1946, {_}: inverse (divide ?3678 ?3679) =<= inverse (inverse (multiply ?3679 (inverse ?3678))) [3679, 3678] by Demod 1919 with 1879 at 2
-Id : 1947, {_}: inverse (divide ?3678 ?3679) =<= divide (inverse (inverse ?3679)) ?3678 [3679, 3678] by Demod 1946 with 286 at 3
-Id : 1966, {_}: inverse (divide ?126 (multiply ?128 ?126)) =>= ?128 [128, 126] by Demod 63 with 1947 at 2
-Id : 748, {_}: multiply ?1528 (inverse ?1529) =<= inverse (inverse (divide (inverse (inverse ?1528)) ?1529)) [1529, 1528] by Super 743 with 286 at 1,1,3
-Id : 1970, {_}: multiply ?1528 (inverse ?1529) =<= inverse (inverse (inverse (divide ?1529 ?1528))) [1529, 1528] by Demod 748 with 1947 at 1,1,3
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 1967, {_}: inverse ?121 =<= inverse (divide ?121 (divide ?120 ?120)) [120, 121] by Demod 50 with 1947 at 3
-Id : 1903, {_}: divide ?3630 (divide ?3629 ?3629) =>= inverse (inverse ?3630) [3629, 3630] by Super 742 with 1879 at 2
-Id : 2257, {_}: inverse ?121 =<= inverse (inverse (inverse ?121)) [121] by Demod 1967 with 1903 at 1,3
-Id : 2261, {_}: multiply ?1528 (inverse ?1529) =<= inverse (divide ?1529 ?1528) [1529, 1528] by Demod 1970 with 2257 at 3
-Id : 2271, {_}: multiply (multiply ?128 ?126) (inverse ?126) =>= ?128 [126, 128] by Demod 1966 with 2261 at 2
-Id : 869, {_}: multiply (divide ?1675 ?1676) ?1676 =>= inverse (inverse ?1675) [1676, 1675] by Super 319 with 682 at 1,1,2
-Id : 873, {_}: multiply (multiply ?1689 ?1688) (inverse ?1688) =>= inverse (inverse ?1689) [1688, 1689] by Super 869 with 33 at 1,2
-Id : 2276, {_}: inverse (inverse ?128) =>= ?128 [128] by Demod 2271 with 873 at 2
-Id : 2434, {_}: a2 === a2 [] by Demod 85 with 2276 at 2
-Id : 85, {_}: inverse (inverse a2) =>= a2 [] by Demod 2 with 47 at 2
-Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP452-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 91
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 0.110270s
-% SZS status Unsatisfiable for GRP453-1.p
-% SZS output start CNFRefutation for GRP453-1.p
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 264, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 268, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 264 with 33 at 2,1,1,3
-Id : 284, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 268 with 33 at 2
-Id : 269, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 264 with 40 at 2,1,1,3
-Id : 285, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 269 with 8 at 1,1,2
-Id : 307, {_}: divide (inverse (inverse ?786)) ?787 =<= inverse (inverse (multiply ?786 (inverse ?787))) [787, 786] by Demod 269 with 8 at 1,1,2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 310, {_}: divide (inverse (inverse (divide ?798 ?798))) ?799 =>= inverse (inverse (inverse (inverse (inverse ?799)))) [799, 798] by Super 307 with 36 at 1,1,3
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 325, {_}: inverse ?799 =<= inverse (inverse (inverse (inverse (inverse ?799)))) [799] by Demod 310 with 50 at 2
-Id : 332, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= divide ?837 (inverse ?836) [836, 837] by Super 33 with 325 at 2,3
-Id : 354, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= multiply ?837 ?836 [836, 837] by Demod 332 with 33 at 3
-Id : 364, {_}: divide (inverse (inverse ?880)) (inverse (inverse (inverse ?881))) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Super 285 with 354 at 1,1,3
-Id : 423, {_}: multiply (inverse (inverse ?880)) (inverse (inverse ?881)) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Demod 364 with 33 at 2
-Id : 448, {_}: divide (inverse (inverse (inverse (inverse ?1012)))) (inverse ?1013) =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Super 285 with 423 at 1,1,3
-Id : 470, {_}: multiply (inverse (inverse (inverse (inverse ?1012)))) ?1013 =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Demod 448 with 33 at 2
-Id : 499, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1108 ?1109))))))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Super 63 with 470 at 1,1,1,2
-Id : 519, {_}: divide (inverse (inverse (multiply ?1108 ?1109))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Demod 499 with 325 at 1,2
-Id : 571, {_}: ?1204 =<= inverse (inverse (inverse (inverse ?1204))) [1204] by Demod 519 with 63 at 2
-Id : 137, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 1535, {_}: multiply ?2972 (divide (inverse ?2973) ?2974) =<= inverse (inverse (divide (inverse (divide ?2973 ?2972)) ?2974)) [2974, 2973, 2972] by Super 571 with 137 at 1,1,3
-Id : 1610, {_}: multiply ?3089 (divide (inverse ?3089) ?3090) =>= inverse (inverse (inverse ?3090)) [3090, 3089] by Super 1535 with 40 at 1,1,3
-Id : 520, {_}: ?1108 =<= inverse (inverse (inverse (inverse ?1108))) [1108] by Demod 519 with 63 at 2
-Id : 565, {_}: multiply ?1187 (inverse (inverse (inverse ?1186))) =>= divide ?1187 ?1186 [1186, 1187] by Super 33 with 520 at 2,3
-Id : 590, {_}: divide (inverse (inverse ?1228)) (inverse (inverse ?1229)) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Super 285 with 565 at 1,1,3
-Id : 652, {_}: multiply (inverse (inverse ?1228)) (inverse ?1229) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Demod 590 with 33 at 2
-Id : 676, {_}: divide (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) (inverse ?1337) =>= inverse (inverse ?1336) [1337, 1336] by Super 63 with 652 at 1,1,1,2
-Id : 716, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 676 with 33 at 2
-Id : 717, {_}: multiply (divide ?1336 ?1337) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 716 with 520 at 1,2
-Id : 729, {_}: inverse (inverse ?1423) =<= divide (divide ?1423 (inverse (inverse (inverse ?1424)))) ?1424 [1424, 1423] by Super 565 with 717 at 2
-Id : 1120, {_}: inverse (inverse ?2062) =<= divide (multiply ?2062 (inverse (inverse ?2063))) ?2063 [2063, 2062] by Demod 729 with 33 at 1,3
-Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
-Id : 1134, {_}: inverse (inverse (inverse (inverse (divide ?2114 ?2114)))) =?= divide (inverse (inverse (inverse (inverse ?2115)))) ?2115 [2115, 2114] by Super 1120 with 55 at 1,3
-Id : 1167, {_}: divide ?2114 ?2114 =?= divide (inverse (inverse (inverse (inverse ?2115)))) ?2115 [2115, 2114] by Demod 1134 with 520 at 2
-Id : 1168, {_}: divide ?2114 ?2114 =?= divide ?2115 ?2115 [2115, 2114] by Demod 1167 with 520 at 1,3
-Id : 1620, {_}: multiply ?3130 (divide ?3129 ?3129) =>= inverse (inverse (inverse (inverse ?3130))) [3129, 3130] by Super 1610 with 1168 at 2,2
-Id : 1658, {_}: multiply ?3130 (divide ?3129 ?3129) =>= ?3130 [3129, 3130] by Demod 1620 with 520 at 3
-Id : 1679, {_}: multiply (inverse (divide ?3178 ?3179)) (divide ?3177 ?3177) =>= inverse (inverse (multiply ?3179 (inverse ?3178))) [3177, 3179, 3178] by Super 284 with 1658 at 2,1,1,3
-Id : 1729, {_}: inverse (divide ?3178 ?3179) =<= inverse (inverse (multiply ?3179 (inverse ?3178))) [3179, 3178] by Demod 1679 with 1658 at 2
-Id : 1730, {_}: inverse (divide ?3178 ?3179) =<= divide (inverse (inverse ?3179)) ?3178 [3179, 3178] by Demod 1729 with 285 at 3
-Id : 1760, {_}: multiply (inverse (inverse ?3336)) ?3337 =>= inverse (divide (inverse ?3337) ?3336) [3337, 3336] by Super 33 with 1730 at 3
-Id : 1861, {_}: multiply (inverse (divide (inverse ?3480) ?3482)) ?3481 =<= inverse (inverse (multiply ?3482 (inverse (divide (inverse ?3481) ?3480)))) [3481, 3482, 3480] by Super 284 with 1760 at 2,1,1,3
-Id : 1743, {_}: inverse (divide ?689 ?688) =<= inverse (inverse (multiply ?688 (inverse ?689))) [688, 689] by Demod 285 with 1730 at 2
-Id : 1928, {_}: multiply (inverse (divide (inverse ?3480) ?3482)) ?3481 =>= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3482, 3480] by Demod 1861 with 1743 at 3
-Id : 1740, {_}: inverse (divide ?126 (multiply ?128 ?126)) =>= ?128 [128, 126] by Demod 63 with 1730 at 2
-Id : 1855, {_}: inverse (divide ?3461 (inverse (divide (inverse ?3461) ?3460))) =>= inverse (inverse ?3460) [3460, 3461] by Super 1740 with 1760 at 2,1,2
-Id : 1942, {_}: inverse (multiply ?3461 (divide (inverse ?3461) ?3460)) =>= inverse (inverse ?3460) [3460, 3461] by Demod 1855 with 33 at 1,2
-Id : 1552, {_}: multiply ?3041 (divide (inverse ?3041) ?3042) =>= inverse (inverse (inverse ?3042)) [3042, 3041] by Super 1535 with 40 at 1,1,3
-Id : 1943, {_}: inverse (inverse (inverse (inverse ?3460))) =>= inverse (inverse ?3460) [3460] by Demod 1942 with 1552 at 1,2
-Id : 1944, {_}: ?3460 =<= inverse (inverse ?3460) [3460] by Demod 1943 with 520 at 2
-Id : 1988, {_}: multiply ?1187 (inverse ?1186) =>= divide ?1187 ?1186 [1186, 1187] by Demod 565 with 1944 at 2,2
-Id : 1992, {_}: inverse (divide ?689 ?688) =<= multiply ?688 (inverse ?689) [688, 689] by Demod 1743 with 1944 at 3
-Id : 1998, {_}: inverse (divide ?1186 ?1187) =>= divide ?1187 ?1186 [1187, 1186] by Demod 1988 with 1992 at 2
-Id : 2689, {_}: multiply (divide ?3482 (inverse ?3480)) ?3481 =<= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3480, 3482] by Demod 1928 with 1998 at 1,2
-Id : 2690, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= inverse (divide (divide (inverse ?3481) ?3480) ?3482) [3481, 3480, 3482] by Demod 2689 with 33 at 1,2
-Id : 2691, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= divide ?3482 (divide (inverse ?3481) ?3480) [3481, 3480, 3482] by Demod 2690 with 1998 at 3
-Id : 2002, {_}: divide (multiply ?128 ?126) ?126 =>= ?128 [126, 128] by Demod 1740 with 1998 at 2
-Id : 1619, {_}: multiply (inverse (multiply ?3126 ?3127)) ?3126 =>= inverse (inverse (inverse ?3127)) [3127, 3126] by Super 1610 with 63 at 2,2
-Id : 2085, {_}: multiply (inverse (multiply ?3126 ?3127)) ?3126 =>= inverse ?3127 [3127, 3126] by Demod 1619 with 1944 at 3
-Id : 2092, {_}: divide (inverse ?3663) ?3662 =>= inverse (multiply ?3662 ?3663) [3662, 3663] by Super 2002 with 2085 at 1,2
-Id : 2692, {_}: multiply (multiply ?3482 ?3480) ?3481 =<= divide ?3482 (inverse (multiply ?3480 ?3481)) [3481, 3480, 3482] by Demod 2691 with 2092 at 2,3
-Id : 2693, {_}: multiply (multiply ?3482 ?3480) ?3481 =?= multiply ?3482 (multiply ?3480 ?3481) [3481, 3480, 3482] by Demod 2692 with 33 at 3
-Id : 2797, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 2693 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP453-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 128.157849s
-% SZS status Unsatisfiable for GRP471-1.p
-% SZS output start CNFRefutation for GRP471-1.p
-Id : 7, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 4, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 466, {_}: divide (inverse (divide (inverse ?2074) (divide ?2075 (divide ?2076 ?2077)))) (multiply (divide ?2077 ?2076) ?2074) =>= ?2075 [2077, 2076, 2075, 2074] by Super 4 with 6 at 2,2
-Id : 2222, {_}: divide (inverse ?10322) (multiply (divide ?10323 ?10324) (divide (divide ?10324 ?10323) (divide ?10322 (divide ?10325 ?10326)))) =>= divide ?10326 ?10325 [10326, 10325, 10324, 10323, 10322] by Super 466 with 4 at 1,1,2
-Id : 498, {_}: divide (inverse ?2307) (multiply (divide ?2311 ?2310) (divide (divide ?2310 ?2311) (divide ?2307 (divide ?2308 ?2309)))) =>= divide ?2309 ?2308 [2309, 2308, 2310, 2311, 2307] by Super 466 with 4 at 1,1,2
-Id : 2240, {_}: divide (inverse ?10483) (multiply (divide ?10484 ?10485) (divide (divide ?10485 ?10484) (divide ?10483 (divide ?10482 ?10481)))) =?= divide (multiply (divide ?10479 ?10480) (divide (divide ?10480 ?10479) (divide ?10478 (divide ?10481 ?10482)))) (inverse ?10478) [10478, 10480, 10479, 10481, 10482, 10485, 10484, 10483] by Super 2222 with 498 at 2,2,2,2,2
-Id : 2367, {_}: divide ?10481 ?10482 =<= divide (multiply (divide ?10479 ?10480) (divide (divide ?10480 ?10479) (divide ?10478 (divide ?10481 ?10482)))) (inverse ?10478) [10478, 10480, 10479, 10482, 10481] by Demod 2240 with 498 at 2
-Id : 2430, {_}: divide ?11142 ?11143 =<= multiply (multiply (divide ?11144 ?11145) (divide (divide ?11145 ?11144) (divide ?11146 (divide ?11142 ?11143)))) ?11146 [11146, 11145, 11144, 11143, 11142] by Demod 2367 with 6 at 3
-Id : 2431, {_}: divide (inverse (divide ?11148 (divide ?11149 (divide ?11150 ?11151)))) (divide (divide ?11151 ?11150) ?11148) =?= multiply (multiply (divide ?11152 ?11153) (divide (divide ?11153 ?11152) (divide ?11154 ?11149))) ?11154 [11154, 11153, 11152, 11151, 11150, 11149, 11148] by Super 2430 with 4 at 2,2,2,1,3
-Id : 2616, {_}: ?11858 =<= multiply (multiply (divide ?11859 ?11860) (divide (divide ?11860 ?11859) (divide ?11861 ?11858))) ?11861 [11861, 11860, 11859, 11858] by Demod 2431 with 4 at 2
-Id : 2673, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (divide (divide (inverse ?12296) ?12298) (divide ?12299 ?12297))) ?12299 [12299, 12296, 12298, 12297] by Super 2616 with 6 at 1,1,3
-Id : 398, {_}: divide (inverse (divide ?1784 (divide ?1785 (divide (inverse ?1786) ?1787)))) (divide (multiply ?1787 ?1786) ?1784) =>= ?1785 [1787, 1786, 1785, 1784] by Super 4 with 6 at 1,2,2
-Id : 1221, {_}: divide (inverse (divide ?5281 (divide ?5282 (multiply (inverse ?5283) ?5284)))) (divide (multiply (inverse ?5284) ?5283) ?5281) =>= ?5282 [5284, 5283, 5282, 5281] by Super 398 with 6 at 2,2,1,1,2
-Id : 15, {_}: divide (inverse (divide ?58 (divide ?59 (multiply ?56 ?57)))) (divide (divide (inverse ?57) ?56) ?58) =>= ?59 [57, 56, 59, 58] by Super 4 with 6 at 2,2,1,1,2
-Id : 1238, {_}: divide (inverse ?5406) (divide (multiply (inverse ?5410) ?5409) (inverse (divide (multiply (inverse ?5409) ?5410) (divide ?5406 (multiply ?5407 ?5408))))) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5409, 5410, 5406] by Super 1221 with 15 at 1,1,2
-Id : 1282, {_}: divide (inverse ?5406) (multiply (multiply (inverse ?5410) ?5409) (divide (multiply (inverse ?5409) ?5410) (divide ?5406 (multiply ?5407 ?5408)))) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5409, 5410, 5406] by Demod 1238 with 6 at 2,2
-Id : 2872, {_}: ?12927 =<= multiply (multiply (divide (inverse ?12928) ?12929) (divide (multiply ?12929 ?12928) (divide ?12930 ?12927))) ?12930 [12930, 12929, 12928, 12927] by Super 2616 with 6 at 1,2,1,3
-Id : 3248, {_}: ?15081 =<= multiply (multiply (multiply (inverse ?15082) ?15083) (divide (multiply (inverse ?15083) ?15082) (divide ?15084 ?15081))) ?15084 [15084, 15083, 15082, 15081] by Super 2872 with 6 at 1,1,3
-Id : 10, {_}: divide (inverse (divide ?32 ?29)) (divide (divide ?33 (divide ?31 ?30)) ?32) =>= inverse (divide ?33 (divide ?29 (divide ?30 ?31))) [30, 31, 33, 29, 32] by Super 7 with 4 at 2,1,1,2
-Id : 22, {_}: inverse (divide ?98 (divide (divide ?101 (divide (divide ?99 ?100) ?98)) (divide ?100 ?99))) =>= ?101 [100, 99, 101, 98] by Super 4 with 10 at 2
-Id : 313, {_}: multiply ?1410 (divide ?1406 (divide (divide ?1407 (divide (divide ?1408 ?1409) ?1406)) (divide ?1409 ?1408))) =>= divide ?1410 ?1407 [1409, 1408, 1407, 1406, 1410] by Super 6 with 22 at 2,3
-Id : 13731, {_}: divide ?59402 ?59403 =<= multiply (divide (multiply (inverse ?59404) ?59405) ?59406) (divide ?59406 (divide (divide ?59403 ?59402) (multiply (inverse ?59405) ?59404))) [59406, 59405, 59404, 59403, 59402] by Super 3248 with 313 at 1,3
-Id : 13819, {_}: divide ?60191 ?60192 =<= multiply (multiply (multiply (inverse ?60193) ?60194) ?60190) (divide (inverse ?60190) (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193))) [60190, 60194, 60193, 60192, 60191] by Super 13731 with 6 at 1,3
-Id : 318, {_}: inverse (divide ?1446 (divide (divide ?1447 (divide (divide ?1448 ?1449) ?1446)) (divide ?1449 ?1448))) =>= ?1447 [1449, 1448, 1447, 1446] by Super 4 with 10 at 2
-Id : 1006, {_}: inverse (inverse (divide ?4256 (divide ?4257 (divide (inverse (divide (divide ?4258 ?4259) ?4257)) (divide ?4259 ?4258))))) =>= ?4256 [4259, 4258, 4257, 4256] by Super 318 with 10 at 1,2
-Id : 10788, {_}: inverse (inverse (inverse (divide ?46213 (divide ?46214 (divide ?46215 ?46216))))) =<= inverse (divide (divide (inverse (divide (divide ?46217 ?46218) (divide ?46213 (divide ?46216 ?46215)))) (divide ?46218 ?46217)) ?46214) [46218, 46217, 46216, 46215, 46214, 46213] by Super 1006 with 10 at 1,1,2
-Id : 31179, {_}: inverse (inverse (inverse (divide (divide ?147814 (divide (divide ?147815 ?147816) (divide ?147817 ?147818))) (divide ?147819 (divide ?147815 ?147816))))) =>= inverse (divide (divide ?147814 (divide ?147818 ?147817)) ?147819) [147819, 147818, 147817, 147816, 147815, 147814] by Super 10788 with 22 at 1,1,1,3
-Id : 23, {_}: divide (inverse (divide ?103 ?104)) (divide (divide ?105 (divide ?106 ?107)) ?103) =>= inverse (divide ?105 (divide ?104 (divide ?107 ?106))) [107, 106, 105, 104, 103] by Super 7 with 4 at 2,1,1,2
-Id : 32, {_}: divide (inverse (multiply ?171 ?170)) (divide (divide ?172 (divide ?173 ?174)) ?171) =>= inverse (divide ?172 (divide (inverse ?170) (divide ?174 ?173))) [174, 173, 172, 170, 171] by Super 23 with 6 at 1,1,2
-Id : 346, {_}: inverse (inverse (divide ?1643 (divide (inverse ?1642) (divide (inverse (multiply (divide ?1645 ?1644) ?1642)) (divide ?1644 ?1645))))) =>= ?1643 [1644, 1645, 1642, 1643] by Super 318 with 32 at 1,2
-Id : 31311, {_}: inverse (divide ?149137 (divide (divide (inverse (multiply (divide ?149135 ?149136) ?149134)) (divide ?149136 ?149135)) (divide ?149138 ?149139))) =>= inverse (divide (divide ?149137 (divide ?149139 ?149138)) (inverse ?149134)) [149139, 149138, 149134, 149136, 149135, 149137] by Super 31179 with 346 at 1,2
-Id : 57522, {_}: inverse (divide ?312686 (divide (divide (inverse (multiply (divide ?312687 ?312688) ?312689)) (divide ?312688 ?312687)) (divide ?312690 ?312691))) =>= inverse (multiply (divide ?312686 (divide ?312691 ?312690)) ?312689) [312691, 312690, 312689, 312688, 312687, 312686] by Demod 31311 with 6 at 1,3
-Id : 3434, {_}: divide ?16101 ?16102 =<= multiply (divide (divide ?16103 ?16104) ?16105) (divide ?16105 (divide (divide ?16102 ?16101) (divide ?16104 ?16103))) [16105, 16104, 16103, 16102, 16101] by Super 2430 with 313 at 1,3
-Id : 3646, {_}: divide (inverse ?16919) ?16920 =<= multiply (divide (divide ?16921 ?16922) ?16923) (divide ?16923 (divide (multiply ?16920 ?16919) (divide ?16922 ?16921))) [16923, 16922, 16921, 16920, 16919] by Super 3434 with 6 at 1,2,2,3
-Id : 3697, {_}: divide (inverse ?17353) ?17354 =<= multiply (divide (multiply ?17355 ?17352) ?17356) (divide ?17356 (divide (multiply ?17354 ?17353) (divide (inverse ?17352) ?17355))) [17356, 17352, 17355, 17354, 17353] by Super 3646 with 6 at 1,1,3
-Id : 154000, {_}: inverse (divide ?867821 (divide (divide (inverse (divide (inverse ?867822) ?867823)) (divide ?867824 (multiply ?867825 ?867826))) (divide ?867827 ?867828))) =>= inverse (multiply (divide ?867821 (divide ?867828 ?867827)) (divide ?867824 (divide (multiply ?867823 ?867822) (divide (inverse ?867826) ?867825)))) [867828, 867827, 867826, 867825, 867824, 867823, 867822, 867821] by Super 57522 with 3697 at 1,1,1,2,1,2
-Id : 412, {_}: divide (inverse ?1885) (divide (multiply ?1889 ?1888) (inverse (divide (divide (inverse ?1888) ?1889) (divide ?1885 (divide ?1886 ?1887))))) =>= divide ?1887 ?1886 [1887, 1886, 1888, 1889, 1885] by Super 398 with 4 at 1,1,2
-Id : 440, {_}: divide (inverse ?1885) (multiply (multiply ?1889 ?1888) (divide (divide (inverse ?1888) ?1889) (divide ?1885 (divide ?1886 ?1887)))) =>= divide ?1887 ?1886 [1887, 1886, 1888, 1889, 1885] by Demod 412 with 6 at 2,2
-Id : 154130, {_}: inverse (divide ?869515 (divide (divide (inverse (divide (inverse ?869516) ?869517)) (divide ?869514 ?869513)) (divide ?869518 ?869519))) =<= inverse (multiply (divide ?869515 (divide ?869519 ?869518)) (divide (inverse ?869510) (divide (multiply ?869517 ?869516) (divide (inverse (divide (divide (inverse ?869512) ?869511) (divide ?869510 (divide ?869513 ?869514)))) (multiply ?869511 ?869512))))) [869511, 869512, 869510, 869519, 869518, 869513, 869514, 869517, 869516, 869515] by Super 154000 with 440 at 2,1,2,1,2
-Id : 31180, {_}: inverse (inverse (inverse (divide (divide ?147825 (divide (divide (inverse (divide ?147821 (divide ?147822 (divide ?147823 ?147824)))) (divide (divide ?147824 ?147823) ?147821)) (divide ?147826 ?147827))) (divide ?147828 ?147822)))) =>= inverse (divide (divide ?147825 (divide ?147827 ?147826)) ?147828) [147828, 147827, 147826, 147824, 147823, 147822, 147821, 147825] by Super 31179 with 4 at 2,2,1,1,1,2
-Id : 31662, {_}: inverse (inverse (inverse (divide (divide ?150376 (divide ?150377 (divide ?150378 ?150379))) (divide ?150380 ?150377)))) =>= inverse (divide (divide ?150376 (divide ?150379 ?150378)) ?150380) [150380, 150379, 150378, 150377, 150376] by Demod 31180 with 4 at 1,2,1,1,1,1,2
-Id : 399, {_}: divide (inverse (divide (inverse ?1789) (divide ?1790 (divide (inverse ?1791) ?1792)))) (multiply (multiply ?1792 ?1791) ?1789) =>= ?1790 [1792, 1791, 1790, 1789] by Super 398 with 6 at 2,2
-Id : 31677, {_}: inverse (inverse (inverse (divide (divide ?150512 (divide (multiply (multiply ?150511 ?150510) ?150508) (divide ?150513 ?150514))) ?150509))) =<= inverse (divide (divide ?150512 (divide ?150514 ?150513)) (inverse (divide (inverse ?150508) (divide ?150509 (divide (inverse ?150510) ?150511))))) [150509, 150514, 150513, 150508, 150510, 150511, 150512] by Super 31662 with 399 at 2,1,1,1,2
-Id : 31809, {_}: inverse (inverse (inverse (divide (divide ?150512 (divide (multiply (multiply ?150511 ?150510) ?150508) (divide ?150513 ?150514))) ?150509))) =<= inverse (multiply (divide ?150512 (divide ?150514 ?150513)) (divide (inverse ?150508) (divide ?150509 (divide (inverse ?150510) ?150511)))) [150509, 150514, 150513, 150508, 150510, 150511, 150512] by Demod 31677 with 6 at 1,3
-Id : 154818, {_}: inverse (divide ?869515 (divide (divide (inverse (divide (inverse ?869516) ?869517)) (divide ?869514 ?869513)) (divide ?869518 ?869519))) =<= inverse (inverse (inverse (divide (divide ?869515 (divide (multiply (multiply (multiply ?869511 ?869512) (divide (divide (inverse ?869512) ?869511) (divide ?869510 (divide ?869513 ?869514)))) ?869510) (divide ?869518 ?869519))) (multiply ?869517 ?869516)))) [869510, 869512, 869511, 869519, 869518, 869513, 869514, 869517, 869516, 869515] by Demod 154130 with 31809 at 3
-Id : 155388, {_}: inverse (divide ?877204 (divide (divide (inverse (divide (inverse ?877205) ?877206)) (divide ?877207 ?877208)) (divide ?877209 ?877210))) =>= inverse (inverse (inverse (divide (divide ?877204 (divide (divide ?877208 ?877207) (divide ?877209 ?877210))) (multiply ?877206 ?877205)))) [877210, 877209, 877208, 877207, 877206, 877205, 877204] by Demod 154818 with 2673 at 1,2,1,1,1,1,3
-Id : 155389, {_}: inverse (divide ?877216 (divide (divide (inverse (divide (inverse ?877217) ?877218)) (divide ?877219 ?877220)) ?877213)) =<= inverse (inverse (inverse (divide (divide ?877216 (divide (divide ?877220 ?877219) (divide (inverse (divide ?877212 (divide ?877213 (divide ?877214 ?877215)))) (divide (divide ?877215 ?877214) ?877212)))) (multiply ?877218 ?877217)))) [877215, 877214, 877212, 877213, 877220, 877219, 877218, 877217, 877216] by Super 155388 with 4 at 2,2,1,2
-Id : 156615, {_}: inverse (divide ?885441 (divide (divide (inverse (divide (inverse ?885442) ?885443)) (divide ?885444 ?885445)) ?885446)) =>= inverse (inverse (inverse (divide (divide ?885441 (divide (divide ?885445 ?885444) ?885446)) (multiply ?885443 ?885442)))) [885446, 885445, 885444, 885443, 885442, 885441] by Demod 155389 with 4 at 2,2,1,1,1,1,3
-Id : 156655, {_}: inverse (divide ?885869 (divide (divide (inverse (divide ?885866 ?885870)) (divide ?885871 ?885872)) ?885873)) =<= inverse (inverse (inverse (divide (divide ?885869 (divide (divide ?885872 ?885871) ?885873)) (multiply ?885870 (divide ?885865 (divide (divide ?885866 (divide (divide ?885867 ?885868) ?885865)) (divide ?885868 ?885867))))))) [885868, 885867, 885865, 885873, 885872, 885871, 885870, 885866, 885869] by Super 156615 with 22 at 1,1,1,1,2,1,2
-Id : 157579, {_}: inverse (divide ?891923 (divide (divide (inverse (divide ?891924 ?891925)) (divide ?891926 ?891927)) ?891928)) =<= inverse (inverse (inverse (divide (divide ?891923 (divide (divide ?891927 ?891926) ?891928)) (divide ?891925 ?891924)))) [891928, 891927, 891926, 891925, 891924, 891923] by Demod 156655 with 313 at 2,1,1,1,3
-Id : 157660, {_}: inverse (divide (inverse (divide ?892784 ?892778)) (divide (divide (inverse (divide ?892781 ?892782)) (divide (divide ?892779 ?892780) ?892783)) ?892784)) =>= inverse (inverse (inverse (divide (inverse (divide ?892783 (divide ?892778 (divide ?892780 ?892779)))) (divide ?892782 ?892781)))) [892783, 892780, 892779, 892782, 892781, 892778, 892784] by Super 157579 with 10 at 1,1,1,1,3
-Id : 164761, {_}: inverse (inverse (divide (inverse (divide ?938345 ?938346)) (divide ?938347 (divide ?938348 (divide ?938349 ?938350))))) =<= inverse (inverse (inverse (divide (inverse (divide ?938348 (divide ?938347 (divide ?938350 ?938349)))) (divide ?938346 ?938345)))) [938350, 938349, 938348, 938347, 938346, 938345] by Demod 157660 with 10 at 1,2
-Id : 345, {_}: inverse (inverse (divide ?1638 (divide ?1637 (divide (inverse (divide (divide ?1640 ?1639) ?1637)) (divide ?1639 ?1640))))) =>= ?1638 [1639, 1640, 1637, 1638] by Super 318 with 10 at 1,2
-Id : 31310, {_}: inverse (divide ?149129 (divide (divide (inverse (divide (divide ?149127 ?149128) ?149132)) (divide ?149128 ?149127)) (divide ?149130 ?149131))) =>= inverse (divide (divide ?149129 (divide ?149131 ?149130)) ?149132) [149131, 149130, 149132, 149128, 149127, 149129] by Super 31179 with 345 at 1,2
-Id : 164877, {_}: inverse (inverse (divide (inverse (divide ?939554 ?939555)) (divide (divide (inverse (divide (divide ?939551 ?939552) ?939553)) (divide ?939552 ?939551)) (divide ?939556 (divide ?939557 ?939558))))) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?939556 (divide ?939557 ?939558)) ?939553)) (divide ?939555 ?939554)))) [939558, 939557, 939556, 939553, 939552, 939551, 939555, 939554] by Super 164761 with 31310 at 1,1,1,1,3
-Id : 177719, {_}: inverse (inverse (divide (divide (inverse (divide ?1018267 ?1018268)) (divide (divide ?1018269 ?1018270) ?1018271)) ?1018272)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1018271 (divide ?1018269 ?1018270)) ?1018272)) (divide ?1018268 ?1018267)))) [1018272, 1018271, 1018270, 1018269, 1018268, 1018267] by Demod 164877 with 31310 at 1,2
-Id : 177759, {_}: inverse (inverse (divide (divide (inverse (divide ?1018695 ?1018696)) (divide (divide (inverse (divide ?1018691 (divide ?1018692 (divide ?1018693 ?1018694)))) (divide (divide ?1018694 ?1018693) ?1018691)) ?1018697)) ?1018698)) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?1018697 ?1018692) ?1018698)) (divide ?1018696 ?1018695)))) [1018698, 1018697, 1018694, 1018693, 1018692, 1018691, 1018696, 1018695] by Super 177719 with 4 at 2,1,1,1,1,1,1,3
-Id : 178625, {_}: inverse (inverse (divide (divide (inverse (divide ?1023630 ?1023631)) (divide ?1023632 ?1023633)) ?1023634)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1023633 ?1023632) ?1023634)) (divide ?1023631 ?1023630)))) [1023634, 1023633, 1023632, 1023631, 1023630] by Demod 177759 with 4 at 1,2,1,1,1,2
-Id : 180647, {_}: inverse (inverse (divide (divide (inverse (divide ?1035759 ?1035760)) (divide (inverse ?1035761) ?1035762)) ?1035763)) =>= inverse (inverse (inverse (divide (inverse (divide (multiply ?1035762 ?1035761) ?1035763)) (divide ?1035760 ?1035759)))) [1035763, 1035762, 1035761, 1035760, 1035759] by Super 178625 with 6 at 1,1,1,1,1,1,3
-Id : 180814, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =<= inverse (inverse (inverse (divide (inverse (divide (multiply (inverse ?1037588) ?1037591) ?1037592)) (divide ?1037590 ?1037589)))) [1037592, 1037588, 1037591, 1037590, 1037589] by Super 180647 with 6 at 2,1,1,1,2
-Id : 187329, {_}: multiply ?1072739 (inverse (inverse (divide (inverse (divide (multiply (inverse ?1072737) ?1072736) ?1072738)) (divide ?1072735 ?1072734)))) =>= divide ?1072739 (inverse (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738))) [1072734, 1072735, 1072738, 1072736, 1072737, 1072739] by Super 6 with 180814 at 2,3
-Id : 187880, {_}: multiply ?1072739 (inverse (inverse (divide (inverse (divide (multiply (inverse ?1072737) ?1072736) ?1072738)) (divide ?1072735 ?1072734)))) =>= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072734, 1072735, 1072738, 1072736, 1072737, 1072739] by Demod 187329 with 6 at 3
-Id : 276296, {_}: inverse (inverse (divide (inverse (divide ?1501612 (divide ?1501613 ?1501614))) (divide ?1501615 (divide ?1501612 (divide ?1501613 ?1501614))))) =>= inverse (inverse (inverse ?1501615)) [1501615, 1501614, 1501613, 1501612] by Super 164761 with 4 at 1,1,1,3
-Id : 276336, {_}: inverse (inverse (divide (inverse (divide (inverse (divide ?1501959 (divide ?1501956 (divide ?1501957 ?1501958)))) (divide (divide ?1501958 ?1501957) ?1501959))) (divide ?1501960 ?1501956))) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501958, 1501957, 1501956, 1501959] by Super 276296 with 4 at 2,2,1,1,2
-Id : 277437, {_}: inverse (inverse (divide (inverse ?1506460) (divide ?1506461 ?1506460))) =>= inverse (inverse (inverse ?1506461)) [1506461, 1506460] by Demod 276336 with 4 at 1,1,1,1,2
-Id : 411, {_}: divide (inverse (divide ?1881 (divide ?1882 (multiply (inverse ?1883) ?1880)))) (divide (multiply (inverse ?1880) ?1883) ?1881) =>= ?1882 [1880, 1883, 1882, 1881] by Super 398 with 6 at 2,2,1,1,2
-Id : 277453, {_}: inverse (inverse (divide (inverse (divide (multiply (inverse ?1506555) ?1506554) ?1506552)) ?1506553)) =<= inverse (inverse (inverse (inverse (divide ?1506552 (divide ?1506553 (multiply (inverse ?1506554) ?1506555)))))) [1506553, 1506552, 1506554, 1506555] by Super 277437 with 411 at 2,1,1,2
-Id : 339, {_}: inverse (divide (inverse ?1603) (divide (divide ?1604 (multiply (divide ?1605 ?1606) ?1603)) (divide ?1606 ?1605))) =>= ?1604 [1606, 1605, 1604, 1603] by Super 318 with 6 at 2,1,2,1,2
-Id : 298734, {_}: inverse ?1602430 =<= inverse (inverse (inverse (divide ?1602430 (multiply (divide ?1602431 ?1602432) (divide ?1602432 ?1602431))))) [1602432, 1602431, 1602430] by Super 277437 with 339 at 1,2
-Id : 277476, {_}: inverse (inverse (divide (inverse (inverse ?1506721)) (multiply ?1506722 ?1506721))) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Super 277437 with 6 at 2,1,1,2
-Id : 298855, {_}: inverse (inverse (inverse (divide ?1603311 ?1603310))) =<= inverse (inverse (inverse (inverse (divide ?1603310 ?1603311)))) [1603310, 1603311] by Super 298734 with 277476 at 1,3
-Id : 299275, {_}: inverse (inverse (divide (inverse (divide (multiply (inverse ?1506555) ?1506554) ?1506552)) ?1506553)) =>= inverse (inverse (inverse (divide (divide ?1506553 (multiply (inverse ?1506554) ?1506555)) ?1506552))) [1506553, 1506552, 1506554, 1506555] by Demod 277453 with 298855 at 3
-Id : 299281, {_}: multiply ?1072739 (inverse (inverse (inverse (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738)))) =>= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072738, 1072737, 1072736, 1072734, 1072735, 1072739] by Demod 187880 with 299275 at 2,2
-Id : 299680, {_}: inverse (inverse (inverse (divide ?1606480 ?1606481))) =<= inverse (inverse (inverse (inverse (divide ?1606481 ?1606480)))) [1606481, 1606480] by Super 298734 with 277476 at 1,3
-Id : 299719, {_}: inverse (inverse (inverse (divide (inverse ?1606741) ?1606742))) =>= inverse (inverse (inverse (inverse (multiply ?1606742 ?1606741)))) [1606742, 1606741] by Super 299680 with 6 at 1,1,1,1,3
-Id : 300712, {_}: inverse (inverse (inverse (divide ?1610501 (inverse ?1610500)))) =<= inverse (inverse (inverse (inverse (inverse (multiply ?1610501 ?1610500))))) [1610500, 1610501] by Super 298855 with 299719 at 1,3
-Id : 303239, {_}: inverse (inverse (inverse (multiply ?1620581 ?1620582))) =<= inverse (inverse (inverse (inverse (inverse (multiply ?1620581 ?1620582))))) [1620582, 1620581] by Demod 300712 with 6 at 1,1,1,2
-Id : 2523, {_}: ?11149 =<= multiply (multiply (divide ?11152 ?11153) (divide (divide ?11153 ?11152) (divide ?11154 ?11149))) ?11154 [11154, 11153, 11152, 11149] by Demod 2431 with 4 at 2
-Id : 303314, {_}: inverse (inverse (inverse (multiply (multiply (divide ?1621150 ?1621151) (divide (divide ?1621151 ?1621150) (divide ?1621152 ?1621149))) ?1621152))) =>= inverse (inverse (inverse (inverse (inverse ?1621149)))) [1621149, 1621152, 1621151, 1621150] by Super 303239 with 2523 at 1,1,1,1,1,3
-Id : 304462, {_}: inverse (inverse (inverse ?1624383)) =<= inverse (inverse (inverse (inverse (inverse ?1624383)))) [1624383] by Demod 303314 with 2523 at 1,1,1,2
-Id : 304463, {_}: inverse (inverse (inverse (divide ?1624385 (divide (divide ?1624386 (divide (divide ?1624387 ?1624388) ?1624385)) (divide ?1624388 ?1624387))))) =>= inverse (inverse (inverse (inverse ?1624386))) [1624388, 1624387, 1624386, 1624385] by Super 304462 with 22 at 1,1,1,1,3
-Id : 305044, {_}: inverse (inverse ?1624386) =<= inverse (inverse (inverse (inverse ?1624386))) [1624386] by Demod 304463 with 22 at 1,1,2
-Id : 309508, {_}: inverse (inverse (inverse (divide ?1603311 ?1603310))) =>= inverse (inverse (divide ?1603310 ?1603311)) [1603310, 1603311] by Demod 298855 with 305044 at 3
-Id : 309601, {_}: multiply ?1072739 (inverse (inverse (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))))) =<= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 299281 with 309508 at 2,2
-Id : 310013, {_}: inverse (inverse ?1628964) =<= inverse (inverse (inverse (inverse ?1628964))) [1628964] by Demod 304463 with 22 at 1,1,2
-Id : 310154, {_}: inverse (inverse (divide ?1629909 (divide ?1629910 (divide (inverse (divide (divide ?1629911 ?1629912) ?1629910)) (divide ?1629912 ?1629911))))) =>= inverse (inverse ?1629909) [1629912, 1629911, 1629910, 1629909] by Super 310013 with 345 at 1,1,3
-Id : 310837, {_}: ?1629909 =<= inverse (inverse ?1629909) [1629909] by Demod 310154 with 345 at 2
-Id : 311136, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =<= multiply ?1072739 (inverse (divide (divide (inverse (divide ?1072734 ?1072735)) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 309601 with 310837 at 2,2
-Id : 299278, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =<= inverse (inverse (inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)))) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 180814 with 299275 at 1,3
-Id : 299285, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =>= inverse (inverse (inverse (divide ?1037592 (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588))))) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 299278 with 298855 at 3
-Id : 309533, {_}: inverse (inverse (divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592)) =>= inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 299285 with 309508 at 3
-Id : 311173, {_}: divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592 =<= inverse (inverse (divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592)) [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 309533 with 310837 at 2
-Id : 311174, {_}: divide (divide (inverse (divide ?1037589 ?1037590)) (multiply (inverse ?1037591) ?1037588)) ?1037592 =>= divide (divide (divide ?1037590 ?1037589) (multiply (inverse ?1037591) ?1037588)) ?1037592 [1037592, 1037588, 1037591, 1037590, 1037589] by Demod 311173 with 310837 at 3
-Id : 311184, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =<= multiply ?1072739 (inverse (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738)) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 311136 with 311174 at 1,2,3
-Id : 328, {_}: inverse (divide ?1523 (divide (divide ?1524 (divide (divide (inverse ?1522) ?1525) ?1523)) (multiply ?1525 ?1522))) =>= ?1524 [1525, 1522, 1524, 1523] by Super 318 with 6 at 2,2,1,2
-Id : 5095, {_}: multiply ?23662 (divide ?23663 (divide (divide ?23664 (divide (divide (inverse ?23665) ?23666) ?23663)) (multiply ?23666 ?23665))) =>= divide ?23662 ?23664 [23666, 23665, 23664, 23663, 23662] by Super 6 with 328 at 2,3
-Id : 5148, {_}: multiply ?24110 (inverse (divide ?24111 (divide ?24109 (divide (inverse (divide (multiply ?24113 ?24112) ?24109)) (divide (inverse ?24112) ?24113))))) =>= divide ?24110 ?24111 [24112, 24113, 24109, 24111, 24110] by Super 5095 with 10 at 2,2
-Id : 722, {_}: inverse (divide ?3136 (divide (divide ?3137 (divide (divide (inverse ?3138) ?3139) ?3136)) (multiply ?3139 ?3138))) =>= ?3137 [3139, 3138, 3137, 3136] by Super 318 with 6 at 2,2,1,2
-Id : 746, {_}: inverse (inverse (divide ?3302 (divide ?3301 (divide (inverse (divide (multiply ?3304 ?3303) ?3301)) (divide (inverse ?3303) ?3304))))) =>= ?3302 [3303, 3304, 3301, 3302] by Super 722 with 10 at 1,2
-Id : 311071, {_}: divide ?3302 (divide ?3301 (divide (inverse (divide (multiply ?3304 ?3303) ?3301)) (divide (inverse ?3303) ?3304))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 746 with 310837 at 2
-Id : 311292, {_}: multiply ?24110 (inverse ?24111) =>= divide ?24110 ?24111 [24111, 24110] by Demod 5148 with 311071 at 1,2,2
-Id : 311301, {_}: multiply ?1072739 (divide ?1072738 (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737))) =>= divide ?1072739 (divide (divide (divide ?1072735 ?1072734) (multiply (inverse ?1072736) ?1072737)) ?1072738) [1072737, 1072736, 1072734, 1072735, 1072738, 1072739] by Demod 311184 with 311292 at 3
-Id : 311313, {_}: divide ?60191 ?60192 =<= divide (multiply (multiply (inverse ?60193) ?60194) ?60190) (divide (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193)) (inverse ?60190)) [60190, 60194, 60193, 60192, 60191] by Demod 13819 with 311301 at 3
-Id : 311314, {_}: divide ?60191 ?60192 =<= divide (multiply (multiply (inverse ?60193) ?60194) ?60190) (multiply (divide (divide ?60192 ?60191) (multiply (inverse ?60194) ?60193)) ?60190) [60190, 60194, 60193, 60192, 60191] by Demod 311313 with 6 at 2,3
-Id : 54, {_}: divide (inverse (divide ?250 ?251)) (divide (divide ?252 (multiply ?253 ?254)) ?250) =>= inverse (divide ?252 (divide ?251 (divide (inverse ?254) ?253))) [254, 253, 252, 251, 250] by Super 23 with 6 at 2,1,2,2
-Id : 55, {_}: divide (inverse (divide (inverse ?256) ?257)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= inverse (divide ?258 (divide ?257 (divide (inverse ?260) ?259))) [260, 259, 258, 257, 256] by Super 54 with 6 at 2,2
-Id : 311016, {_}: inverse (divide ?1603311 ?1603310) =<= inverse (inverse (divide ?1603310 ?1603311)) [1603310, 1603311] by Demod 309508 with 310837 at 2
-Id : 311017, {_}: inverse (divide ?1603311 ?1603310) =>= divide ?1603310 ?1603311 [1603310, 1603311] by Demod 311016 with 310837 at 3
-Id : 311424, {_}: divide (divide ?257 (inverse ?256)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= inverse (divide ?258 (divide ?257 (divide (inverse ?260) ?259))) [260, 259, 258, 256, 257] by Demod 55 with 311017 at 1,2
-Id : 311425, {_}: divide (divide ?257 (inverse ?256)) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (divide (inverse ?260) ?259)) ?258 [260, 259, 258, 256, 257] by Demod 311424 with 311017 at 3
-Id : 311594, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (divide (inverse ?260) ?259)) ?258 [260, 259, 258, 256, 257] by Demod 311425 with 6 at 1,2
-Id : 311596, {_}: divide ?60191 ?60192 =<= divide (divide (multiply (inverse ?60193) ?60194) (divide (inverse ?60193) (inverse ?60194))) (divide ?60192 ?60191) [60194, 60193, 60192, 60191] by Demod 311314 with 311594 at 3
-Id : 179540, {_}: inverse (inverse (divide (divide (inverse (divide (inverse ?1029056) ?1029057)) (divide ?1029058 ?1029059)) ?1029060)) =>= inverse (inverse (inverse (divide (inverse (divide (divide ?1029059 ?1029058) ?1029060)) (multiply ?1029057 ?1029056)))) [1029060, 1029059, 1029058, 1029057, 1029056] by Super 178625 with 6 at 2,1,1,1,3
-Id : 186333, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1068110) ?1068111)) (divide ?1068112 ?1068113)) ?1068114)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1068113 ?1068112) ?1068114)) (multiply (inverse ?1068111) ?1068110)))) [1068114, 1068113, 1068112, 1068111, 1068110] by Super 179540 with 6 at 1,1,1,1,1,2
-Id : 186556, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1070554) ?1070555)) (divide (inverse ?1070553) ?1070556)) ?1070557)) =>= inverse (inverse (inverse (divide (inverse (divide (multiply ?1070556 ?1070553) ?1070557)) (multiply (inverse ?1070555) ?1070554)))) [1070557, 1070556, 1070553, 1070555, 1070554] by Super 186333 with 6 at 1,1,1,1,1,1,3
-Id : 179745, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1031256 ?1031255) ?1031257)) (multiply (inverse ?1031253) ?1031254)))) [1031257, 1031256, 1031255, 1031253, 1031254] by Super 179540 with 6 at 1,1,1,1,1,2
-Id : 277438, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =<= inverse (inverse (inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))))) [1506464, 1506463, 1506465, 1506466] by Super 277437 with 4 at 2,1,1,2
-Id : 299272, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =>= inverse (inverse (inverse (divide (divide ?1506464 (divide ?1506465 ?1506466)) ?1506463))) [1506464, 1506463, 1506465, 1506466] by Demod 277438 with 298855 at 3
-Id : 299290, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =<= inverse (inverse (inverse (inverse (divide (divide (multiply (inverse ?1031253) ?1031254) (divide ?1031255 ?1031256)) ?1031257)))) [1031257, 1031256, 1031255, 1031253, 1031254] by Demod 179745 with 299272 at 1,3
-Id : 299299, {_}: inverse (inverse (divide (divide (inverse (multiply (inverse ?1031254) ?1031253)) (divide ?1031255 ?1031256)) ?1031257)) =>= inverse (inverse (inverse (divide ?1031257 (divide (multiply (inverse ?1031253) ?1031254) (divide ?1031255 ?1031256))))) [1031257, 1031256, 1031255, 1031253, 1031254] by Demod 299290 with 298855 at 3
-Id : 299300, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =?= inverse (inverse (inverse (divide (inverse (divide (multiply ?1070556 ?1070553) ?1070557)) (multiply (inverse ?1070555) ?1070554)))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 186556 with 299299 at 2
-Id : 300336, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =>= inverse (inverse (inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 299300 with 299719 at 3
-Id : 309498, {_}: inverse (inverse (inverse (divide ?1070557 (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556))))) =>= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070556, 1070553, 1070554, 1070555, 1070557] by Demod 300336 with 305044 at 3
-Id : 309684, {_}: inverse (inverse (divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557)) =>= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 309498 with 309508 at 2
-Id : 311181, {_}: divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557 =<= inverse (inverse (multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557))) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 309684 with 310837 at 2
-Id : 311182, {_}: divide (divide (multiply (inverse ?1070555) ?1070554) (divide (inverse ?1070553) ?1070556)) ?1070557 =>= multiply (multiply (inverse ?1070555) ?1070554) (divide (multiply ?1070556 ?1070553) ?1070557) [1070557, 1070556, 1070553, 1070554, 1070555] by Demod 311181 with 310837 at 3
-Id : 311600, {_}: divide ?60191 ?60192 =<= multiply (multiply (inverse ?60193) ?60194) (divide (multiply (inverse ?60194) ?60193) (divide ?60192 ?60191)) [60194, 60193, 60192, 60191] by Demod 311596 with 311182 at 3
-Id : 311603, {_}: divide (inverse ?5406) (divide (multiply ?5407 ?5408) ?5406) =>= divide (inverse ?5408) ?5407 [5408, 5407, 5406] by Demod 1282 with 311600 at 2,2
-Id : 276834, {_}: inverse (inverse (divide (inverse ?1501956) (divide ?1501960 ?1501956))) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501956] by Demod 276336 with 4 at 1,1,1,1,2
-Id : 311035, {_}: divide (inverse ?1501956) (divide ?1501960 ?1501956) =>= inverse (inverse (inverse ?1501960)) [1501960, 1501956] by Demod 276834 with 310837 at 2
-Id : 311036, {_}: divide (inverse ?1501956) (divide ?1501960 ?1501956) =>= inverse ?1501960 [1501960, 1501956] by Demod 311035 with 310837 at 3
-Id : 311604, {_}: inverse (multiply ?5407 ?5408) =<= divide (inverse ?5408) ?5407 [5408, 5407] by Demod 311603 with 311036 at 2
-Id : 311708, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (divide (inverse (multiply ?12298 ?12296)) (divide ?12299 ?12297))) ?12299 [12299, 12296, 12298, 12297] by Demod 2673 with 311604 at 1,2,1,3
-Id : 311709, {_}: ?12297 =<= multiply (multiply (multiply ?12298 ?12296) (inverse (multiply (divide ?12299 ?12297) (multiply ?12298 ?12296)))) ?12299 [12299, 12296, 12298, 12297] by Demod 311708 with 311604 at 2,1,3
-Id : 311866, {_}: ?12297 =<= multiply (divide (multiply ?12298 ?12296) (multiply (divide ?12299 ?12297) (multiply ?12298 ?12296))) ?12299 [12299, 12296, 12298, 12297] by Demod 311709 with 311292 at 1,3
-Id : 311110, {_}: divide (inverse (inverse ?1506721)) (multiply ?1506722 ?1506721) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Demod 277476 with 310837 at 2
-Id : 311111, {_}: divide ?1506721 (multiply ?1506722 ?1506721) =>= inverse (inverse (inverse ?1506722)) [1506722, 1506721] by Demod 311110 with 310837 at 1,2
-Id : 311112, {_}: divide ?1506721 (multiply ?1506722 ?1506721) =>= inverse ?1506722 [1506722, 1506721] by Demod 311111 with 310837 at 3
-Id : 311867, {_}: ?12297 =<= multiply (inverse (divide ?12299 ?12297)) ?12299 [12299, 12297] by Demod 311866 with 311112 at 1,3
-Id : 311868, {_}: ?12297 =<= multiply (divide ?12297 ?12299) ?12299 [12299, 12297] by Demod 311867 with 311017 at 1,3
-Id : 31329, {_}: inverse (inverse (inverse (divide (divide ?147825 (divide ?147822 (divide ?147826 ?147827))) (divide ?147828 ?147822)))) =>= inverse (divide (divide ?147825 (divide ?147827 ?147826)) ?147828) [147828, 147827, 147826, 147822, 147825] by Demod 31180 with 4 at 1,2,1,1,1,1,2
-Id : 31603, {_}: multiply ?149797 (inverse (inverse (divide (divide ?149792 (divide ?149793 (divide ?149794 ?149795))) (divide ?149796 ?149793)))) =>= divide ?149797 (inverse (divide (divide ?149792 (divide ?149795 ?149794)) ?149796)) [149796, 149795, 149794, 149793, 149792, 149797] by Super 6 with 31329 at 2,3
-Id : 33302, {_}: multiply ?159935 (inverse (inverse (divide (divide ?159936 (divide ?159937 (divide ?159938 ?159939))) (divide ?159940 ?159937)))) =>= multiply ?159935 (divide (divide ?159936 (divide ?159939 ?159938)) ?159940) [159940, 159939, 159938, 159937, 159936, 159935] by Demod 31603 with 6 at 3
-Id : 33303, {_}: multiply ?159946 (inverse (inverse (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943))) =>= multiply ?159946 (divide (divide ?159947 (divide ?159949 ?159948)) (inverse (divide ?159942 (divide ?159943 (divide ?159944 ?159945))))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Super 33302 with 4 at 2,1,1,2,2
-Id : 33719, {_}: multiply ?159946 (inverse (inverse (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943))) =>= multiply ?159946 (multiply (divide ?159947 (divide ?159949 ?159948)) (divide ?159942 (divide ?159943 (divide ?159944 ?159945)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 33303 with 6 at 2,3
-Id : 311080, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =<= multiply ?159946 (multiply (divide ?159947 (divide ?159949 ?159948)) (divide ?159942 (divide ?159943 (divide ?159944 ?159945)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 33719 with 310837 at 2,2
-Id : 158025, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =<= inverse (inverse (inverse (divide (inverse (divide ?892783 (divide ?892778 (divide ?892780 ?892779)))) (divide ?892782 ?892781)))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 157660 with 10 at 1,2
-Id : 300347, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =<= inverse (inverse (inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 158025 with 299719 at 3
-Id : 309517, {_}: inverse (inverse (divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))))) =>= inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 300347 with 305044 at 3
-Id : 311023, {_}: divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =<= inverse (inverse (multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 309517 with 310837 at 2
-Id : 311024, {_}: divide (inverse (divide ?892781 ?892782)) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =>= multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))) [892780, 892779, 892783, 892778, 892782, 892781] by Demod 311023 with 310837 at 3
-Id : 311478, {_}: divide (divide ?892782 ?892781) (divide ?892778 (divide ?892783 (divide ?892779 ?892780))) =<= multiply (divide ?892782 ?892781) (divide ?892783 (divide ?892778 (divide ?892780 ?892779))) [892780, 892779, 892783, 892778, 892781, 892782] by Demod 311024 with 311017 at 1,2
-Id : 311484, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =?= multiply ?159946 (divide (divide ?159947 (divide ?159949 ?159948)) (divide ?159943 (divide ?159942 (divide ?159945 ?159944)))) [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 311080 with 311478 at 2,3
-Id : 31729, {_}: inverse (inverse (inverse (divide (divide ?150997 ?150994) (divide ?150999 (inverse (divide ?150998 (divide ?150994 (divide ?150995 ?150996)))))))) =>= inverse (divide (divide ?150997 (divide ?150998 (divide ?150996 ?150995))) ?150999) [150996, 150995, 150998, 150999, 150994, 150997] by Super 31662 with 4 at 2,1,1,1,1,2
-Id : 36383, {_}: inverse (inverse (inverse (divide (divide ?176720 ?176721) (multiply ?176722 (divide ?176723 (divide ?176721 (divide ?176724 ?176725))))))) =>= inverse (divide (divide ?176720 (divide ?176723 (divide ?176725 ?176724))) ?176722) [176725, 176724, 176723, 176722, 176721, 176720] by Demod 31729 with 6 at 2,1,1,1,2
-Id : 36463, {_}: inverse (inverse (inverse (divide ?177473 (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479))))))) =>= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177479, 177478, 177472, 177474, 177475, 177477, 177476, 177473] by Super 36383 with 4 at 1,1,1,1,2
-Id : 309587, {_}: inverse (inverse (divide (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)))) ?177473)) =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177479, 177478, 177472, 177474, 177475, 177477, 177476] by Demod 36463 with 309508 at 2
-Id : 311007, {_}: divide (multiply ?177476 (divide ?177477 (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)))) ?177473 =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177479, 177478, 177472, 177474, 177475, 177477, 177476] by Demod 309587 with 310837 at 2
-Id : 178159, {_}: inverse (inverse (divide (divide (inverse (divide ?1018695 ?1018696)) (divide ?1018692 ?1018697)) ?1018698)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1018697 ?1018692) ?1018698)) (divide ?1018696 ?1018695)))) [1018698, 1018697, 1018692, 1018696, 1018695] by Demod 177759 with 4 at 1,2,1,1,1,2
-Id : 178479, {_}: multiply ?1021991 (inverse (inverse (divide (inverse (divide (divide ?1021989 ?1021988) ?1021990)) (divide ?1021987 ?1021986)))) =>= divide ?1021991 (inverse (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990))) [1021986, 1021987, 1021990, 1021988, 1021989, 1021991] by Super 6 with 178159 at 2,3
-Id : 178887, {_}: multiply ?1021991 (inverse (inverse (divide (inverse (divide (divide ?1021989 ?1021988) ?1021990)) (divide ?1021987 ?1021986)))) =>= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021986, 1021987, 1021990, 1021988, 1021989, 1021991] by Demod 178479 with 6 at 3
-Id : 299293, {_}: multiply ?1021991 (inverse (inverse (inverse (divide (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989)) ?1021990)))) =>= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021990, 1021989, 1021988, 1021986, 1021987, 1021991] by Demod 178887 with 299272 at 2,2
-Id : 309531, {_}: multiply ?1021991 (inverse (inverse (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))))) =<= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 299293 with 309508 at 2,2
-Id : 311175, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =<= multiply ?1021991 (inverse (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990)) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 309531 with 310837 at 2,2
-Id : 311300, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =<= divide ?1021991 (divide (divide (inverse (divide ?1021986 ?1021987)) (divide ?1021988 ?1021989)) ?1021990) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 311175 with 311292 at 3
-Id : 311471, {_}: multiply ?1021991 (divide ?1021990 (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989))) =>= divide ?1021991 (divide (divide (divide ?1021987 ?1021986) (divide ?1021988 ?1021989)) ?1021990) [1021989, 1021988, 1021986, 1021987, 1021990, 1021991] by Demod 311300 with 311017 at 1,1,2,3
-Id : 312117, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= inverse (divide (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) ?177476) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 311007 with 311471 at 1,2
-Id : 312118, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= divide ?177476 (divide (inverse (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) (divide ?177477 (divide ?177479 ?177478))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312117 with 311017 at 3
-Id : 312119, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= divide ?177476 (inverse (multiply (divide ?177477 (divide ?177479 ?177478)) (divide ?177472 (divide ?177473 (divide ?177474 ?177475))))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312118 with 311604 at 2,3
-Id : 312120, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= multiply ?177476 (multiply (divide ?177477 (divide ?177479 ?177478)) (divide ?177472 (divide ?177473 (divide ?177474 ?177475)))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312119 with 6 at 3
-Id : 312121, {_}: divide (divide ?177476 (divide (divide (divide (divide ?177475 ?177474) ?177472) (divide ?177478 ?177479)) ?177477)) ?177473 =<= multiply ?177476 (divide (divide ?177477 (divide ?177479 ?177478)) (divide ?177473 (divide ?177472 (divide ?177475 ?177474)))) [177473, 177477, 177479, 177478, 177472, 177474, 177475, 177476] by Demod 312120 with 311478 at 2,3
-Id : 312122, {_}: multiply ?159946 (divide (divide ?159947 (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949))) ?159943) =>= divide (divide ?159946 (divide (divide (divide (divide ?159945 ?159944) ?159942) (divide ?159948 ?159949)) ?159947)) ?159943 [159943, 159949, 159948, 159942, 159944, 159945, 159947, 159946] by Demod 311484 with 312121 at 3
-Id : 26, {_}: divide (inverse (divide ?127 ?128)) (divide (divide ?129 (multiply ?130 ?126)) ?127) =>= inverse (divide ?129 (divide ?128 (divide (inverse ?126) ?130))) [126, 130, 129, 128, 127] by Super 23 with 6 at 2,1,2,2
-Id : 673, {_}: inverse (divide ?2882 (divide (divide ?2883 (divide (multiply ?2884 ?2885) ?2882)) (divide (inverse ?2885) ?2884))) =>= ?2883 [2885, 2884, 2883, 2882] by Super 4 with 26 at 2
-Id : 1528, {_}: inverse (divide ?6677 (divide (divide ?6678 (divide (multiply (inverse ?6679) ?6680) ?6677)) (multiply (inverse ?6680) ?6679))) =>= ?6678 [6680, 6679, 6678, 6677] by Super 673 with 6 at 2,2,1,2
-Id : 1549, {_}: inverse (inverse (divide ?6831 (divide (inverse ?6830) (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833))))) =>= ?6831 [6832, 6833, 6830, 6831] by Super 1528 with 32 at 1,2
-Id : 311073, {_}: divide ?6831 (divide (inverse ?6830) (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833))) =>= ?6831 [6832, 6833, 6830, 6831] by Demod 1549 with 310837 at 2
-Id : 311743, {_}: divide ?6831 (inverse (multiply (divide (inverse (multiply (multiply (inverse ?6833) ?6832) ?6830)) (multiply (inverse ?6832) ?6833)) ?6830)) =>= ?6831 [6830, 6832, 6833, 6831] by Demod 311073 with 311604 at 2,2
-Id : 311744, {_}: divide ?6831 (inverse (multiply (inverse (multiply (multiply (inverse ?6832) ?6833) (multiply (multiply (inverse ?6833) ?6832) ?6830))) ?6830)) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311743 with 311604 at 1,1,2,2
-Id : 311850, {_}: multiply ?6831 (multiply (inverse (multiply (multiply (inverse ?6832) ?6833) (multiply (multiply (inverse ?6833) ?6832) ?6830))) ?6830) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311744 with 6 at 2
-Id : 179801, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1031802) ?1031803)) (divide ?1031804 ?1031805)) ?1031801)) =<= inverse (inverse (inverse (divide (inverse (divide (divide ?1031805 ?1031804) (inverse ?1031801))) (multiply ?1031803 ?1031802)))) [1031801, 1031805, 1031804, 1031803, 1031802] by Super 179540 with 6 at 1,1,2
-Id : 182767, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1047817) ?1047818)) (divide ?1047819 ?1047820)) ?1047821)) =>= inverse (inverse (inverse (divide (inverse (multiply (divide ?1047820 ?1047819) ?1047821)) (multiply ?1047818 ?1047817)))) [1047821, 1047820, 1047819, 1047818, 1047817] by Demod 179801 with 6 at 1,1,1,1,1,3
-Id : 190010, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1087858) ?1087859)) (multiply ?1087860 ?1087861)) ?1087862)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide (inverse ?1087861) ?1087860) ?1087862)) (multiply ?1087859 ?1087858)))) [1087862, 1087861, 1087860, 1087859, 1087858] by Super 182767 with 6 at 2,1,1,1,2
-Id : 190267, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1090617) ?1090618)) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =>= inverse (inverse (inverse (divide (inverse (multiply (multiply (inverse ?1090619) ?1090616) ?1090620)) (multiply ?1090618 ?1090617)))) [1090620, 1090619, 1090616, 1090618, 1090617] by Super 190010 with 6 at 1,1,1,1,1,1,3
-Id : 182806, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1048196) ?1048197)) (multiply ?1048198 ?1048195)) ?1048199)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide (inverse ?1048195) ?1048198) ?1048199)) (multiply ?1048197 ?1048196)))) [1048199, 1048195, 1048198, 1048197, 1048196] by Super 182767 with 6 at 2,1,1,1,2
-Id : 490, {_}: divide (inverse (divide (inverse ?2255) (divide ?2256 (multiply ?2257 ?2254)))) (multiply (divide (inverse ?2254) ?2257) ?2255) =>= ?2256 [2254, 2257, 2256, 2255] by Super 466 with 6 at 2,2,1,1,2
-Id : 277455, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =<= inverse (inverse (inverse (inverse (divide (inverse ?1506563) (divide ?1506564 (multiply ?1506565 ?1506566)))))) [1506564, 1506563, 1506565, 1506566] by Super 277437 with 490 at 2,1,1,2
-Id : 299269, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =>= inverse (inverse (inverse (divide (divide ?1506564 (multiply ?1506565 ?1506566)) (inverse ?1506563)))) [1506564, 1506563, 1506565, 1506566] by Demod 277455 with 298855 at 3
-Id : 299304, {_}: inverse (inverse (divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564)) =>= inverse (inverse (inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563))) [1506564, 1506563, 1506565, 1506566] by Demod 299269 with 6 at 1,1,1,3
-Id : 299306, {_}: inverse (inverse (multiply (divide (inverse (divide (inverse ?1048196) ?1048197)) (multiply ?1048198 ?1048195)) ?1048199)) =>= inverse (inverse (inverse (inverse (multiply (divide (multiply ?1048197 ?1048196) (multiply ?1048198 ?1048195)) ?1048199)))) [1048199, 1048195, 1048198, 1048197, 1048196] by Demod 182806 with 299304 at 1,3
-Id : 299307, {_}: inverse (inverse (inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)))) =<= inverse (inverse (inverse (divide (inverse (multiply (multiply (inverse ?1090619) ?1090616) ?1090620)) (multiply ?1090618 ?1090617)))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 190267 with 299306 at 2
-Id : 300335, {_}: inverse (inverse (inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)))) =<= inverse (inverse (inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 299307 with 299719 at 3
-Id : 309523, {_}: inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =<= inverse (inverse (inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 300335 with 305044 at 2
-Id : 309524, {_}: inverse (inverse (multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620)) =<= inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 309523 with 305044 at 3
-Id : 311029, {_}: multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620 =<= inverse (inverse (multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620))) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 309524 with 310837 at 2
-Id : 311030, {_}: multiply (divide (multiply ?1090618 ?1090617) (multiply (inverse ?1090616) ?1090619)) ?1090620 =<= multiply (multiply ?1090618 ?1090617) (multiply (multiply (inverse ?1090619) ?1090616) ?1090620) [1090620, 1090619, 1090616, 1090617, 1090618] by Demod 311029 with 310837 at 3
-Id : 311851, {_}: multiply ?6831 (multiply (inverse (multiply (divide (multiply (inverse ?6832) ?6833) (multiply (inverse ?6832) ?6833)) ?6830)) ?6830) =>= ?6831 [6830, 6833, 6832, 6831] by Demod 311850 with 311030 at 1,1,2,2
-Id : 692, {_}: inverse (inverse (divide ?3016 (divide (inverse ?3015) (divide (inverse (multiply (divide (inverse ?3018) ?3017) ?3015)) (multiply ?3017 ?3018))))) =>= ?3016 [3017, 3018, 3015, 3016] by Super 673 with 32 at 1,2
-Id : 277278, {_}: inverse (inverse (inverse (inverse ?1505137))) =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Super 692 with 276834 at 2
-Id : 309511, {_}: inverse (inverse ?1505137) =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Demod 277278 with 305044 at 2
-Id : 311129, {_}: ?1505137 =<= inverse (divide (inverse (multiply (divide (inverse ?1505138) ?1505139) ?1505137)) (multiply ?1505139 ?1505138)) [1505139, 1505138, 1505137] by Demod 309511 with 310837 at 2
-Id : 311117, {_}: divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564 =<= inverse (inverse (inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563))) [1506564, 1506563, 1506565, 1506566] by Demod 299304 with 310837 at 2
-Id : 311118, {_}: divide (inverse (multiply (divide (inverse ?1506566) ?1506565) ?1506563)) ?1506564 =>= inverse (multiply (divide ?1506564 (multiply ?1506565 ?1506566)) ?1506563) [1506564, 1506563, 1506565, 1506566] by Demod 311117 with 310837 at 3
-Id : 311205, {_}: ?1505137 =<= inverse (inverse (multiply (divide (multiply ?1505139 ?1505138) (multiply ?1505139 ?1505138)) ?1505137)) [1505138, 1505139, 1505137] by Demod 311129 with 311118 at 1,3
-Id : 311206, {_}: ?1505137 =<= multiply (divide (multiply ?1505139 ?1505138) (multiply ?1505139 ?1505138)) ?1505137 [1505138, 1505139, 1505137] by Demod 311205 with 310837 at 3
-Id : 311852, {_}: multiply ?6831 (multiply (inverse ?6830) ?6830) =>= ?6831 [6830, 6831] by Demod 311851 with 311206 at 1,1,2,2
-Id : 312318, {_}: multiply ?1630838 (multiply ?1630837 (inverse ?1630837)) =>= ?1630838 [1630837, 1630838] by Super 311852 with 310837 at 1,2,2
-Id : 312456, {_}: multiply ?1630838 (divide ?1630837 ?1630837) =>= ?1630838 [1630837, 1630838] by Demod 312318 with 311292 at 2,2
-Id : 312737, {_}: divide (divide ?1631485 (divide (divide (divide (divide ?1631486 ?1631487) ?1631488) (divide (divide ?1631486 ?1631487) ?1631488)) ?1631489)) ?1631489 =>= ?1631485 [1631489, 1631488, 1631487, 1631486, 1631485] by Super 312121 with 312456 at 3
-Id : 164905, {_}: inverse (inverse (divide (inverse (divide ?939850 (divide ?939851 ?939852))) (divide ?939849 (divide ?939850 (divide ?939851 ?939852))))) =>= inverse (inverse (inverse ?939849)) [939849, 939852, 939851, 939850] by Super 164761 with 4 at 1,1,1,3
-Id : 276099, {_}: inverse (inverse (inverse ?1499672)) =<= inverse (divide (inverse (divide (divide ?1499671 ?1499670) ?1499672)) (divide ?1499670 ?1499671)) [1499670, 1499671, 1499672] by Super 345 with 164905 at 2
-Id : 311033, {_}: inverse ?1499672 =<= inverse (divide (inverse (divide (divide ?1499671 ?1499670) ?1499672)) (divide ?1499670 ?1499671)) [1499670, 1499671, 1499672] by Demod 276099 with 310837 at 2
-Id : 309603, {_}: inverse (inverse (divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464)) =>= inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))) [1506464, 1506463, 1506465, 1506466] by Demod 299272 with 309508 at 3
-Id : 311134, {_}: divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464 =<= inverse (inverse (divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)))) [1506464, 1506463, 1506465, 1506466] by Demod 309603 with 310837 at 2
-Id : 311135, {_}: divide (inverse (divide (divide ?1506466 ?1506465) ?1506463)) ?1506464 =>= divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)) [1506464, 1506463, 1506465, 1506466] by Demod 311134 with 310837 at 3
-Id : 311365, {_}: inverse ?1499672 =<= inverse (divide ?1499672 (divide (divide ?1499670 ?1499671) (divide ?1499670 ?1499671))) [1499671, 1499670, 1499672] by Demod 311033 with 311135 at 1,3
-Id : 311372, {_}: inverse ?1499672 =<= divide (divide (divide ?1499670 ?1499671) (divide ?1499670 ?1499671)) ?1499672 [1499671, 1499670, 1499672] by Demod 311365 with 311017 at 3
-Id : 313817, {_}: divide (divide ?1631485 (inverse ?1631489)) ?1631489 =>= ?1631485 [1631489, 1631485] by Demod 312737 with 311372 at 2,1,2
-Id : 313818, {_}: divide (multiply ?1631485 ?1631489) ?1631489 =>= ?1631485 [1631489, 1631485] by Demod 313817 with 6 at 1,2
-Id : 317392, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =<= divide (divide ?1642981 (divide (divide (divide (divide ?1642982 ?1642983) ?1642984) (divide ?1642985 ?1642986)) (multiply ?1642980 (divide (divide (divide ?1642982 ?1642983) ?1642984) (divide ?1642985 ?1642986))))) ?1642987 [1642986, 1642985, 1642984, 1642983, 1642982, 1642987, 1642980, 1642981] by Super 312122 with 313818 at 1,2,2
-Id : 318522, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =<= divide (divide ?1642981 (inverse ?1642980)) ?1642987 [1642987, 1642980, 1642981] by Demod 317392 with 311112 at 2,1,3
-Id : 318523, {_}: multiply ?1642981 (divide ?1642980 ?1642987) =>= divide (multiply ?1642981 ?1642980) ?1642987 [1642987, 1642980, 1642981] by Demod 318522 with 6 at 1,3
-Id : 311394, {_}: divide (divide ?1506463 (divide ?1506466 ?1506465)) ?1506464 =?= divide ?1506463 (divide ?1506464 (divide ?1506465 ?1506466)) [1506464, 1506465, 1506466, 1506463] by Demod 311135 with 311017 at 1,2
-Id : 277640, {_}: inverse ?1508034 =<= inverse (inverse (inverse (divide ?1508034 (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035))))) [1508036, 1508035, 1508034] by Super 277437 with 339 at 1,2
-Id : 309536, {_}: inverse ?1508034 =<= inverse (inverse (divide (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035)) ?1508034)) [1508036, 1508035, 1508034] by Demod 277640 with 309508 at 3
-Id : 310975, {_}: inverse ?1508034 =<= divide (multiply (divide ?1508035 ?1508036) (divide ?1508036 ?1508035)) ?1508034 [1508036, 1508035, 1508034] by Demod 309536 with 310837 at 3
-Id : 312719, {_}: inverse ?1631352 =<= divide (divide ?1631351 ?1631351) ?1631352 [1631351, 1631352] by Super 310975 with 312456 at 1,3
-Id : 314397, {_}: divide (divide ?1637990 (divide ?1637991 ?1637992)) (divide ?1637989 ?1637989) =>= divide ?1637990 (inverse (divide ?1637992 ?1637991)) [1637989, 1637992, 1637991, 1637990] by Super 311394 with 312719 at 2,3
-Id : 311378, {_}: divide ?3302 (divide ?3301 (divide (divide ?3301 (multiply ?3304 ?3303)) (divide (inverse ?3303) ?3304))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 311071 with 311017 at 1,2,2,2
-Id : 312063, {_}: divide ?3302 (divide ?3301 (divide (divide ?3301 (multiply ?3304 ?3303)) (inverse (multiply ?3304 ?3303)))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 311378 with 311604 at 2,2,2,2
-Id : 312064, {_}: divide ?3302 (divide ?3301 (multiply (divide ?3301 (multiply ?3304 ?3303)) (multiply ?3304 ?3303))) =>= ?3302 [3303, 3304, 3301, 3302] by Demod 312063 with 6 at 2,2,2
-Id : 312065, {_}: divide ?3302 (divide ?3301 ?3301) =>= ?3302 [3301, 3302] by Demod 312064 with 311868 at 2,2,2
-Id : 314879, {_}: divide ?1637990 (divide ?1637991 ?1637992) =<= divide ?1637990 (inverse (divide ?1637992 ?1637991)) [1637992, 1637991, 1637990] by Demod 314397 with 312065 at 2
-Id : 314880, {_}: divide ?1637990 (divide ?1637991 ?1637992) =<= multiply ?1637990 (divide ?1637992 ?1637991) [1637992, 1637991, 1637990] by Demod 314879 with 6 at 3
-Id : 320415, {_}: divide ?1642981 (divide ?1642987 ?1642980) =?= divide (multiply ?1642981 ?1642980) ?1642987 [1642980, 1642987, 1642981] by Demod 318523 with 314880 at 2
-Id : 343753, {_}: multiply ?1701701 ?1701702 =<= multiply (divide ?1701701 (divide ?1701703 ?1701702)) ?1701703 [1701703, 1701702, 1701701] by Super 311868 with 320415 at 1,3
-Id : 311818, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (divide ?257 (inverse (multiply ?259 ?260))) ?258 [260, 259, 258, 256, 257] by Demod 311594 with 311604 at 2,1,3
-Id : 311820, {_}: divide (multiply ?257 ?256) (multiply (divide ?258 (multiply ?259 ?260)) ?256) =>= divide (multiply ?257 (multiply ?259 ?260)) ?258 [260, 259, 258, 256, 257] by Demod 311818 with 6 at 1,3
-Id : 317517, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =?= divide (multiply ?1643886 (multiply ?1643888 ?1643889)) (multiply ?1643885 (multiply ?1643888 ?1643889)) [1643889, 1643888, 1643885, 1643887, 1643886] by Super 311820 with 313818 at 1,2,2
-Id : 32072, {_}: inverse (inverse (inverse (divide (divide ?152561 (divide ?152562 (multiply ?152563 ?152564))) (divide ?152565 ?152562)))) =>= inverse (divide (divide ?152561 (divide (inverse ?152564) ?152563)) ?152565) [152565, 152564, 152563, 152562, 152561] by Super 31662 with 6 at 2,2,1,1,1,1,2
-Id : 691, {_}: inverse (inverse (divide ?3011 (divide ?3010 (divide (inverse (divide (divide (inverse ?3013) ?3012) ?3010)) (multiply ?3012 ?3013))))) =>= ?3011 [3012, 3013, 3010, 3011] by Super 673 with 10 at 1,2
-Id : 32186, {_}: inverse (divide ?153559 (divide (divide (inverse (divide (divide (inverse ?153557) ?153558) ?153562)) (multiply ?153558 ?153557)) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153562, 153558, 153557, 153559] by Super 32072 with 691 at 1,2
-Id : 311187, {_}: inverse (divide ?153559 (divide (divide ?153562 (divide (multiply ?153558 ?153557) (divide ?153558 (inverse ?153557)))) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153557, 153558, 153562, 153559] by Demod 32186 with 311135 at 1,2,1,2
-Id : 311196, {_}: inverse (divide ?153559 (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561))) =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153561, 153560, 153557, 153558, 153562, 153559] by Demod 311187 with 6 at 2,2,1,2,1,2
-Id : 311391, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= inverse (divide (divide ?153559 (divide (inverse ?153561) ?153560)) ?153562) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311196 with 311017 at 2
-Id : 311392, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (divide ?153559 (divide (inverse ?153561) ?153560)) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311391 with 311017 at 3
-Id : 312039, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (divide ?153559 (inverse (multiply ?153560 ?153561))) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 311392 with 311604 at 2,2,3
-Id : 312040, {_}: divide (divide (divide ?153562 (divide (multiply ?153558 ?153557) (multiply ?153558 ?153557))) (multiply ?153560 ?153561)) ?153559 =>= divide ?153562 (multiply ?153559 (multiply ?153560 ?153561)) [153559, 153561, 153560, 153557, 153558, 153562] by Demod 312039 with 6 at 2,3
-Id : 312075, {_}: divide (divide ?153562 (multiply ?153560 ?153561)) ?153559 =?= divide ?153562 (multiply ?153559 (multiply ?153560 ?153561)) [153559, 153561, 153560, 153562] by Demod 312040 with 312065 at 1,1,2
-Id : 318365, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =?= divide (divide (multiply ?1643886 (multiply ?1643888 ?1643889)) (multiply ?1643888 ?1643889)) ?1643885 [1643889, 1643888, 1643885, 1643887, 1643886] by Demod 317517 with 312075 at 3
-Id : 318366, {_}: divide (multiply ?1643886 ?1643887) (multiply ?1643885 ?1643887) =>= divide ?1643886 ?1643885 [1643885, 1643887, 1643886] by Demod 318365 with 313818 at 1,3
-Id : 343774, {_}: multiply ?1701846 (multiply ?1701845 ?1701844) =<= multiply (divide ?1701846 (divide ?1701843 ?1701845)) (multiply ?1701843 ?1701844) [1701843, 1701844, 1701845, 1701846] by Super 343753 with 318366 at 2,1,3
-Id : 178704, {_}: inverse (inverse (divide (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) (inverse ?1024392))) =>= inverse (inverse (inverse (divide (inverse (multiply (divide ?1024396 ?1024395) ?1024392)) (divide ?1024394 ?1024393)))) [1024392, 1024396, 1024395, 1024394, 1024393] by Super 178625 with 6 at 1,1,1,1,1,3
-Id : 179107, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =<= inverse (inverse (inverse (divide (inverse (multiply (divide ?1024396 ?1024395) ?1024392)) (divide ?1024394 ?1024393)))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 178704 with 6 at 1,1,2
-Id : 300345, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =<= inverse (inverse (inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 179107 with 299719 at 3
-Id : 309518, {_}: inverse (inverse (multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392)) =>= inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 300345 with 305044 at 3
-Id : 311123, {_}: multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392 =<= inverse (inverse (multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392))) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 309518 with 310837 at 2
-Id : 311124, {_}: multiply (divide (inverse (divide ?1024393 ?1024394)) (divide ?1024395 ?1024396)) ?1024392 =>= multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392) [1024392, 1024396, 1024395, 1024394, 1024393] by Demod 311123 with 310837 at 3
-Id : 311459, {_}: multiply (divide (divide ?1024394 ?1024393) (divide ?1024395 ?1024396)) ?1024392 =?= multiply (divide ?1024394 ?1024393) (multiply (divide ?1024396 ?1024395) ?1024392) [1024392, 1024396, 1024395, 1024393, 1024394] by Demod 311124 with 311017 at 1,1,2
-Id : 314145, {_}: multiply (divide (divide ?1636195 ?1636196) (inverse ?1636193)) ?1636197 =<= multiply (divide ?1636195 ?1636196) (multiply (divide ?1636193 (divide ?1636194 ?1636194)) ?1636197) [1636194, 1636197, 1636193, 1636196, 1636195] by Super 311459 with 312719 at 2,1,2
-Id : 315602, {_}: multiply (multiply (divide ?1636195 ?1636196) ?1636193) ?1636197 =<= multiply (divide ?1636195 ?1636196) (multiply (divide ?1636193 (divide ?1636194 ?1636194)) ?1636197) [1636194, 1636197, 1636193, 1636196, 1636195] by Demod 314145 with 6 at 1,2
-Id : 315603, {_}: multiply (multiply (divide ?1636195 ?1636196) ?1636193) ?1636197 =>= multiply (divide ?1636195 ?1636196) (multiply ?1636193 ?1636197) [1636197, 1636193, 1636196, 1636195] by Demod 315602 with 312065 at 1,2,3
-Id : 320945, {_}: multiply ?1653480 ?1653482 =<= multiply (divide ?1653480 (divide ?1653481 ?1653482)) ?1653481 [1653481, 1653482, 1653480] by Super 311868 with 320415 at 1,3
-Id : 343542, {_}: multiply (multiply ?1699948 ?1699949) ?1699951 =<= multiply (divide ?1699948 (divide ?1699950 ?1699949)) (multiply ?1699950 ?1699951) [1699950, 1699951, 1699949, 1699948] by Super 315603 with 320945 at 1,2
-Id : 394401, {_}: multiply ?1701846 (multiply ?1701845 ?1701844) =?= multiply (multiply ?1701846 ?1701845) ?1701844 [1701844, 1701845, 1701846] by Demod 343774 with 343542 at 3
-Id : 395259, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 394401 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP471-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 10.893625s
-% SZS status Unsatisfiable for GRP477-1.p
-% SZS output start CNFRefutation for GRP477-1.p
-Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 7, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 4, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 9, {_}: divide (inverse (divide (divide (divide ?26 ?27) (divide ?23 ?22)) ?25)) (divide ?27 ?26) =?= inverse (divide (divide (divide ?22 ?23) ?24) (divide ?25 ?24)) [24, 25, 22, 23, 27, 26] by Super 7 with 4 at 2,1,1,2
-Id : 8947, {_}: inverse (divide (divide (divide ?66899 ?66900) ?66901) (divide (divide ?66902 (divide ?66900 ?66899)) ?66901)) =>= ?66902 [66902, 66901, 66900, 66899] by Super 4 with 9 at 2
-Id : 9487, {_}: inverse (divide (divide (divide (inverse ?70062) ?70063) ?70064) (divide (divide ?70065 (multiply ?70063 ?70062)) ?70064)) =>= ?70065 [70065, 70064, 70063, 70062] by Super 8947 with 6 at 2,1,2,1,2
-Id : 13, {_}: divide (inverse (divide (divide (divide ?48 ?49) (inverse ?47)) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Super 4 with 6 at 2,1,1,2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?88 ?89) ?90) (multiply ?91 ?90))) (divide ?89 ?88) =>= ?91 [91, 90, 89, 88] by Demod 13 with 6 at 1,1,1,2
-Id : 27, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (divide (divide ?113 ?112) (inverse (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114)))) =>= ?117 [114, 112, 113, 117, 116, 115] by Super 23 with 4 at 1,1,1,1,2
-Id : 35, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (multiply (divide ?113 ?112) (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114))) =>= ?117 [114, 112, 113, 117, 116, 115] by Demod 27 with 6 at 2,2
-Id : 9506, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?70226 ?70225) ?70227) (divide ?70222 ?70227))) (divide ?70225 ?70226)) ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222, 70227, 70225, 70226] by Super 9487 with 35 at 1,2,1,2
-Id : 9604, {_}: inverse (divide (divide ?70222 ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222] by Demod 9506 with 4 at 1,1,1,2
-Id : 27713, {_}: divide (divide (inverse (divide (divide (divide ?169617 ?169618) (divide ?169619 ?169620)) ?169621)) (divide ?169618 ?169617)) (divide ?169619 ?169620) =>= ?169621 [169621, 169620, 169619, 169618, 169617] by Super 4 with 9 at 1,2
-Id : 27714, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) (divide (inverse (divide (divide (divide ?169623 ?169624) ?169625) (divide ?169626 ?169625))) (divide ?169624 ?169623))) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169625, 169624, 169623, 169628, 169627] by Super 27713 with 4 at 2,2
-Id : 28344, {_}: divide (divide (inverse (divide (divide (divide ?173215 ?173216) ?173217) ?173218)) (divide ?173216 ?173215)) ?173217 =>= ?173218 [173218, 173217, 173216, 173215] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28449, {_}: divide (divide (inverse (multiply (divide (divide ?174106 ?174107) ?174108) ?174105)) (divide ?174107 ?174106)) ?174108 =>= inverse ?174105 [174105, 174108, 174107, 174106] by Super 28344 with 6 at 1,1,1,2
-Id : 28805, {_}: multiply (divide (inverse (multiply (divide (divide ?175142 ?175143) (inverse ?175145)) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Super 6 with 28449 at 3
-Id : 29852, {_}: multiply (divide (inverse (multiply (multiply (divide ?180549 ?180550) ?180551) ?180552)) (divide ?180550 ?180549)) ?180551 =>= inverse ?180552 [180552, 180551, 180550, 180549] by Demod 28805 with 6 at 1,1,1,1,2
-Id : 33202, {_}: multiply (divide (inverse (multiply (multiply (divide (inverse ?199058) ?199059) ?199060) ?199061)) (multiply ?199059 ?199058)) ?199060 =>= inverse ?199061 [199061, 199060, 199059, 199058] by Super 29852 with 6 at 2,1,2
-Id : 33304, {_}: multiply (divide (inverse (multiply (multiply (multiply (inverse ?199942) ?199941) ?199943) ?199944)) (multiply (inverse ?199941) ?199942)) ?199943 =>= inverse ?199944 [199944, 199943, 199941, 199942] by Super 33202 with 6 at 1,1,1,1,1,2
-Id : 43, {_}: divide (inverse (divide (divide (divide (inverse ?171) ?172) ?173) (divide ?174 ?173))) (multiply ?172 ?171) =>= ?174 [174, 173, 172, 171] by Super 4 with 6 at 2,2
-Id : 48, {_}: divide (inverse (divide (divide ?205 ?206) (divide ?207 ?206))) (multiply (divide ?203 ?202) (divide (divide (divide ?202 ?203) ?204) (divide ?205 ?204))) =>= ?207 [204, 202, 203, 207, 206, 205] by Super 43 with 4 at 1,1,1,1,2
-Id : 8271, {_}: inverse (divide (divide (divide ?62998 ?62997) ?62999) (divide (divide ?63000 (divide ?62997 ?62998)) ?62999)) =>= ?63000 [63000, 62999, 62997, 62998] by Super 4 with 9 at 2
-Id : 8914, {_}: divide ?66588 (multiply (divide ?66589 ?66590) (divide (divide (divide ?66590 ?66589) ?66591) (divide (divide ?66585 ?66586) ?66591))) =>= divide ?66588 (divide ?66586 ?66585) [66586, 66585, 66591, 66590, 66589, 66588] by Super 48 with 8271 at 1,2
-Id : 27904, {_}: divide (divide (inverse (divide (divide (divide ?171441 ?171442) (divide ?171443 ?171444)) (divide ?171440 ?171439))) (divide ?171442 ?171441)) (divide ?171443 ?171444) =?= multiply (divide ?171436 ?171437) (divide (divide (divide ?171437 ?171436) ?171438) (divide (divide ?171439 ?171440) ?171438)) [171438, 171437, 171436, 171439, 171440, 171444, 171443, 171442, 171441] by Super 27713 with 8914 at 1,1,1,2
-Id : 8270, {_}: divide (divide (inverse (divide (divide (divide ?62988 ?62989) (divide ?62990 ?62991)) ?62992)) (divide ?62989 ?62988)) (divide ?62990 ?62991) =>= ?62992 [62992, 62991, 62990, 62989, 62988] by Super 4 with 9 at 1,2
-Id : 28135, {_}: divide ?171440 ?171439 =<= multiply (divide ?171436 ?171437) (divide (divide (divide ?171437 ?171436) ?171438) (divide (divide ?171439 ?171440) ?171438)) [171438, 171437, 171436, 171439, 171440] by Demod 27904 with 8270 at 2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?48 ?49) ?47) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Demod 13 with 6 at 1,1,1,2
-Id : 22, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (divide (divide ?82 ?81) (inverse (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83)))) =>= ?86 [83, 81, 82, 86, 85, 84] by Super 4 with 18 at 1,1,1,1,2
-Id : 32, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (multiply (divide ?82 ?81) (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83))) =>= ?86 [83, 81, 82, 86, 85, 84] by Demod 22 with 6 at 2,2
-Id : 8902, {_}: divide ?66500 (multiply (divide ?66501 ?66502) (divide (multiply (divide ?66502 ?66501) ?66503) (multiply (divide ?66497 ?66498) ?66503))) =>= divide ?66500 (divide ?66498 ?66497) [66498, 66497, 66503, 66502, 66501, 66500] by Super 32 with 8271 at 1,2
-Id : 27903, {_}: divide (divide (inverse (divide (divide (divide ?171431 ?171432) (divide ?171433 ?171434)) (divide ?171430 ?171429))) (divide ?171432 ?171431)) (divide ?171433 ?171434) =?= multiply (divide ?171426 ?171427) (divide (multiply (divide ?171427 ?171426) ?171428) (multiply (divide ?171429 ?171430) ?171428)) [171428, 171427, 171426, 171429, 171430, 171434, 171433, 171432, 171431] by Super 27713 with 8902 at 1,1,1,2
-Id : 28134, {_}: divide ?171430 ?171429 =<= multiply (divide ?171426 ?171427) (divide (multiply (divide ?171427 ?171426) ?171428) (multiply (divide ?171429 ?171430) ?171428)) [171428, 171427, 171426, 171429, 171430] by Demod 27903 with 8270 at 2
-Id : 34242, {_}: divide (divide (inverse (divide ?204167 ?204168)) (divide ?204171 ?204170)) ?204172 =<= inverse (divide (multiply (divide ?204172 (divide ?204170 ?204171)) ?204169) (multiply (divide ?204168 ?204167) ?204169)) [204169, 204172, 204170, 204171, 204168, 204167] by Super 28449 with 28134 at 1,1,1,2
-Id : 34778, {_}: divide (divide (divide (inverse (divide ?206532 ?206533)) (divide ?206534 ?206535)) ?206536) (divide (divide ?206535 ?206534) ?206536) =>= divide ?206533 ?206532 [206536, 206535, 206534, 206533, 206532] by Super 18 with 34242 at 1,2
-Id : 54527, {_}: divide ?300655 ?300656 =<= multiply (divide (divide ?300655 ?300656) (inverse (divide ?300653 ?300654))) (divide ?300654 ?300653) [300654, 300653, 300656, 300655] by Super 28135 with 34778 at 2,3
-Id : 55213, {_}: divide ?304381 ?304382 =<= multiply (multiply (divide ?304381 ?304382) (divide ?304383 ?304384)) (divide ?304384 ?304383) [304384, 304383, 304382, 304381] by Demod 54527 with 6 at 1,3
-Id : 55316, {_}: divide (inverse (divide (divide (divide ?305230 ?305231) ?305232) (divide ?305233 ?305232))) (divide ?305231 ?305230) =?= multiply (multiply ?305233 (divide ?305234 ?305235)) (divide ?305235 ?305234) [305235, 305234, 305233, 305232, 305231, 305230] by Super 55213 with 4 at 1,1,3
-Id : 55555, {_}: ?305233 =<= multiply (multiply ?305233 (divide ?305234 ?305235)) (divide ?305235 ?305234) [305235, 305234, 305233] by Demod 55316 with 4 at 2
-Id : 27948, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) ?169626) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169628, 169627] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28234, {_}: multiply (divide (inverse (divide (divide (divide ?172298 ?172299) (inverse ?172301)) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Super 6 with 27948 at 3
-Id : 28487, {_}: multiply (divide (inverse (divide (multiply (divide ?172298 ?172299) ?172301) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 9011, {_}: inverse (divide (divide (divide ?67439 ?67440) (inverse ?67438)) (multiply (divide ?67441 (divide ?67440 ?67439)) ?67438)) =>= ?67441 [67441, 67438, 67440, 67439] by Super 8947 with 6 at 2,1,2
-Id : 9220, {_}: inverse (divide (multiply (divide ?68482 ?68483) ?68484) (multiply (divide ?68485 (divide ?68483 ?68482)) ?68484)) =>= ?68485 [68485, 68484, 68483, 68482] by Demod 9011 with 6 at 1,1,2
-Id : 9262, {_}: inverse (divide (multiply (divide (inverse ?68840) ?68841) ?68842) (multiply (divide ?68843 (multiply ?68841 ?68840)) ?68842)) =>= ?68843 [68843, 68842, 68841, 68840] by Super 9220 with 6 at 2,1,2,1,2
-Id : 34818, {_}: inverse (divide (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) (divide (divide ?206979 ?206978) ?206984)) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206978, 206979, 206984, 206980, 206981, 206982] by Super 9604 with 34242 at 3
-Id : 54516, {_}: inverse (divide ?300558 ?300557) =<= divide (divide (inverse (divide ?300559 ?300560)) (divide ?300560 ?300559)) (inverse (divide ?300557 ?300558)) [300560, 300559, 300557, 300558] by Super 34818 with 34778 at 1,2
-Id : 54778, {_}: inverse (divide ?300558 ?300557) =<= multiply (divide (inverse (divide ?300559 ?300560)) (divide ?300560 ?300559)) (divide ?300557 ?300558) [300560, 300559, 300557, 300558] by Demod 54516 with 6 at 3
-Id : 58787, {_}: inverse (divide (inverse (divide ?321392 ?321393)) (multiply (divide ?321396 (multiply (divide ?321395 ?321394) (divide ?321394 ?321395))) (divide ?321393 ?321392))) =>= ?321396 [321394, 321395, 321396, 321393, 321392] by Super 9262 with 54778 at 1,1,2
-Id : 12, {_}: divide (inverse (divide (divide (divide (inverse ?42) ?41) ?43) (divide ?44 ?43))) (multiply ?41 ?42) =>= ?44 [44, 43, 41, 42] by Super 4 with 6 at 2,2
-Id : 54402, {_}: divide (inverse (divide ?299508 ?299507)) (multiply (divide ?299509 ?299510) (divide ?299507 ?299508)) =>= divide ?299510 ?299509 [299510, 299509, 299507, 299508] by Super 12 with 34778 at 1,1,2
-Id : 59136, {_}: inverse (divide (multiply (divide ?321395 ?321394) (divide ?321394 ?321395)) ?321396) =>= ?321396 [321396, 321394, 321395] by Demod 58787 with 54402 at 1,2
-Id : 59503, {_}: multiply (divide ?323772 (divide ?323771 ?323770)) (divide ?323771 ?323770) =>= ?323772 [323770, 323771, 323772] by Super 28487 with 59136 at 1,1,2
-Id : 60069, {_}: divide ?327147 (divide ?327148 ?327149) =<= multiply ?327147 (divide ?327149 ?327148) [327149, 327148, 327147] by Super 55555 with 59503 at 1,3
-Id : 60669, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?329868) ?329869) ?329870) (divide ?329866 ?329867))) (multiply (inverse ?329869) ?329868)) ?329870 =>= inverse (divide ?329867 ?329866) [329867, 329866, 329870, 329869, 329868] by Super 33304 with 60069 at 1,1,1,2
-Id : 29399, {_}: multiply (divide (inverse (divide (multiply (divide ?178179 ?178180) ?178181) ?178182)) (divide ?178180 ?178179)) ?178181 =>= ?178182 [178182, 178181, 178180, 178179] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 32341, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?194066) ?194067) ?194068) ?194069)) (multiply ?194067 ?194066)) ?194068 =>= ?194069 [194069, 194068, 194067, 194066] by Super 29399 with 6 at 2,1,2
-Id : 32441, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?194936) ?194935) ?194937) ?194938)) (multiply (inverse ?194935) ?194936)) ?194937 =>= ?194938 [194938, 194937, 194935, 194936] by Super 32341 with 6 at 1,1,1,1,1,2
-Id : 61017, {_}: divide ?329866 ?329867 =<= inverse (divide ?329867 ?329866) [329867, 329866] by Demod 60669 with 32441 at 2
-Id : 61512, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70222, 70228, 70224] by Demod 9604 with 61017 at 2
-Id : 61513, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= divide (multiply ?70224 ?70223) (multiply ?70222 ?70223) [70223, 70222, 70228, 70224] by Demod 61512 with 61017 at 3
-Id : 60072, {_}: multiply (divide ?327160 (divide ?327161 ?327162)) (divide ?327161 ?327162) =>= ?327160 [327162, 327161, 327160] by Super 28487 with 59136 at 1,1,2
-Id : 60073, {_}: multiply (divide ?327168 (divide (inverse (divide (divide (divide ?327164 ?327165) ?327166) (divide ?327167 ?327166))) (divide ?327165 ?327164))) ?327167 =>= ?327168 [327167, 327166, 327165, 327164, 327168] by Super 60072 with 4 at 2,2
-Id : 64649, {_}: multiply (divide ?338211 ?338212) ?338212 =>= ?338211 [338212, 338211] by Demod 60073 with 4 at 2,1,2
-Id : 61711, {_}: divide ?332019 ?332020 =<= inverse (divide ?332020 ?332019) [332020, 332019] by Demod 60669 with 32441 at 2
-Id : 61786, {_}: divide (inverse ?332481) ?332482 =>= inverse (multiply ?332482 ?332481) [332482, 332481] by Super 61711 with 6 at 1,3
-Id : 64688, {_}: multiply (inverse (multiply ?338450 ?338449)) ?338450 =>= inverse ?338449 [338449, 338450] by Super 64649 with 61786 at 1,2
-Id : 70472, {_}: divide (divide ?351323 ?351324) (divide (inverse (multiply ?351321 ?351322)) ?351324) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Super 61513 with 64688 at 2,3
-Id : 70841, {_}: divide (divide ?351323 ?351324) (inverse (multiply ?351324 (multiply ?351321 ?351322))) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Demod 70472 with 61786 at 2,2
-Id : 70842, {_}: multiply (divide ?351323 ?351324) (multiply ?351324 (multiply ?351321 ?351322)) =>= divide (multiply ?351323 ?351321) (inverse ?351322) [351322, 351321, 351324, 351323] by Demod 70841 with 6 at 2
-Id : 70843, {_}: multiply (divide ?351323 ?351324) (multiply ?351324 (multiply ?351321 ?351322)) =>= multiply (multiply ?351323 ?351321) ?351322 [351322, 351321, 351324, 351323] by Demod 70842 with 6 at 3
-Id : 67, {_}: divide (inverse (divide (divide (multiply ?287 ?288) ?289) (divide ?290 ?289))) (divide (inverse ?288) ?287) =>= ?290 [290, 289, 288, 287] by Super 4 with 6 at 1,1,1,1,2
-Id : 14, {_}: divide (inverse (divide (divide (multiply ?51 ?52) ?53) (divide ?54 ?53))) (divide (inverse ?52) ?51) =>= ?54 [54, 53, 52, 51] by Super 4 with 6 at 1,1,1,1,2
-Id : 70, {_}: divide (inverse (divide (divide (multiply (divide (inverse ?307) ?306) (divide (divide (multiply ?306 ?307) ?308) (divide ?309 ?308))) ?310) (divide ?311 ?310))) ?309 =>= ?311 [311, 310, 309, 308, 306, 307] by Super 67 with 14 at 2,2
-Id : 60413, {_}: divide (inverse (divide (divide (divide (divide (inverse ?307) ?306) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310) (divide ?311 ?310))) ?309 =>= ?311 [311, 310, 308, 309, 306, 307] by Demod 70 with 60069 at 1,1,1,1,2
-Id : 61462, {_}: divide (divide (divide ?311 ?310) (divide (divide (divide (inverse ?307) ?306) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310)) ?309 =>= ?311 [308, 309, 306, 307, 310, 311] by Demod 60413 with 61017 at 1,2
-Id : 62183, {_}: divide (divide (divide ?311 ?310) (divide (divide (inverse (multiply ?306 ?307)) (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308))) ?310)) ?309 =>= ?311 [308, 309, 307, 306, 310, 311] by Demod 61462 with 61786 at 1,1,2,1,2
-Id : 62184, {_}: divide (divide (divide ?311 ?310) (divide (inverse (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307))) ?310)) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62183 with 61786 at 1,2,1,2
-Id : 62185, {_}: divide (divide (divide ?311 ?310) (inverse (multiply ?310 (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307))))) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62184 with 61786 at 2,1,2
-Id : 62194, {_}: divide (multiply (divide ?311 ?310) (multiply ?310 (multiply (divide (divide ?309 ?308) (divide (multiply ?306 ?307) ?308)) (multiply ?306 ?307)))) ?309 =>= ?311 [307, 306, 308, 309, 310, 311] by Demod 62185 with 6 at 1,2
-Id : 61520, {_}: divide (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (divide (inverse ?52) ?51) =>= ?54 [52, 51, 53, 54] by Demod 14 with 61017 at 1,2
-Id : 62166, {_}: divide (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (inverse (multiply ?51 ?52)) =>= ?54 [52, 51, 53, 54] by Demod 61520 with 61786 at 2,2
-Id : 62205, {_}: multiply (divide (divide ?54 ?53) (divide (multiply ?51 ?52) ?53)) (multiply ?51 ?52) =>= ?54 [52, 51, 53, 54] by Demod 62166 with 6 at 2
-Id : 62206, {_}: divide (multiply (divide ?311 ?310) (multiply ?310 ?309)) ?309 =>= ?311 [309, 310, 311] by Demod 62194 with 62205 at 2,2,1,2
-Id : 64698, {_}: multiply ?338511 ?338513 =<= multiply (divide ?338511 ?338512) (multiply ?338512 ?338513) [338512, 338513, 338511] by Super 64649 with 62206 at 1,2
-Id : 88169, {_}: multiply ?351323 (multiply ?351321 ?351322) =?= multiply (multiply ?351323 ?351321) ?351322 [351322, 351321, 351323] by Demod 70843 with 64698 at 2
-Id : 88454, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 88169 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP477-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Last chance: 1246132826.23
-Last chance: all is indexed 1246132846.24
-Last chance: failed over 100 goal 1246132846.24
-FAILURE in 0 iterations
-% SZS status Timeout for GRP506-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- inverse is 94
- multiply is 96
- prove_these_axioms_4 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-Last chance: 1246133118.1
-Last chance: all is indexed 1246133138.1
-Last chance: failed over 100 goal 1246133138.1
-FAILURE in 0 iterations
-% SZS status Timeout for GRP508-1.p
-Order
- == is 100
- _ is 99
- a is 98
- join is 95
- meet is 97
- prove_normal_axioms_1 is 96
- single_axiom is 94
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-Found proof, 13.508368s
-% SZS status Unsatisfiable for LAT080-1.p
-% SZS output start CNFRefutation for LAT080-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) (meet (join (meet ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) (meet ?8 (join ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Id : 5, {_}: join (meet (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12) (meet (join (meet ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)) (meet (join (meet ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)) (meet ?16 (join ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)))) (join ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)))) (join (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12)) =>= ?11 [16, 15, 14, 13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 ?14 ?15 ?16
-Id : 39, {_}: join (meet (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290) (meet (join (meet ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))) (meet ?289 (join ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))))) (join (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290)) =>= join (meet ?288 ?289) (meet ?289 (join ?288 ?289)) [292, 291, 290, 289, 288, 287] by Super 5 with 4 at 1,2,1,2,2
-Id : 42, {_}: join (meet (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))))) ?324) (meet (join (meet ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet 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(join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 317, 318, 323] by Demod 126 with 4 at 1,2,1,1,2
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?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 130 with 4 at 2,2,1,1,2,2
-Id : 132, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet 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?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 131 with 4 at 2,1,1,2,2,2,1,2,2
-Id : 133, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) 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?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 132 with 4 at 1,2,1,2,2,2,1,2,2
-Id : 134, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 133 with 4 at 2,2,2,2,1,2,2
-Id : 135, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 134 with 4 at 2,1,1,2,2,2
-Id : 136, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324)) =?= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 135 with 4 at 1,2,1,2,2,2
-Id : 714, {_}: join (meet (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383) (meet (join (meet ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)) (meet (join (meet ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)) (meet (join (meet ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)) (meet ?1390 (join ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)))) (join ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)))) (join ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)))) (join (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383)) =>= ?1382 [1390, 1389, 1388, 1387, 1386, 1385, 1384, 1383, 1382, 1381] by Demod 136 with 4 at 3
-Id : 1147, {_}: join (meet (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512) (meet ?2511 (join (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512)) =>= ?2511 [2512, 2511, 2510] by Super 714 with 4 at 1,2,2
-Id : 748, {_}: join (meet (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913) (meet ?1912 (join (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913)) =>= ?1912 [1913, 1912, 1916] by Super 714 with 4 at 1,2,2
-Id : 1164, {_}: join (meet (join (meet (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643) (meet ?2643 (join (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643))) ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643, 2642] by Super 1147 with 748 at 1,2,2,2
-Id : 1544, {_}: join (meet ?2643 ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643] by Demod 1164 with 748 at 1,1,2
-Id : 13, {_}: join (meet (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113) (meet (join (meet ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))) (meet ?107 (join ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))))) (join (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113)) =>= join (meet ?106 ?107) (meet ?107 (join ?106 ?107)) [115, 114, 113, 107, 106, 112] by Super 5 with 4 at 1,2,1,2,2
-Id : 1092, {_}: join (meet (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2039, 2038, 2040] by Super 13 with 748 at 2,2,2,1,2,2,2
-Id : 1218, {_}: join (meet (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1092 with 748 at 2,1,1,1,2
-Id : 1219, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1218 with 748 at 1,2,1,1,2
-Id : 1220, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1219 with 748 at 2,2,2,1,1,2
-Id : 1221, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1220 with 748 at 2,1,1,2,1,1,2,2
-Id : 1222, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1221 with 748 at 1,2,1,2,1,1,2,2
-Id : 1223, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1222 with 748 at 2,2,1,1,2,2
-Id : 1224, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1223 with 748 at 2,1,1,2,2,2,1,2,2
-Id : 1225, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1224 with 748 at 1,2,1,2,2,2,1,2,2
-Id : 1226, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1225 with 748 at 2,2,2,2,1,2,2
-Id : 1227, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1226 with 748 at 2,1,1,2,2,2
-Id : 1228, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =?= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1227 with 748 at 1,2,1,2,2,2
-Id : 2531, {_}: join (meet (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436) (meet (join (meet ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)) (meet ?4435 (join ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)))) (join (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436)) =>= ?4435 [4438, 4437, 4436, 4435, 4434] by Demod 1228 with 748 at 3
-Id : 2540, {_}: join (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))))) ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4516, 4515, 4514, 4513, 4512, 4511, 4510, 4509] by Super 2531 with 4 at 1,2,2,2
-Id : 2926, {_}: join (meet ?4510 ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4514, 4513, 4512, 4511, 4516, 4509, 4515, 4510] by Demod 2540 with 4 at 1,1,2
-Id : 2927, {_}: join (meet ?4510 ?4515) (meet ?4510 (join ?4510 ?4515)) =?= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4515, 4510] by Demod 2926 with 4 at 1,2,2
-Id : 2928, {_}: ?4510 =<= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4510] by Demod 2927 with 1544 at 2
-Id : 4152, {_}: ?6409 =<= join (meet ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409)) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6413, 6412, 6411, 6410, 6409] by Super 1544 with 2928 at 2
-Id : 1229, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2043, 2042, 2041, 2039, 2040] by Demod 1228 with 748 at 3
-Id : 2544, {_}: join (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))))) ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4552, 4551, 4550, 4549, 4548, 4547] by Super 2531 with 1229 at 1,2,2,2
-Id : 2938, {_}: join (meet ?4548 ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4550, 4549, 4552, 4547, 4551, 4548] by Demod 2544 with 1229 at 1,1,2
-Id : 2939, {_}: join (meet ?4548 ?4551) (meet ?4548 (join ?4548 ?4551)) =?= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4551, 4548] by Demod 2938 with 1229 at 1,2,2
-Id : 2940, {_}: ?4548 =<= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4548] by Demod 2939 with 1544 at 2
-Id : 2998, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet ?2039 (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2041, 2039, 2040] by Demod 1229 with 2940 at 1,2,2
-Id : 4435, {_}: join (meet ?7069 ?7068) (meet ?7068 (join ?7069 ?7068)) =>= ?7068 [7068, 7069] by Super 2998 with 4152 at 2
-Id : 4973, {_}: ?7997 =<= meet (meet (join ?7998 (join ?7997 ?7999)) (join ?8000 ?7997)) ?7997 [8000, 7999, 7998, 7997] by Super 4152 with 4435 at 3
-Id : 7418, {_}: meet ?10627 ?10628 =<= meet (meet (join ?10629 ?10627) (join ?10630 (meet ?10627 ?10628))) (meet ?10627 ?10628) [10630, 10629, 10628, 10627] by Super 4973 with 1544 at 2,1,1,3
-Id : 3035, {_}: ?5143 =<= join (meet ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143)) (meet ?5143 (join ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143))) [5146, 5145, 5144, 5143] by Demod 2939 with 1544 at 2
-Id : 3039, {_}: ?5175 =<= join (meet ?5174 (join (join (meet ?5175 ?5175) (meet ?5175 (join ?5175 ?5175))) ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Super 3035 with 1544 at 1,2,2,2,3
-Id : 3217, {_}: ?5175 =<= join (meet ?5174 (join ?5175 ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Demod 3039 with 1544 at 1,2,1,3
-Id : 4899, {_}: ?7757 =<= meet (meet (join ?7758 (join ?7757 ?7759)) (join ?7760 ?7757)) ?7757 [7760, 7759, 7758, 7757] by Super 4152 with 4435 at 3
-Id : 4939, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6412, 6411, 6410, 6413, 6409] by Demod 4152 with 4899 at 2,1,3
-Id : 4940, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 ?6409)) [6413, 6409] by Demod 4939 with 4899 at 2,2,2,3
-Id : 4941, {_}: ?7815 =<= join (meet ?7815 ?7815) (join ?7815 ?7815) [7815] by Super 4940 with 4899 at 2,3
-Id : 5068, {_}: ?8129 =<= join (meet (meet ?8129 ?8129) (join ?8129 ?8129)) (meet ?8129 ?8129) [8129] by Super 3217 with 4941 at 2,2,3
-Id : 5072, {_}: ?8141 =<= meet (meet ?8141 (join ?8142 ?8141)) ?8141 [8142, 8141] by Super 4899 with 4941 at 1,1,3
-Id : 5084, {_}: join ?8151 (meet ?8151 (join (meet ?8151 (join ?8152 ?8151)) ?8151)) =>= ?8151 [8152, 8151] by Super 4435 with 5072 at 1,2
-Id : 5705, {_}: ?8954 =<= meet (meet (join ?8955 ?8954) (join ?8956 ?8954)) ?8954 [8956, 8955, 8954] by Super 4899 with 5084 at 2,1,1,3
-Id : 5955, {_}: join ?9293 ?9293 =<= meet (meet (join ?9294 (join ?9293 ?9293)) ?9293) (join ?9293 ?9293) [9294, 9293] by Super 5705 with 4941 at 2,1,3
-Id : 5957, {_}: join ?9299 ?9299 =<= meet (meet ?9299 ?9299) (join ?9299 ?9299) [9299] by Super 5955 with 4941 at 1,1,3
-Id : 6022, {_}: ?8129 =<= join (join ?8129 ?8129) (meet ?8129 ?8129) [8129] by Demod 5068 with 5957 at 1,3
-Id : 7628, {_}: meet ?11050 ?11050 =<= meet (meet (join ?11051 ?11050) ?11050) (meet ?11050 ?11050) [11051, 11050] by Super 7418 with 6022 at 2,1,3
-Id : 6024, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) (join (meet ?9306 ?9306) (join ?9306 ?9306))) =>= join ?9306 ?9306 [9306] by Super 4435 with 5957 at 1,2
-Id : 6144, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) ?9306) =>= join ?9306 ?9306 [9306] by Demod 6024 with 4941 at 2,2,2
-Id : 6187, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Super 5084 with 6144 at 2,1,2,2,2
-Id : 5117, {_}: ?8275 =<= meet (meet ?8275 (join ?8276 ?8275)) ?8275 [8276, 8275] by Super 4899 with 4941 at 1,1,3
-Id : 5128, {_}: join ?8312 ?8312 =<= meet (meet (join ?8312 ?8312) ?8312) (join ?8312 ?8312) [8312] by Super 5117 with 4941 at 2,1,3
-Id : 6199, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (join ?9444 ?9444) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6187 with 5128 at 1,2,2,2
-Id : 6200, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6199 with 6144 at 2,2,2
-Id : 6201, {_}: join (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6200 with 5128 at 2,2
-Id : 6718, {_}: ?10018 =<= meet (meet (meet (join ?10018 ?10018) ?10018) (join ?10019 ?10018)) ?10018 [10019, 10018] by Super 4899 with 6201 at 1,1,3
-Id : 6736, {_}: ?10071 =<= meet (join ?10071 ?10071) ?10071 [10071] by Super 6718 with 5128 at 1,3
-Id : 7650, {_}: meet ?11113 ?11113 =<= meet ?11113 (meet ?11113 ?11113) [11113] by Super 7628 with 6736 at 1,3
-Id : 7731, {_}: join (meet ?11160 ?11160) (meet ?11160 (join ?11160 (meet ?11160 ?11160))) =>= ?11160 [11160] by Super 1544 with 7650 at 1,2
-Id : 6841, {_}: join ?10124 (meet (join ?10124 ?10124) (join (join ?10124 ?10124) ?10124)) =>= join ?10124 ?10124 [10124] by Super 1544 with 6736 at 1,2
-Id : 6817, {_}: join (join ?9306 ?9306) ?9306 =>= join ?9306 ?9306 [9306] by Demod 6144 with 6736 at 2,2
-Id : 6906, {_}: join ?10124 (meet (join ?10124 ?10124) (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6841 with 6817 at 2,2,2
-Id : 1656, {_}: join (meet ?3234 ?3235) (meet ?3234 (join ?3234 ?3235)) =>= ?3234 [3235, 3234] by Demod 1164 with 748 at 1,1,2
-Id : 1661, {_}: join (meet (meet ?3267 ?3268) (meet ?3267 (join ?3267 ?3268))) (meet (meet ?3267 ?3268) ?3267) =>= meet ?3267 ?3268 [3268, 3267] by Super 1656 with 1544 at 2,2,2
-Id : 8992, {_}: meet ?12671 (join ?12672 ?12672) =<= meet (meet (join ?12673 ?12671) ?12672) (meet ?12671 (join ?12672 ?12672)) [12673, 12672, 12671] by Super 7418 with 4940 at 2,1,3
-Id : 6822, {_}: join ?9444 (join ?9444 ?9444) =<= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6201 with 6736 at 1,2
-Id : 6823, {_}: join ?9444 (join ?9444 ?9444) =>= ?9444 [9444] by Demod 6822 with 6736 at 3
-Id : 9646, {_}: meet (join ?13551 ?13551) (join ?13552 ?13552) =<= meet (meet ?13551 ?13552) (meet (join ?13551 ?13551) (join ?13552 ?13552)) [13552, 13551] by Super 8992 with 6823 at 1,1,3
-Id : 9670, {_}: meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624)) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Super 9646 with 7650 at 1,3
-Id : 6333, {_}: meet ?9575 ?9575 =<= meet (meet (join ?9576 (meet ?9575 ?9575)) ?9575) (meet ?9575 ?9575) [9576, 9575] by Super 5705 with 5068 at 2,1,3
-Id : 6336, {_}: meet ?9583 ?9583 =<= meet (meet ?9583 ?9583) (meet ?9583 ?9583) [9583] by Super 6333 with 6022 at 1,1,3
-Id : 6405, {_}: meet ?9659 ?9659 =<= join (join (meet ?9659 ?9659) (meet ?9659 ?9659)) (meet ?9659 ?9659) [9659] by Super 6022 with 6336 at 2,3
-Id : 7013, {_}: meet ?9659 ?9659 =<= join (meet ?9659 ?9659) (meet ?9659 ?9659) [9659] by Demod 6405 with 6817 at 3
-Id : 9768, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Demod 9670 with 7013 at 2,2
-Id : 9769, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (meet ?13624 ?13624)) [13624] by Demod 9768 with 7013 at 2,2,3
-Id : 10286, {_}: join (meet (meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Super 1661 with 9769 at 1,2,2
-Id : 10416, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10286 with 9769 at 1,1,2
-Id : 7044, {_}: meet ?10282 ?10282 =<= join (meet (meet ?10282 ?10282) (meet ?10282 ?10282)) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Super 4940 with 7013 at 2,2,3
-Id : 7086, {_}: meet ?10282 ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7044 with 6336 at 1,3
-Id : 10417, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10416 with 7086 at 2,2,1,2
-Id : 10418, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10417 with 6336 at 2,1,2
-Id : 7467, {_}: meet ?10854 ?10854 =<= meet (meet (join ?10855 ?10854) (meet ?10854 ?10854)) (meet ?10854 ?10854) [10855, 10854] by Super 7418 with 7013 at 2,1,3
-Id : 10419, {_}: join (meet ?14243 ?14243) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10418 with 7467 at 1,2
-Id : 10420, {_}: meet ?14243 ?14243 =<= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10419 with 7086 at 2
-Id : 10421, {_}: meet ?14243 ?14243 =<= meet (join ?14243 ?14243) (meet ?14243 ?14243) [14243] by Demod 10420 with 9769 at 3
-Id : 10483, {_}: join (meet (meet (join ?14359 ?14359) (meet ?14359 ?14359)) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Super 1661 with 10421 at 1,2,2
-Id : 10517, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10483 with 10421 at 1,1,2
-Id : 10518, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) ?14359)) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10517 with 6022 at 2,2,1,2
-Id : 10519, {_}: join (meet (meet ?14359 ?14359) ?14359) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10518 with 6736 at 2,1,2
-Id : 10520, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10519 with 5957 at 2,2
-Id : 10521, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet ?14359 ?14359 [14359] by Demod 10520 with 10421 at 3
-Id : 10992, {_}: join (meet (meet (meet ?14539 ?14539) ?14539) (join ?14539 ?14539)) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Super 4435 with 10521 at 2,2,2
-Id : 8999, {_}: meet (meet ?12702 ?12702) (join ?12702 ?12702) =<= meet (meet (join ?12703 (meet ?12702 ?12702)) ?12702) (join ?12702 ?12702) [12703, 12702] by Super 8992 with 5957 at 2,3
-Id : 10037, {_}: join ?14089 ?14089 =<= meet (meet (join ?14090 (meet ?14089 ?14089)) ?14089) (join ?14089 ?14089) [14090, 14089] by Demod 8999 with 5957 at 2
-Id : 10046, {_}: join ?14111 ?14111 =<= meet (meet (meet ?14111 ?14111) ?14111) (join ?14111 ?14111) [14111] by Super 10037 with 7013 at 1,1,3
-Id : 11120, {_}: join (join ?14539 ?14539) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Demod 10992 with 10046 at 1,2
-Id : 11121, {_}: join (join ?14539 ?14539) (meet ?14539 ?14539) =>= join ?14539 ?14539 [14539] by Demod 11120 with 10421 at 2,2
-Id : 11122, {_}: ?14539 =<= join ?14539 ?14539 [14539] by Demod 11121 with 6022 at 2
-Id : 11192, {_}: join ?10124 (meet ?10124 (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6906 with 11122 at 1,2,2
-Id : 11193, {_}: join ?10124 (meet ?10124 ?10124) =>= join ?10124 ?10124 [10124] by Demod 11192 with 11122 at 2,2,2
-Id : 11194, {_}: join ?10124 (meet ?10124 ?10124) =>= ?10124 [10124] by Demod 11193 with 11122 at 3
-Id : 11206, {_}: join (meet ?11160 ?11160) (meet ?11160 ?11160) =>= ?11160 [11160] by Demod 7731 with 11194 at 2,2,2
-Id : 11207, {_}: meet ?11160 ?11160 =>= ?11160 [11160] by Demod 11206 with 11122 at 2
-Id : 11456, {_}: a === a [] by Demod 2 with 11207 at 2
-Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-% SZS output end CNFRefutation for LAT080-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- join is 95
- meet is 96
- prove_normal_axioms_8 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-Found proof, 13.702259s
-% SZS status Unsatisfiable for LAT087-1.p
-% SZS output start CNFRefutation for LAT087-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) (meet (join (meet ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) (meet ?8 (join ?3 (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Id : 5, {_}: join (meet (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12) (meet (join (meet ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)) (meet (join (meet ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)) (meet ?16 (join ?11 (meet (meet (join ?13 (join ?11 ?14)) (join ?15 ?11)) ?11)))) (join ?10 (join (join (meet ?13 ?11) (meet ?11 ?14)) ?11)))) (join (join (meet ?10 ?11) (meet ?11 (join ?10 ?11))) ?12)) =>= ?11 [16, 15, 14, 13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 ?14 ?15 ?16
-Id : 39, {_}: join (meet (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290) (meet (join (meet ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))) (meet ?289 (join ?287 (join (join (meet ?291 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) ?292)) (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))))))) (join (join (meet ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))) (meet (join (meet ?288 ?289) (meet ?289 (join ?288 ?289))) (join ?287 (join (meet ?288 ?289) (meet ?289 (join ?288 ?289)))))) ?290)) =>= join (meet ?288 ?289) (meet ?289 (join ?288 ?289)) [292, 291, 290, 289, 288, 287] by Super 5 with 4 at 1,2,1,2,2
-Id : 42, {_}: join (meet (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))))) ?324) (meet (join (meet ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 318, 317, 323] by Super 39 with 4 at 2,2,2,1,2,2,2
-Id : 126, {_}: join (meet (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet 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(join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 325, 324, 322, 321, 320, 319, 317, 318, 323] by Demod 126 with 4 at 1,2,1,1,2
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?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [326, 322, 321, 320, 319, 317, 325, 324, 318, 323] by Demod 128 with 4 at 2,1,1,2,1,1,2,2
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?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet 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?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 131 with 4 at 2,1,1,2,2,2,1,2,2
-Id : 133, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))))))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 132 with 4 at 1,2,1,2,2,2,1,2,2
-Id : 134, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))))) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 133 with 4 at 2,2,2,2,1,2,2
-Id : 135, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet (join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))))) (join ?323 ?318))) ?324)) =>= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 134 with 4 at 2,1,1,2,2,2
-Id : 136, {_}: join (meet (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324) (meet (join (meet ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join ?323 (join (join (meet ?325 ?318) (meet ?318 ?326)) ?318)))) (join (join (meet ?323 ?318) (meet ?318 (join ?323 ?318))) ?324)) =?= join (meet (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318))))) (meet (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))) (join (join (meet ?317 ?318) (meet ?318 (join ?317 ?318))) (join (meet ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)) (meet (join (meet ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)) (meet ?322 (join ?318 (meet (meet (join ?319 (join ?318 ?320)) (join ?321 ?318)) ?318)))) (join ?317 (join (join (meet ?319 ?318) (meet ?318 ?320)) ?318)))))) [322, 321, 320, 319, 317, 326, 325, 324, 318, 323] by Demod 135 with 4 at 1,2,1,2,2,2
-Id : 714, {_}: join (meet (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383) (meet (join (meet ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)) (meet (join (meet ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)) (meet (join (meet ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)) (meet ?1390 (join ?1382 (meet (meet (join ?1387 (join ?1382 ?1388)) (join ?1389 ?1382)) ?1382)))) (join ?1386 (join (join (meet ?1387 ?1382) (meet ?1382 ?1388)) ?1382)))) (join ?1381 (join (join (meet ?1384 ?1382) (meet ?1382 ?1385)) ?1382)))) (join (join (meet ?1381 ?1382) (meet ?1382 (join ?1381 ?1382))) ?1383)) =>= ?1382 [1390, 1389, 1388, 1387, 1386, 1385, 1384, 1383, 1382, 1381] by Demod 136 with 4 at 3
-Id : 1147, {_}: join (meet (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512) (meet ?2511 (join (join (meet (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511) (meet ?2511 (join (join (meet ?2510 ?2511) (meet ?2511 (join ?2510 ?2511))) ?2511))) ?2512)) =>= ?2511 [2512, 2511, 2510] by Super 714 with 4 at 1,2,2
-Id : 748, {_}: join (meet (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913) (meet ?1912 (join (join (meet (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912) (meet ?1912 (join (join (meet ?1916 ?1912) (meet ?1912 (join ?1916 ?1912))) ?1912))) ?1913)) =>= ?1912 [1913, 1912, 1916] by Super 714 with 4 at 1,2,2
-Id : 1164, {_}: join (meet (join (meet (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643) (meet ?2643 (join (join (meet (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643) (meet ?2643 (join (join (meet ?2642 ?2643) (meet ?2643 (join ?2642 ?2643))) ?2643))) ?2643))) ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643, 2642] by Super 1147 with 748 at 1,2,2,2
-Id : 1544, {_}: join (meet ?2643 ?2644) (meet ?2643 (join ?2643 ?2644)) =>= ?2643 [2644, 2643] by Demod 1164 with 748 at 1,1,2
-Id : 13, {_}: join (meet (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113) (meet (join (meet ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))) (meet ?107 (join ?112 (join (join (meet ?114 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) ?115)) (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))))))) (join (join (meet ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))) (meet (join (meet ?106 ?107) (meet ?107 (join ?106 ?107))) (join ?112 (join (meet ?106 ?107) (meet ?107 (join ?106 ?107)))))) ?113)) =>= join (meet ?106 ?107) (meet ?107 (join ?106 ?107)) [115, 114, 113, 107, 106, 112] by Super 5 with 4 at 1,2,1,2,2
-Id : 1092, {_}: join (meet (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2039, 2038, 2040] by Super 13 with 748 at 2,2,2,1,2,2,2
-Id : 1218, {_}: join (meet (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1092 with 748 at 2,1,1,1,2
-Id : 1219, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2042, 2041, 2038, 2039, 2040] by Demod 1218 with 748 at 1,2,1,1,2
-Id : 1220, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1219 with 748 at 2,2,2,1,1,2
-Id : 1221, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2043, 2038, 2042, 2041, 2039, 2040] by Demod 1220 with 748 at 2,1,1,2,1,1,2,2
-Id : 1222, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1221 with 748 at 1,2,1,2,1,1,2,2
-Id : 1223, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1222 with 748 at 2,2,1,1,2,2
-Id : 1224, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1223 with 748 at 2,1,1,2,2,2,1,2,2
-Id : 1225, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))))))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1224 with 748 at 1,2,1,2,2,2,1,2,2
-Id : 1226, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)))) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1225 with 748 at 2,2,2,2,1,2,2
-Id : 1227, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet (join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039))) (join ?2040 ?2039))) ?2041)) =>= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1226 with 748 at 2,1,1,2,2,2
-Id : 1228, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =?= join (meet (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039) (meet ?2039 (join (join (meet (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039) (meet ?2039 (join (join (meet ?2038 ?2039) (meet ?2039 (join ?2038 ?2039))) ?2039))) ?2039)) [2038, 2043, 2042, 2041, 2039, 2040] by Demod 1227 with 748 at 1,2,1,2,2,2
-Id : 2531, {_}: join (meet (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436) (meet (join (meet ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)) (meet ?4435 (join ?4434 (join (join (meet ?4437 ?4435) (meet ?4435 ?4438)) ?4435)))) (join (join (meet ?4434 ?4435) (meet ?4435 (join ?4434 ?4435))) ?4436)) =>= ?4435 [4438, 4437, 4436, 4435, 4434] by Demod 1228 with 748 at 3
-Id : 1229, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet (join (meet ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)) (meet ?2039 (join ?2040 (join (join (meet ?2042 ?2039) (meet ?2039 ?2043)) ?2039)))) (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2043, 2042, 2041, 2039, 2040] by Demod 1228 with 748 at 3
-Id : 2544, {_}: join (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))))) ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4552, 4551, 4550, 4549, 4548, 4547] by Super 2531 with 1229 at 1,2,2,2
-Id : 2938, {_}: join (meet ?4548 ?4551) (meet (join (meet (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) (join (join (meet ?4547 ?4548) (meet ?4548 (join ?4547 ?4548))) (join (join (meet ?4552 (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))))) (meet (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))) ?4553)) (join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)))))))) (join ?4548 ?4551)) =>= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4553, 4550, 4549, 4552, 4547, 4551, 4548] by Demod 2544 with 1229 at 1,1,2
-Id : 2939, {_}: join (meet ?4548 ?4551) (meet ?4548 (join ?4548 ?4551)) =?= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4551, 4548] by Demod 2938 with 1229 at 1,2,2
-Id : 2940, {_}: ?4548 =<= join (meet ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548)) (meet ?4548 (join ?4547 (join (join (meet ?4549 ?4548) (meet ?4548 ?4550)) ?4548))) [4550, 4549, 4547, 4548] by Demod 2939 with 1544 at 2
-Id : 2998, {_}: join (meet (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041) (meet ?2039 (join (join (meet ?2040 ?2039) (meet ?2039 (join ?2040 ?2039))) ?2041)) =>= ?2039 [2041, 2039, 2040] by Demod 1229 with 2940 at 1,2,2
-Id : 2540, {_}: join (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))))) ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4516, 4515, 4514, 4513, 4512, 4511, 4510, 4509] by Super 2531 with 4 at 1,2,2,2
-Id : 2926, {_}: join (meet ?4510 ?4515) (meet (join (meet (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) (join (join (meet ?4509 ?4510) (meet ?4510 (join ?4509 ?4510))) (join (join (meet ?4516 (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))))) (meet (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))) ?4517)) (join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)))))))) (join ?4510 ?4515)) =>= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4517, 4514, 4513, 4512, 4511, 4516, 4509, 4515, 4510] by Demod 2540 with 4 at 1,1,2
-Id : 2927, {_}: join (meet ?4510 ?4515) (meet ?4510 (join ?4510 ?4515)) =?= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4515, 4510] by Demod 2926 with 4 at 1,2,2
-Id : 2928, {_}: ?4510 =<= join (meet ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510)) (meet (join (meet ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)) (meet ?4514 (join ?4510 (meet (meet (join ?4511 (join ?4510 ?4512)) (join ?4513 ?4510)) ?4510)))) (join ?4509 (join (join (meet ?4511 ?4510) (meet ?4510 ?4512)) ?4510))) [4514, 4513, 4512, 4511, 4509, 4510] by Demod 2927 with 1544 at 2
-Id : 4152, {_}: ?6409 =<= join (meet ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409)) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6413, 6412, 6411, 6410, 6409] by Super 1544 with 2928 at 2
-Id : 4435, {_}: join (meet ?7069 ?7068) (meet ?7068 (join ?7069 ?7068)) =>= ?7068 [7068, 7069] by Super 2998 with 4152 at 2
-Id : 1656, {_}: join (meet ?3234 ?3235) (meet ?3234 (join ?3234 ?3235)) =>= ?3234 [3235, 3234] by Demod 1164 with 748 at 1,1,2
-Id : 1661, {_}: join (meet (meet ?3267 ?3268) (meet ?3267 (join ?3267 ?3268))) (meet (meet ?3267 ?3268) ?3267) =>= meet ?3267 ?3268 [3268, 3267] by Super 1656 with 1544 at 2,2,2
-Id : 4973, {_}: ?7997 =<= meet (meet (join ?7998 (join ?7997 ?7999)) (join ?8000 ?7997)) ?7997 [8000, 7999, 7998, 7997] by Super 4152 with 4435 at 3
-Id : 7418, {_}: meet ?10627 ?10628 =<= meet (meet (join ?10629 ?10627) (join ?10630 (meet ?10627 ?10628))) (meet ?10627 ?10628) [10630, 10629, 10628, 10627] by Super 4973 with 1544 at 2,1,1,3
-Id : 4899, {_}: ?7757 =<= meet (meet (join ?7758 (join ?7757 ?7759)) (join ?7760 ?7757)) ?7757 [7760, 7759, 7758, 7757] by Super 4152 with 4435 at 3
-Id : 4939, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 (meet (meet (join ?6410 (join ?6409 ?6411)) (join ?6412 ?6409)) ?6409))) [6412, 6411, 6410, 6413, 6409] by Demod 4152 with 4899 at 2,1,3
-Id : 4940, {_}: ?6409 =<= join (meet ?6409 ?6409) (meet ?6413 (join ?6409 ?6409)) [6413, 6409] by Demod 4939 with 4899 at 2,2,2,3
-Id : 8992, {_}: meet ?12671 (join ?12672 ?12672) =<= meet (meet (join ?12673 ?12671) ?12672) (meet ?12671 (join ?12672 ?12672)) [12673, 12672, 12671] by Super 7418 with 4940 at 2,1,3
-Id : 4941, {_}: ?7815 =<= join (meet ?7815 ?7815) (join ?7815 ?7815) [7815] by Super 4940 with 4899 at 2,3
-Id : 5072, {_}: ?8141 =<= meet (meet ?8141 (join ?8142 ?8141)) ?8141 [8142, 8141] by Super 4899 with 4941 at 1,1,3
-Id : 5084, {_}: join ?8151 (meet ?8151 (join (meet ?8151 (join ?8152 ?8151)) ?8151)) =>= ?8151 [8152, 8151] by Super 4435 with 5072 at 1,2
-Id : 5705, {_}: ?8954 =<= meet (meet (join ?8955 ?8954) (join ?8956 ?8954)) ?8954 [8956, 8955, 8954] by Super 4899 with 5084 at 2,1,1,3
-Id : 5955, {_}: join ?9293 ?9293 =<= meet (meet (join ?9294 (join ?9293 ?9293)) ?9293) (join ?9293 ?9293) [9294, 9293] by Super 5705 with 4941 at 2,1,3
-Id : 5957, {_}: join ?9299 ?9299 =<= meet (meet ?9299 ?9299) (join ?9299 ?9299) [9299] by Super 5955 with 4941 at 1,1,3
-Id : 6024, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) (join (meet ?9306 ?9306) (join ?9306 ?9306))) =>= join ?9306 ?9306 [9306] by Super 4435 with 5957 at 1,2
-Id : 6144, {_}: join (join ?9306 ?9306) (meet (join ?9306 ?9306) ?9306) =>= join ?9306 ?9306 [9306] by Demod 6024 with 4941 at 2,2,2
-Id : 6187, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Super 5084 with 6144 at 2,1,2,2,2
-Id : 5117, {_}: ?8275 =<= meet (meet ?8275 (join ?8276 ?8275)) ?8275 [8276, 8275] by Super 4899 with 4941 at 1,1,3
-Id : 5128, {_}: join ?8312 ?8312 =<= meet (meet (join ?8312 ?8312) ?8312) (join ?8312 ?8312) [8312] by Super 5117 with 4941 at 2,1,3
-Id : 6199, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join (join ?9444 ?9444) (meet (join ?9444 ?9444) ?9444))) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6187 with 5128 at 1,2,2,2
-Id : 6200, {_}: join (meet (join ?9444 ?9444) ?9444) (meet (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444)) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6199 with 6144 at 2,2,2
-Id : 6201, {_}: join (meet (join ?9444 ?9444) ?9444) (join ?9444 ?9444) =>= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6200 with 5128 at 2,2
-Id : 6718, {_}: ?10018 =<= meet (meet (meet (join ?10018 ?10018) ?10018) (join ?10019 ?10018)) ?10018 [10019, 10018] by Super 4899 with 6201 at 1,1,3
-Id : 6736, {_}: ?10071 =<= meet (join ?10071 ?10071) ?10071 [10071] by Super 6718 with 5128 at 1,3
-Id : 6822, {_}: join ?9444 (join ?9444 ?9444) =<= meet (join ?9444 ?9444) ?9444 [9444] by Demod 6201 with 6736 at 1,2
-Id : 6823, {_}: join ?9444 (join ?9444 ?9444) =>= ?9444 [9444] by Demod 6822 with 6736 at 3
-Id : 9646, {_}: meet (join ?13551 ?13551) (join ?13552 ?13552) =<= meet (meet ?13551 ?13552) (meet (join ?13551 ?13551) (join ?13552 ?13552)) [13552, 13551] by Super 8992 with 6823 at 1,1,3
-Id : 3035, {_}: ?5143 =<= join (meet ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143)) (meet ?5143 (join ?5144 (join (join (meet ?5145 ?5143) (meet ?5143 ?5146)) ?5143))) [5146, 5145, 5144, 5143] by Demod 2939 with 1544 at 2
-Id : 3039, {_}: ?5175 =<= join (meet ?5174 (join (join (meet ?5175 ?5175) (meet ?5175 (join ?5175 ?5175))) ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Super 3035 with 1544 at 1,2,2,2,3
-Id : 3217, {_}: ?5175 =<= join (meet ?5174 (join ?5175 ?5175)) (meet ?5175 (join ?5174 (join ?5175 ?5175))) [5174, 5175] by Demod 3039 with 1544 at 1,2,1,3
-Id : 5068, {_}: ?8129 =<= join (meet (meet ?8129 ?8129) (join ?8129 ?8129)) (meet ?8129 ?8129) [8129] by Super 3217 with 4941 at 2,2,3
-Id : 6022, {_}: ?8129 =<= join (join ?8129 ?8129) (meet ?8129 ?8129) [8129] by Demod 5068 with 5957 at 1,3
-Id : 7628, {_}: meet ?11050 ?11050 =<= meet (meet (join ?11051 ?11050) ?11050) (meet ?11050 ?11050) [11051, 11050] by Super 7418 with 6022 at 2,1,3
-Id : 7650, {_}: meet ?11113 ?11113 =<= meet ?11113 (meet ?11113 ?11113) [11113] by Super 7628 with 6736 at 1,3
-Id : 9670, {_}: meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624)) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Super 9646 with 7650 at 1,3
-Id : 6333, {_}: meet ?9575 ?9575 =<= meet (meet (join ?9576 (meet ?9575 ?9575)) ?9575) (meet ?9575 ?9575) [9576, 9575] by Super 5705 with 5068 at 2,1,3
-Id : 6336, {_}: meet ?9583 ?9583 =<= meet (meet ?9583 ?9583) (meet ?9583 ?9583) [9583] by Super 6333 with 6022 at 1,1,3
-Id : 6405, {_}: meet ?9659 ?9659 =<= join (join (meet ?9659 ?9659) (meet ?9659 ?9659)) (meet ?9659 ?9659) [9659] by Super 6022 with 6336 at 2,3
-Id : 6817, {_}: join (join ?9306 ?9306) ?9306 =>= join ?9306 ?9306 [9306] by Demod 6144 with 6736 at 2,2
-Id : 7013, {_}: meet ?9659 ?9659 =<= join (meet ?9659 ?9659) (meet ?9659 ?9659) [9659] by Demod 6405 with 6817 at 3
-Id : 9768, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (join (meet ?13624 ?13624) (meet ?13624 ?13624))) [13624] by Demod 9670 with 7013 at 2,2
-Id : 9769, {_}: meet (join ?13624 ?13624) (meet ?13624 ?13624) =<= meet (meet ?13624 ?13624) (meet (join ?13624 ?13624) (meet ?13624 ?13624)) [13624] by Demod 9768 with 7013 at 2,2,3
-Id : 10286, {_}: join (meet (meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Super 1661 with 9769 at 1,2,2
-Id : 10416, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (join (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243))))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10286 with 9769 at 1,1,2
-Id : 7044, {_}: meet ?10282 ?10282 =<= join (meet (meet ?10282 ?10282) (meet ?10282 ?10282)) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Super 4940 with 7013 at 2,2,3
-Id : 7086, {_}: meet ?10282 ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7044 with 6336 at 1,3
-Id : 10417, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet (meet ?14243 ?14243) (meet ?14243 ?14243))) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10416 with 7086 at 2,2,1,2
-Id : 10418, {_}: join (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10417 with 6336 at 2,1,2
-Id : 7467, {_}: meet ?10854 ?10854 =<= meet (meet (join ?10855 ?10854) (meet ?10854 ?10854)) (meet ?10854 ?10854) [10855, 10854] by Super 7418 with 7013 at 2,1,3
-Id : 10419, {_}: join (meet ?14243 ?14243) (meet (meet (join ?14243 ?14243) (meet ?14243 ?14243)) (meet ?14243 ?14243)) =>= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10418 with 7467 at 1,2
-Id : 10420, {_}: meet ?14243 ?14243 =<= meet (meet ?14243 ?14243) (meet (join ?14243 ?14243) (meet ?14243 ?14243)) [14243] by Demod 10419 with 7086 at 2
-Id : 10421, {_}: meet ?14243 ?14243 =<= meet (join ?14243 ?14243) (meet ?14243 ?14243) [14243] by Demod 10420 with 9769 at 3
-Id : 10483, {_}: join (meet (meet (join ?14359 ?14359) (meet ?14359 ?14359)) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Super 1661 with 10421 at 1,2,2
-Id : 10517, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) (join (join ?14359 ?14359) (meet ?14359 ?14359)))) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10483 with 10421 at 1,1,2
-Id : 10518, {_}: join (meet (meet ?14359 ?14359) (meet (join ?14359 ?14359) ?14359)) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10517 with 6022 at 2,2,1,2
-Id : 10519, {_}: join (meet (meet ?14359 ?14359) ?14359) (meet (meet ?14359 ?14359) (join ?14359 ?14359)) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10518 with 6736 at 2,1,2
-Id : 10520, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet (join ?14359 ?14359) (meet ?14359 ?14359) [14359] by Demod 10519 with 5957 at 2,2
-Id : 10521, {_}: join (meet (meet ?14359 ?14359) ?14359) (join ?14359 ?14359) =>= meet ?14359 ?14359 [14359] by Demod 10520 with 10421 at 3
-Id : 10992, {_}: join (meet (meet (meet ?14539 ?14539) ?14539) (join ?14539 ?14539)) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Super 4435 with 10521 at 2,2,2
-Id : 8999, {_}: meet (meet ?12702 ?12702) (join ?12702 ?12702) =<= meet (meet (join ?12703 (meet ?12702 ?12702)) ?12702) (join ?12702 ?12702) [12703, 12702] by Super 8992 with 5957 at 2,3
-Id : 10037, {_}: join ?14089 ?14089 =<= meet (meet (join ?14090 (meet ?14089 ?14089)) ?14089) (join ?14089 ?14089) [14090, 14089] by Demod 8999 with 5957 at 2
-Id : 10046, {_}: join ?14111 ?14111 =<= meet (meet (meet ?14111 ?14111) ?14111) (join ?14111 ?14111) [14111] by Super 10037 with 7013 at 1,1,3
-Id : 11120, {_}: join (join ?14539 ?14539) (meet (join ?14539 ?14539) (meet ?14539 ?14539)) =>= join ?14539 ?14539 [14539] by Demod 10992 with 10046 at 1,2
-Id : 11121, {_}: join (join ?14539 ?14539) (meet ?14539 ?14539) =>= join ?14539 ?14539 [14539] by Demod 11120 with 10421 at 2,2
-Id : 11122, {_}: ?14539 =<= join ?14539 ?14539 [14539] by Demod 11121 with 6022 at 2
-Id : 11280, {_}: ?14616 =<= join (meet (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616) (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) (meet ?14616 (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) [14618, 14617, 14616] by Super 2940 with 11122 at 2,2,3
-Id : 7731, {_}: join (meet ?11160 ?11160) (meet ?11160 (join ?11160 (meet ?11160 ?11160))) =>= ?11160 [11160] by Super 1544 with 7650 at 1,2
-Id : 6841, {_}: join ?10124 (meet (join ?10124 ?10124) (join (join ?10124 ?10124) ?10124)) =>= join ?10124 ?10124 [10124] by Super 1544 with 6736 at 1,2
-Id : 6906, {_}: join ?10124 (meet (join ?10124 ?10124) (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6841 with 6817 at 2,2,2
-Id : 11192, {_}: join ?10124 (meet ?10124 (join ?10124 ?10124)) =>= join ?10124 ?10124 [10124] by Demod 6906 with 11122 at 1,2,2
-Id : 11193, {_}: join ?10124 (meet ?10124 ?10124) =>= join ?10124 ?10124 [10124] by Demod 11192 with 11122 at 2,2,2
-Id : 11194, {_}: join ?10124 (meet ?10124 ?10124) =>= ?10124 [10124] by Demod 11193 with 11122 at 3
-Id : 11206, {_}: join (meet ?11160 ?11160) (meet ?11160 ?11160) =>= ?11160 [11160] by Demod 7731 with 11194 at 2,2,2
-Id : 11207, {_}: meet ?11160 ?11160 =>= ?11160 [11160] by Demod 11206 with 11122 at 2
-Id : 11417, {_}: ?14616 =<= join (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616) (meet ?14616 (join (join (meet ?14617 ?14616) (meet ?14616 ?14618)) ?14616)) [14618, 14617, 14616] by Demod 11280 with 11207 at 1,3
-Id : 11210, {_}: ?10282 =<= join (meet ?10282 ?10282) (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 7086 with 11207 at 2
-Id : 11211, {_}: ?10282 =<= join ?10282 (meet ?10283 (meet ?10282 ?10282)) [10283, 10282] by Demod 11210 with 11207 at 1,3
-Id : 11212, {_}: ?10282 =<= join ?10282 (meet ?10283 ?10282) [10283, 10282] by Demod 11211 with 11207 at 2,2,3
-Id : 12052, {_}: ?15606 =<= join (join (meet ?15607 ?15606) (meet ?15606 ?15608)) ?15606 [15608, 15607, 15606] by Demod 11417 with 11212 at 3
-Id : 12070, {_}: ?15688 =<= join (join ?15688 (meet ?15688 ?15689)) ?15688 [15689, 15688] by Super 12052 with 11207 at 1,1,3
-Id : 12545, {_}: join (meet (join ?16137 (meet ?16137 ?16138)) ?16137) (meet (join ?16137 (meet ?16137 ?16138)) ?16137) =>= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Super 1544 with 12070 at 2,2,2
-Id : 12628, {_}: meet (join ?16137 (meet ?16137 ?16138)) ?16137 =>= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Demod 12545 with 11122 at 2
-Id : 11515, {_}: ?14875 =<= meet (meet (join ?14876 (join ?14875 ?14877)) ?14875) ?14875 [14877, 14876, 14875] by Super 4899 with 11122 at 2,1,3
-Id : 11529, {_}: ?14934 =<= meet (meet (join ?14934 ?14935) ?14934) ?14934 [14935, 14934] by Super 11515 with 11122 at 1,1,3
-Id : 12090, {_}: ?15773 =<= join (meet ?15774 ?15773) ?15773 [15774, 15773] by Super 12052 with 11212 at 1,3
-Id : 12194, {_}: join (meet (meet ?15862 ?15861) ?15861) (meet (meet ?15862 ?15861) ?15861) =>= meet ?15862 ?15861 [15861, 15862] by Super 1544 with 12090 at 2,2,2
-Id : 12248, {_}: meet (meet ?15862 ?15861) ?15861 =>= meet ?15862 ?15861 [15861, 15862] by Demod 12194 with 11122 at 2
-Id : 12318, {_}: ?14934 =<= meet (join ?14934 ?14935) ?14934 [14935, 14934] by Demod 11529 with 12248 at 3
-Id : 12629, {_}: ?16137 =<= join ?16137 (meet ?16137 ?16138) [16138, 16137] by Demod 12628 with 12318 at 2
-Id : 12769, {_}: a === a [] by Demod 2 with 12629 at 2
-Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-% SZS output end CNFRefutation for LAT087-1.p
-Order
- == is 100
- _ is 99
- a is 97
- b is 98
- join is 94
- meet is 96
- prove_wal_axioms_2 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-Found proof, 13.254951s
-% SZS status Unsatisfiable for LAT093-1.p
-% SZS output start CNFRefutation for LAT093-1.p
-Id : 4, {_}: join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) (meet (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) (meet (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) (meet ?7 (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) =>= ?3 [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Id : 5, {_}: join (meet (join (meet ?9 ?10) (meet ?10 (join ?9 ?10))) ?11) (meet (join (meet ?9 (join (join (meet ?10 ?12) (meet ?13 ?10)) ?10)) (meet (join (meet ?10 (meet (meet (join ?10 ?12) (join ?13 ?10)) ?10)) (meet ?14 (join ?10 (meet (meet (join ?10 ?12) (join ?13 ?10)) ?10)))) (join ?9 (join (join (meet ?10 ?12) (meet ?13 ?10)) ?10)))) (join (join (meet ?9 ?10) (meet ?10 (join ?9 ?10))) ?11)) =>= ?10 [14, 13, 12, 11, 10, 9] by single_axiom ?9 ?10 ?11 ?12 ?13 ?14
-Id : 33, {_}: join (meet (join (meet ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))) (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) (join ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))))) ?218) (meet (join (meet ?215 (join (join (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) ?219) (meet ?220 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (meet ?217 (join ?215 (join (join (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) ?219) (meet ?220 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))) (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))))))) (join (join (meet ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))) (meet (join (meet ?216 ?217) (meet ?217 (join ?216 ?217))) (join ?215 (join (meet ?216 ?217) (meet ?217 (join ?216 ?217)))))) ?218)) =>= join (meet ?216 ?217) (meet ?217 (join ?216 ?217)) [220, 219, 218, 217, 216, 215] by Super 5 with 4 at 1,2,1,2,2
-Id : 36, {_}: join (meet (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))))) ?250) (meet (join (meet ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join 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?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 245, 244, 249] by Super 33 with 4 at 2,2,2,1,2,2,2
-Id : 118, {_}: join (meet (join (meet ?249 ?245) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) 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?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 244, 245, 249] by Demod 36 with 4 at 2,1,1,1,2
-Id : 119, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 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(meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 250, 248, 247, 246, 244, 245, 249] by Demod 118 with 4 at 1,2,1,1,2
-Id : 120, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet 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(join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [252, 251, 248, 247, 246, 244, 250, 245, 249] by Demod 119 with 4 at 2,2,2,1,1,2
-Id : 121, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 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?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 120 with 4 at 1,1,1,2,1,1,2,2
-Id : 122, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) 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?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 121 with 4 at 2,2,1,2,1,1,2,2
-Id : 123, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join 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(meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 122 with 4 at 2,2,1,1,2,2
-Id : 124, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 123 with 4 at 1,1,1,2,2,2,1,2,2
-Id : 125, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))))))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 124 with 4 at 2,2,1,2,2,2,1,2,2
-Id : 126, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))))) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 125 with 4 at 2,2,2,2,1,2,2
-Id : 127, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 ?245) (meet (join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))))) (join ?249 ?245))) ?250)) =>= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 126 with 4 at 2,1,1,2,2,2
-Id : 128, {_}: join (meet (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250) (meet (join (meet ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join ?249 (join (join (meet ?245 ?251) (meet ?252 ?245)) ?245)))) (join (join (meet ?249 ?245) (meet ?245 (join ?249 ?245))) ?250)) =?= join (meet (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245))))) (meet (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))) (join (join (meet ?244 ?245) (meet ?245 (join ?244 ?245))) (join (meet ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)) (meet (join (meet ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)) (meet ?248 (join ?245 (meet (meet (join ?245 ?246) (join ?247 ?245)) ?245)))) (join ?244 (join (join (meet ?245 ?246) (meet ?247 ?245)) ?245)))))) [248, 247, 246, 244, 252, 251, 250, 245, 249] by Demod 127 with 4 at 1,2,1,2,2,2
-Id : 704, {_}: join (meet (join (meet ?1213 ?1214) (meet ?1214 (join ?1213 ?1214))) ?1215) (meet (join (meet ?1213 (join (join (meet ?1214 ?1216) (meet ?1217 ?1214)) ?1214)) (meet (join (meet ?1218 (join (join (meet ?1214 ?1219) (meet ?1220 ?1214)) ?1214)) (meet (join (meet ?1214 (meet (meet (join ?1214 ?1219) (join ?1220 ?1214)) ?1214)) (meet ?1221 (join ?1214 (meet (meet (join ?1214 ?1219) (join ?1220 ?1214)) ?1214)))) (join ?1218 (join (join (meet ?1214 ?1219) (meet ?1220 ?1214)) ?1214)))) (join ?1213 (join (join (meet ?1214 ?1216) (meet ?1217 ?1214)) ?1214)))) (join (join (meet ?1213 ?1214) (meet ?1214 (join ?1213 ?1214))) ?1215)) =>= ?1214 [1221, 1220, 1219, 1218, 1217, 1216, 1215, 1214, 1213] by Demod 128 with 4 at 3
-Id : 1103, {_}: join (meet (join (meet (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032) (meet ?2032 (join (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032))) ?2033) (meet ?2032 (join (join (meet (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032) (meet ?2032 (join (join (meet ?2031 ?2032) (meet ?2032 (join ?2031 ?2032))) ?2032))) ?2033)) =>= ?2032 [2033, 2032, 2031] by Super 704 with 4 at 1,2,2
-Id : 726, {_}: join (meet (join (meet (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532) (meet ?1532 (join (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532))) ?1533) (meet ?1532 (join (join (meet (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532) (meet ?1532 (join (join (meet ?1536 ?1532) (meet ?1532 (join ?1536 ?1532))) ?1532))) ?1533)) =>= ?1532 [1533, 1532, 1536] by Super 704 with 4 at 1,2,2
-Id : 1120, {_}: join (meet (join (meet (join (meet (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156) (meet ?2156 (join (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156))) ?2156) (meet ?2156 (join (join (meet (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156) (meet ?2156 (join (join (meet ?2155 ?2156) (meet ?2156 (join ?2155 ?2156))) ?2156))) ?2156))) ?2157) (meet ?2156 (join ?2156 ?2157)) =>= ?2156 [2157, 2156, 2155] by Super 1103 with 726 at 1,2,2,2
-Id : 1492, {_}: join (meet ?2156 ?2157) (meet ?2156 (join ?2156 ?2157)) =>= ?2156 [2157, 2156] by Demod 1120 with 726 at 1,1,2
-Id : 12, {_}: join (meet (join (meet ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))) (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) (join ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))))) ?87) (meet (join (meet ?86 (join (join (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) ?88) (meet ?89 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (meet ?82 (join ?86 (join (join (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) ?88) (meet ?89 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))) (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))))))) (join (join (meet ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))) (meet (join (meet ?81 ?82) (meet ?82 (join ?81 ?82))) (join ?86 (join (meet ?81 ?82) (meet ?82 (join ?81 ?82)))))) ?87)) =>= join (meet ?81 ?82) (meet ?82 (join ?81 ?82)) [89, 88, 87, 82, 81, 86] by Super 5 with 4 at 1,2,1,2,2
-Id : 1056, {_}: join (meet (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1647, 1646, 1648] by Super 12 with 726 at 2,2,2,1,2,2,2
-Id : 1168, {_}: join (meet (join (meet ?1648 ?1647) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1646, 1647, 1648] by Demod 1056 with 726 at 2,1,1,1,2
-Id : 1169, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1649, 1646, 1647, 1648] by Demod 1168 with 726 at 1,2,1,1,2
-Id : 1170, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1651, 1650, 1646, 1649, 1647, 1648] by Demod 1169 with 726 at 2,2,2,1,1,2
-Id : 1171, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1170 with 726 at 1,1,1,2,1,1,2,2
-Id : 1172, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1171 with 726 at 2,2,1,2,1,1,2,2
-Id : 1173, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1172 with 726 at 2,2,1,1,2,2
-Id : 1174, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1173 with 726 at 1,1,1,2,2,2,1,2,2
-Id : 1175, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))))))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1174 with 726 at 2,2,1,2,2,2,1,2,2
-Id : 1176, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)))) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1175 with 726 at 2,2,2,2,1,2,2
-Id : 1177, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet (join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647))) (join ?1648 ?1647))) ?1649)) =>= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1176 with 726 at 2,1,1,2,2,2
-Id : 1178, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =?= join (meet (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647) (meet ?1647 (join (join (meet (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647) (meet ?1647 (join (join (meet ?1646 ?1647) (meet ?1647 (join ?1646 ?1647))) ?1647))) ?1647)) [1646, 1651, 1650, 1649, 1647, 1648] by Demod 1177 with 726 at 1,2,1,2,2,2
-Id : 1179, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet (join (meet ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)) (meet ?1647 (join ?1648 (join (join (meet ?1647 ?1650) (meet ?1651 ?1647)) ?1647)))) (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =>= ?1647 [1651, 1650, 1649, 1647, 1648] by Demod 1178 with 726 at 3
-Id : 2457, {_}: join (meet (join (meet ?3744 ?3745) (meet ?3745 (join ?3744 ?3745))) ?3746) (meet (join (meet ?3744 (join (join (meet ?3745 ?3747) (meet ?3748 ?3745)) ?3745)) (meet ?3745 (join ?3744 (join (join (meet ?3745 ?3747) (meet ?3748 ?3745)) ?3745)))) (join (join (meet ?3744 ?3745) (meet ?3745 (join ?3744 ?3745))) ?3746)) =>= ?3745 [3748, 3747, 3746, 3745, 3744] by Demod 1178 with 726 at 3
-Id : 2470, {_}: join (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))))))) ?3857) (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))))) (join ?3854 ?3857)) =>= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3859, 3858, 3857, 3856, 3855, 3854, 3853] by Super 2457 with 1179 at 1,2,2,2
-Id : 2846, {_}: join (meet ?3854 ?3857) (meet (join (meet (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) (join (join (meet ?3853 ?3854) (meet ?3854 (join ?3853 ?3854))) (join (join (meet (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))) ?3858) (meet ?3859 (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))) (join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)))))))) (join ?3854 ?3857)) =>= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3859, 3858, 3856, 3855, 3853, 3857, 3854] by Demod 2470 with 1179 at 1,1,2
-Id : 2847, {_}: join (meet ?3854 ?3857) (meet ?3854 (join ?3854 ?3857)) =?= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3856, 3855, 3853, 3857, 3854] by Demod 2846 with 1179 at 1,2,2
-Id : 2848, {_}: ?3854 =<= join (meet ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854)) (meet ?3854 (join ?3853 (join (join (meet ?3854 ?3855) (meet ?3856 ?3854)) ?3854))) [3856, 3855, 3853, 3854] by Demod 2847 with 1492 at 2
-Id : 2894, {_}: join (meet (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649) (meet ?1647 (join (join (meet ?1648 ?1647) (meet ?1647 (join ?1648 ?1647))) ?1649)) =>= ?1647 [1649, 1647, 1648] by Demod 1179 with 2848 at 1,2,2
-Id : 2466, {_}: join (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))))))) ?3822) (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))))) (join ?3818 ?3822)) =>= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3824, 3823, 3822, 3821, 3820, 3819, 3818, 3817] by Super 2457 with 4 at 1,2,2,2
-Id : 2834, {_}: join (meet ?3818 ?3822) (meet (join (meet (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) (join (join (meet ?3817 ?3818) (meet ?3818 (join ?3817 ?3818))) (join (join (meet (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))) ?3823) (meet ?3824 (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))) (join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)))))))) (join ?3818 ?3822)) =>= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3824, 3823, 3821, 3820, 3819, 3817, 3822, 3818] by Demod 2466 with 4 at 1,1,2
-Id : 2835, {_}: join (meet ?3818 ?3822) (meet ?3818 (join ?3818 ?3822)) =?= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3821, 3820, 3819, 3817, 3822, 3818] by Demod 2834 with 4 at 1,2,2
-Id : 2836, {_}: ?3818 =<= join (meet ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818)) (meet (join (meet ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)) (meet ?3821 (join ?3818 (meet (meet (join ?3818 ?3819) (join ?3820 ?3818)) ?3818)))) (join ?3817 (join (join (meet ?3818 ?3819) (meet ?3820 ?3818)) ?3818))) [3821, 3820, 3819, 3817, 3818] by Demod 2835 with 1492 at 2
-Id : 3353, {_}: ?4683 =<= join (meet ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683)) (meet ?4686 (join ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683))) [4686, 4685, 4684, 4683] by Super 2894 with 2836 at 2
-Id : 3629, {_}: join (meet ?5382 ?5381) (meet ?5381 (join ?5382 ?5381)) =>= ?5381 [5381, 5382] by Super 2894 with 3353 at 2
-Id : 4066, {_}: ?5811 =<= meet (meet (join ?5811 ?5812) (join ?5813 ?5811)) ?5811 [5813, 5812, 5811] by Super 3353 with 3629 at 3
-Id : 4517, {_}: meet ?6536 ?6537 =<= meet (meet ?6537 (join ?6538 (meet ?6536 ?6537))) (meet ?6536 ?6537) [6538, 6537, 6536] by Super 4066 with 3629 at 1,1,3
-Id : 4020, {_}: ?5649 =<= meet (meet (join ?5649 ?5650) (join ?5651 ?5649)) ?5649 [5651, 5650, 5649] by Super 3353 with 3629 at 3
-Id : 4518, {_}: meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542 =<= meet (meet ?6542 (join ?6543 (meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542))) ?6542 [6543, 6541, 6540, 6542] by Super 4517 with 4020 at 2,3
-Id : 4585, {_}: ?6542 =<= meet (meet ?6542 (join ?6543 (meet (meet (join ?6542 ?6540) (join ?6541 ?6542)) ?6542))) ?6542 [6541, 6540, 6543, 6542] by Demod 4518 with 4020 at 2
-Id : 4586, {_}: ?6542 =<= meet (meet ?6542 (join ?6543 ?6542)) ?6542 [6543, 6542] by Demod 4585 with 4020 at 2,2,1,3
-Id : 1596, {_}: join (meet ?2660 ?2661) (meet ?2660 (join ?2660 ?2661)) =>= ?2660 [2661, 2660] by Demod 1120 with 726 at 1,1,2
-Id : 1601, {_}: join (meet (meet ?2691 ?2692) (meet ?2691 (join ?2691 ?2692))) (meet (meet ?2691 ?2692) ?2691) =>= meet ?2691 ?2692 [2692, 2691] by Super 1596 with 1492 at 2,2,2
-Id : 4161, {_}: meet ?6000 ?6001 =<= meet (meet ?6000 (join ?6002 (meet ?6000 ?6001))) (meet ?6000 ?6001) [6002, 6001, 6000] by Super 4066 with 1492 at 1,1,3
-Id : 4166, {_}: meet ?6025 (join ?6025 ?6024) =<= meet (meet ?6025 ?6025) (meet ?6025 (join ?6025 ?6024)) [6024, 6025] by Super 4161 with 1492 at 2,1,3
-Id : 4239, {_}: join (meet ?6108 (join ?6108 ?6108)) (meet (meet ?6108 ?6108) ?6108) =>= meet ?6108 ?6108 [6108] by Super 1601 with 4166 at 1,2
-Id : 1974, {_}: join (meet (meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900))) (meet (meet ?2899 ?2900) ?2899)) (meet (meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900))) (meet ?2899 ?2900)) =>= meet (meet ?2899 ?2900) (meet ?2899 (join ?2899 ?2900)) [2900, 2899] by Super 1492 with 1601 at 2,2,2
-Id : 4530, {_}: meet ?6595 (join ?6595 ?6594) =<= meet (meet (join ?6595 ?6594) ?6595) (meet ?6595 (join ?6595 ?6594)) [6594, 6595] by Super 4517 with 1492 at 2,1,3
-Id : 4634, {_}: join ?6728 (meet ?6728 (join (meet ?6728 (join ?6729 ?6728)) ?6728)) =>= ?6728 [6729, 6728] by Super 3629 with 4586 at 1,2
-Id : 5854, {_}: meet ?8039 (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) =<= meet (meet (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) ?8039) (meet ?8039 ?8039) [8040, 8039] by Super 4530 with 4634 at 2,2,3
-Id : 5885, {_}: meet ?8039 ?8039 =<= meet (meet (join ?8039 (meet ?8039 (join (meet ?8039 (join ?8040 ?8039)) ?8039))) ?8039) (meet ?8039 ?8039) [8040, 8039] by Demod 5854 with 4634 at 2,2
-Id : 5886, {_}: meet ?8039 ?8039 =<= meet (meet ?8039 ?8039) (meet ?8039 ?8039) [8039] by Demod 5885 with 4634 at 1,1,3
-Id : 5940, {_}: join (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Super 1974 with 5886 at 2,2,2
-Id : 6002, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 5940 with 4166 at 1,1,2
-Id : 6003, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6002 with 5886 at 1,2,1,2
-Id : 6004, {_}: join (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet ?8123 ?8123)) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6003 with 5886 at 2,1,2
-Id : 6005, {_}: join (meet ?8123 ?8123) (meet (meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)))) (meet ?8123 ?8123)) =>= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6004 with 4586 at 1,2
-Id : 6006, {_}: join (meet ?8123 ?8123) (meet (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) (meet ?8123 ?8123)) =<= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6005 with 4166 at 1,2,2
-Id : 6007, {_}: join (meet ?8123 ?8123) (meet ?8123 ?8123) =<= meet (meet (meet ?8123 ?8123) (meet ?8123 ?8123)) (meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123))) [8123] by Demod 6006 with 4586 at 2,2
-Id : 6008, {_}: join (meet ?8123 ?8123) (meet ?8123 ?8123) =<= meet (meet ?8123 ?8123) (join (meet ?8123 ?8123) (meet ?8123 ?8123)) [8123] by Demod 6007 with 4166 at 3
-Id : 7068, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet (meet (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355)) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Super 4239 with 6008 at 1,2
-Id : 7098, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet (meet ?9355 ?9355) (meet ?9355 ?9355)) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Demod 7068 with 5886 at 1,2,2
-Id : 7099, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355) =>= meet (meet ?9355 ?9355) (meet ?9355 ?9355) [9355] by Demod 7098 with 5886 at 2,2
-Id : 7100, {_}: join (join (meet ?9355 ?9355) (meet ?9355 ?9355)) (meet ?9355 ?9355) =>= meet ?9355 ?9355 [9355] by Demod 7099 with 5886 at 3
-Id : 7401, {_}: meet ?9521 ?9521 =<= meet (meet (join (meet ?9521 ?9521) ?9522) (meet ?9521 ?9521)) (meet ?9521 ?9521) [9522, 9521] by Super 4020 with 7100 at 2,1,3
-Id : 13724, {_}: join (meet ?15407 ?15407) (meet (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (join (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (meet ?15407 ?15407))) =>= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Super 1492 with 7401 at 1,2
-Id : 4041, {_}: ?4683 =<= join (meet ?4683 ?4683) (meet ?4686 (join ?4683 (meet (meet (join ?4683 ?4684) (join ?4685 ?4683)) ?4683))) [4685, 4684, 4686, 4683] by Demod 3353 with 4020 at 2,1,3
-Id : 4042, {_}: ?4683 =<= join (meet ?4683 ?4683) (meet ?4686 (join ?4683 ?4683)) [4686, 4683] by Demod 4041 with 4020 at 2,2,2,3
-Id : 4536, {_}: meet ?6617 (join ?6616 ?6616) =<= meet (meet (join ?6616 ?6616) ?6616) (meet ?6617 (join ?6616 ?6616)) [6616, 6617] by Super 4517 with 4042 at 2,1,3
-Id : 7400, {_}: join (meet (join (meet ?9519 ?9519) (meet ?9519 ?9519)) (meet ?9519 ?9519)) (meet (meet ?9519 ?9519) (meet ?9519 ?9519)) =>= meet ?9519 ?9519 [9519] by Super 3629 with 7100 at 2,2,2
-Id : 7034, {_}: meet ?9263 ?9263 =<= meet (join (meet ?9263 ?9263) (meet ?9263 ?9263)) (meet ?9263 ?9263) [9263] by Super 4586 with 6008 at 1,3
-Id : 7430, {_}: join (meet ?9519 ?9519) (meet (meet ?9519 ?9519) (meet ?9519 ?9519)) =>= meet ?9519 ?9519 [9519] by Demod 7400 with 7034 at 1,2
-Id : 7431, {_}: join (meet ?9519 ?9519) (meet ?9519 ?9519) =>= meet ?9519 ?9519 [9519] by Demod 7430 with 5886 at 2,2
-Id : 7539, {_}: meet ?9566 (join (meet ?9565 ?9565) (meet ?9565 ?9565)) =<= meet (meet (join (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Super 4536 with 7431 at 2,2,3
-Id : 7732, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet (join (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7539 with 7431 at 2,2
-Id : 7733, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet (meet ?9565 ?9565) (meet ?9565 ?9565)) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7732 with 7431 at 1,1,3
-Id : 7734, {_}: meet ?9566 (meet ?9565 ?9565) =<= meet (meet ?9565 ?9565) (meet ?9566 (meet ?9565 ?9565)) [9565, 9566] by Demod 7733 with 5886 at 1,3
-Id : 7988, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet (meet ?9922 ?9922) (join (meet ?9922 ?9922) (meet ?9921 (meet ?9922 ?9922)))) =>= meet ?9922 ?9922 [9922, 9921] by Super 1492 with 7734 at 1,2
-Id : 7550, {_}: meet ?9591 ?9591 =<= join (meet (meet ?9591 ?9591) (meet ?9591 ?9591)) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Super 4042 with 7431 at 2,2,3
-Id : 7707, {_}: meet ?9591 ?9591 =<= join (meet ?9591 ?9591) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 7550 with 5886 at 1,3
-Id : 8067, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet (meet ?9922 ?9922) (meet ?9922 ?9922)) =>= meet ?9922 ?9922 [9922, 9921] by Demod 7988 with 7707 at 2,2,2
-Id : 8068, {_}: join (meet ?9921 (meet ?9922 ?9922)) (meet ?9922 ?9922) =>= meet ?9922 ?9922 [9922, 9921] by Demod 8067 with 5886 at 2,2
-Id : 13909, {_}: join (meet ?15407 ?15407) (meet (meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407)) (meet ?15407 ?15407)) =>= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13724 with 8068 at 2,2,2
-Id : 13910, {_}: meet ?15407 ?15407 =<= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13909 with 7707 at 2
-Id : 5848, {_}: join (meet ?8021 (meet ?8021 (join (meet ?8021 (join ?8022 ?8021)) ?8021))) (meet ?8021 ?8021) =>= ?8021 [8022, 8021] by Super 1492 with 4634 at 2,2,2
-Id : 4640, {_}: ?6750 =<= meet (meet ?6750 (join ?6751 ?6750)) ?6750 [6751, 6750] by Demod 4585 with 4020 at 2,2,1,3
-Id : 4645, {_}: meet ?6768 (join ?6767 ?6768) =<= meet (meet (meet ?6768 (join ?6767 ?6768)) ?6768) (meet ?6768 (join ?6767 ?6768)) [6767, 6768] by Super 4640 with 3629 at 2,1,3
-Id : 4708, {_}: meet ?6768 (join ?6767 ?6768) =<= meet ?6768 (meet ?6768 (join ?6767 ?6768)) [6767, 6768] by Demod 4645 with 4586 at 1,3
-Id : 5910, {_}: join (meet ?8021 (join (meet ?8021 (join ?8022 ?8021)) ?8021)) (meet ?8021 ?8021) =>= ?8021 [8022, 8021] by Demod 5848 with 4708 at 1,2
-Id : 9401, {_}: meet (meet ?11248 ?11249) ?11248 =<= meet (meet (meet ?11248 ?11249) (meet ?11248 ?11249)) (meet (meet ?11248 ?11249) ?11248) [11249, 11248] by Super 4161 with 1601 at 2,1,3
-Id : 9402, {_}: meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Super 9401 with 4020 at 1,2,3
-Id : 9552, {_}: meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253) (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Demod 9402 with 4020 at 1,2
-Id : 9553, {_}: meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253)) =<= meet (meet ?11253 (meet (meet (join ?11253 ?11251) (join ?11252 ?11253)) ?11253)) (meet ?11253 (meet (join ?11253 ?11251) (join ?11252 ?11253))) [11252, 11251, 11253] by Demod 9552 with 4020 at 1,1,3
-Id : 18238, {_}: meet ?19914 (meet (join ?19914 ?19915) (join ?19916 ?19914)) =<= meet (meet ?19914 ?19914) (meet ?19914 (meet (join ?19914 ?19915) (join ?19916 ?19914))) [19916, 19915, 19914] by Demod 9553 with 4020 at 2,1,3
-Id : 11581, {_}: meet ?13378 (join ?13379 ?13379) =<= meet (meet (meet ?13378 (join ?13379 ?13379)) ?13379) (meet ?13378 (join ?13379 ?13379)) [13379, 13378] by Super 4640 with 4042 at 2,1,3
-Id : 11600, {_}: meet (join ?13442 ?13441) (join ?13442 ?13442) =<= meet ?13442 (meet (join ?13442 ?13441) (join ?13442 ?13442)) [13441, 13442] by Super 11581 with 4020 at 1,3
-Id : 18285, {_}: meet ?20107 (meet (join ?20107 ?20106) (join ?20107 ?20107)) =<= meet (meet ?20107 ?20107) (meet (join ?20107 ?20106) (join ?20107 ?20107)) [20106, 20107] by Super 18238 with 11600 at 2,3
-Id : 18491, {_}: meet (join ?20107 ?20106) (join ?20107 ?20107) =<= meet (meet ?20107 ?20107) (meet (join ?20107 ?20106) (join ?20107 ?20107)) [20106, 20107] by Demod 18285 with 11600 at 2
-Id : 18514, {_}: join (meet (join ?20180 ?20181) (join ?20180 ?20180)) (meet (meet (join ?20180 ?20181) (join ?20180 ?20180)) (join (meet ?20180 ?20180) (meet (join ?20180 ?20181) (join ?20180 ?20180)))) =>= meet (join ?20180 ?20181) (join ?20180 ?20180) [20181, 20180] by Super 3629 with 18491 at 1,2
-Id : 18667, {_}: join (meet (join ?20180 ?20181) (join ?20180 ?20180)) (meet (meet (join ?20180 ?20181) (join ?20180 ?20180)) ?20180) =>= meet (join ?20180 ?20181) (join ?20180 ?20180) [20181, 20180] by Demod 18514 with 4042 at 2,2,2
-Id : 18856, {_}: join (meet (join ?20559 ?20560) (join ?20559 ?20559)) ?20559 =>= meet (join ?20559 ?20560) (join ?20559 ?20559) [20560, 20559] by Demod 18667 with 4020 at 2,2
-Id : 4044, {_}: join ?5696 (meet ?5696 (join (meet (join ?5696 ?5697) (join ?5698 ?5696)) ?5696)) =>= ?5696 [5698, 5697, 5696] by Super 3629 with 4020 at 1,2
-Id : 18864, {_}: join (meet ?20588 (join ?20588 ?20588)) ?20588 =<= meet (join ?20588 (meet ?20588 (join (meet (join ?20588 ?20586) (join ?20587 ?20588)) ?20588))) (join ?20588 ?20588) [20587, 20586, 20588] by Super 18856 with 4044 at 1,1,2
-Id : 19017, {_}: join (meet ?20588 (join ?20588 ?20588)) ?20588 =>= meet ?20588 (join ?20588 ?20588) [20588] by Demod 18864 with 4044 at 1,3
-Id : 19112, {_}: join (meet ?20758 (meet ?20758 (join ?20758 ?20758))) (meet ?20758 ?20758) =>= ?20758 [20758] by Super 5910 with 19017 at 2,1,2
-Id : 19134, {_}: join (meet ?20758 (join ?20758 ?20758)) (meet ?20758 ?20758) =>= ?20758 [20758] by Demod 19112 with 4708 at 1,2
-Id : 12695, {_}: ?14373 =<= join (meet ?14375 (join (join (meet ?14373 (join (meet ?14373 (join ?14374 ?14373)) ?14373)) (meet ?14373 ?14373)) ?14373)) (meet ?14373 (join ?14375 (join ?14373 ?14373))) [14374, 14375, 14373] by Super 2848 with 5910 at 1,2,2,2,3
-Id : 12774, {_}: ?14373 =<= join (meet ?14375 (join ?14373 ?14373)) (meet ?14373 (join ?14375 (join ?14373 ?14373))) [14375, 14373] by Demod 12695 with 5910 at 1,2,1,3
-Id : 23235, {_}: join ?23859 ?23859 =>= ?23859 [23859] by Super 4042 with 12774 at 3
-Id : 23429, {_}: join (meet ?20758 ?20758) (meet ?20758 ?20758) =>= ?20758 [20758] by Demod 19134 with 23235 at 2,1,2
-Id : 23430, {_}: meet ?20758 ?20758 =>= ?20758 [20758] by Demod 23429 with 23235 at 2
-Id : 23444, {_}: ?15407 =<= meet (join (meet ?15407 ?15407) ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 13910 with 23430 at 2
-Id : 23445, {_}: ?15407 =<= meet (join ?15407 ?15408) (meet ?15407 ?15407) [15408, 15407] by Demod 23444 with 23430 at 1,1,3
-Id : 23446, {_}: ?15407 =<= meet (join ?15407 ?15408) ?15407 [15408, 15407] by Demod 23445 with 23430 at 2,3
-Id : 23618, {_}: ?24079 =<= join (meet (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079) (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) (meet ?24079 (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) [24081, 24080, 24079] by Super 2848 with 23235 at 2,2,3
-Id : 23720, {_}: ?24079 =<= join (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079) (meet ?24079 (join (join (meet ?24079 ?24080) (meet ?24081 ?24079)) ?24079)) [24081, 24080, 24079] by Demod 23618 with 23430 at 1,3
-Id : 23476, {_}: ?9591 =<= join (meet ?9591 ?9591) (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 7707 with 23430 at 2
-Id : 23477, {_}: ?9591 =<= join ?9591 (meet ?9592 (meet ?9591 ?9591)) [9592, 9591] by Demod 23476 with 23430 at 1,3
-Id : 23478, {_}: ?9591 =<= join ?9591 (meet ?9592 ?9591) [9592, 9591] by Demod 23477 with 23430 at 2,2,3
-Id : 23792, {_}: ?24251 =<= join (join (meet ?24251 ?24252) (meet ?24253 ?24251)) ?24251 [24253, 24252, 24251] by Demod 23720 with 23478 at 3
-Id : 23793, {_}: ?24256 =<= join (join (meet ?24256 ?24255) ?24256) ?24256 [24255, 24256] by Super 23792 with 23430 at 2,1,3
-Id : 23892, {_}: join (meet ?24386 ?24387) ?24386 =<= meet ?24386 (join (meet ?24386 ?24387) ?24386) [24387, 24386] by Super 23446 with 23793 at 1,3
-Id : 24037, {_}: ?24612 =<= meet (join (meet ?24612 ?24613) ?24612) ?24612 [24613, 24612] by Super 4586 with 23892 at 1,3
-Id : 23902, {_}: join (meet (join (meet ?24420 ?24421) ?24420) ?24420) (meet (join (meet ?24420 ?24421) ?24420) ?24420) =>= join (meet ?24420 ?24421) ?24420 [24421, 24420] by Super 1492 with 23793 at 2,2,2
-Id : 23961, {_}: meet (join (meet ?24420 ?24421) ?24420) ?24420 =>= join (meet ?24420 ?24421) ?24420 [24421, 24420] by Demod 23902 with 23235 at 2
-Id : 24344, {_}: ?24612 =<= join (meet ?24612 ?24613) ?24612 [24613, 24612] by Demod 24037 with 23961 at 3
-Id : 24361, {_}: join (meet (meet ?24861 ?24862) ?24861) (meet (meet ?24861 ?24862) ?24861) =>= meet ?24861 ?24862 [24862, 24861] by Super 1492 with 24344 at 2,2,2
-Id : 24421, {_}: meet (meet ?24861 ?24862) ?24861 =>= meet ?24861 ?24862 [24862, 24861] by Demod 24361 with 23235 at 2
-Id : 4078, {_}: meet ?5865 ?5866 =<= meet (meet ?5866 (join ?5867 (meet ?5865 ?5866))) (meet ?5865 ?5866) [5867, 5866, 5865] by Super 4066 with 3629 at 1,1,3
-Id : 24583, {_}: ?25104 =<= join ?25104 (meet ?25104 ?25105) [25105, 25104] by Super 23478 with 24421 at 2,3
-Id : 24726, {_}: meet ?25313 ?25314 =<= meet (meet ?25314 ?25313) (meet ?25313 ?25314) [25314, 25313] by Super 4078 with 24583 at 2,1,3
-Id : 24889, {_}: meet (meet ?25590 ?25591) (meet ?25591 ?25590) =?= meet (meet ?25591 ?25590) (meet ?25590 ?25591) [25591, 25590] by Super 24421 with 24726 at 1,2
-Id : 24922, {_}: meet ?25591 ?25590 =<= meet (meet ?25591 ?25590) (meet ?25590 ?25591) [25590, 25591] by Demod 24889 with 24726 at 2
-Id : 24923, {_}: meet ?25591 ?25590 =?= meet ?25590 ?25591 [25590, 25591] by Demod 24922 with 24726 at 3
-Id : 25184, {_}: meet a b === meet a b [] by Demod 2 with 24923 at 2
-Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-% SZS output end CNFRefutation for LAT093-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H7 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246133454.3
-Last chance: all is indexed 1246133474.31
-Last chance: failed over 100 goal 1246133474.31
-FAILURE in 0 iterations
-% SZS status Timeout for LAT138-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H2 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-Last chance: 1246133746.97
-Last chance: all is indexed 1246133766.97
-Last chance: failed over 100 goal 1246133766.98
-FAILURE in 0 iterations
-% SZS status Timeout for LAT140-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H34 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H28 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-Last chance: 1246134039.87
-Last chance: all is indexed 1246134059.87
-Last chance: failed over 100 goal 1246134059.88
-FAILURE in 0 iterations
-% SZS status Timeout for LAT146-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H34 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Last chance: 1246134333.91
-Last chance: all is indexed 1246134353.91
-Last chance: failed over 100 goal 1246134353.91
-FAILURE in 0 iterations
-% SZS status Timeout for LAT148-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H40 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246134627.27
-Last chance: all is indexed 1246134647.28
-Last chance: failed over 100 goal 1246134647.28
-FAILURE in 0 iterations
-% SZS status Timeout for LAT152-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246134920.07
-Last chance: all is indexed 1246134940.08
-Last chance: failed over 100 goal 1246134940.08
-FAILURE in 0 iterations
-% SZS status Timeout for LAT156-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H50 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Last chance: 1246135214.14
-Last chance: all is indexed 1246135234.14
-Last chance: failed over 100 goal 1246135234.14
-FAILURE in 0 iterations
-% SZS status Timeout for LAT159-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H76 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Last chance: 1246135504.86
-Last chance: all is indexed 1246135524.86
-Last chance: failed over 100 goal 1246135524.86
-FAILURE in 0 iterations
-% SZS status Timeout for LAT164-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H77 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-Last chance: 1246135795.06
-Last chance: all is indexed 1246135815.06
-Last chance: failed over 100 goal 1246135815.06
-FAILURE in 0 iterations
-% SZS status Timeout for LAT165-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H77 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H78 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-Last chance: 1246136085.64
-Last chance: all is indexed 1246136105.64
-Last chance: failed over 100 goal 1246136105.64
-FAILURE in 0 iterations
-% SZS status Timeout for LAT166-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Last chance: 1246136377.63
-Last chance: all is indexed 1246136397.63
-Last chance: failed over 100 goal 1246136397.63
-FAILURE in 0 iterations
-% SZS status Timeout for LAT169-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Last chance: 1246136669.04
-Last chance: all is indexed 1246136689.04
-Last chance: failed over 100 goal 1246136689.04
-FAILURE in 0 iterations
-% SZS status Timeout for LAT170-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H40 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-Last chance: 1246136959.2
-Last chance: all is indexed 1246136979.21
-Last chance: failed over 100 goal 1246136979.26
-FAILURE in 0 iterations
-% SZS status Timeout for LAT173-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H79_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H32 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-Last chance: 1246137255.78
-Last chance: all is indexed 1246137275.78
-Last chance: failed over 100 goal 1246137275.78
-FAILURE in 0 iterations
-% SZS status Timeout for LAT175-1.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_cubed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Last chance: 1246137545.94
-Last chance: all is indexed 1246137565.94
-Last chance: failed over 100 goal 1246137565.94
-FAILURE in 0 iterations
-% SZS status Timeout for RNG009-7.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Last chance: 1246137836.07
-Last chance: all is indexed 1246137856.07
-Last chance: failed over 100 goal 1246137856.07
-FAILURE in 0 iterations
-% SZS status Timeout for RNG019-6.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- distributivity_of_difference1 is 71
- distributivity_of_difference2 is 70
- distributivity_of_difference3 is 69
- distributivity_of_difference4 is 68
- inverse_product1 is 73
- inverse_product2 is 72
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- product_of_inverses is 74
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Last chance: 1246138127.54
-Last chance: all is indexed 1246138147.55
-Last chance: failed over 100 goal 1246138147.55
-FAILURE in 0 iterations
-% SZS status Timeout for RNG019-7.p
-Order
- == is 100
- _ is 99
- add is 95
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form2 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 97
- v is 96
- x is 98
- y is 94
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-Last chance: 1246138417.94
-Last chance: all is indexed 1246138437.94
-Last chance: failed over 100 goal 1246138437.94
-FAILURE in 0 iterations
-% SZS status Timeout for RNG020-6.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 92
- additive_identity is 90
- additive_inverse is 91
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- b is 97
- c is 95
- commutativity_for_addition is 79
- commutator is 75
- d is 94
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 88
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 86
- multiply is 96
- prove_teichmuller_identity is 89
- right_additive_identity is 87
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 85
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-Last chance: 1246138709.57
-Last chance: all is indexed 1246138729.58
-Last chance: failed over 100 goal 1246138729.58
-FAILURE in 0 iterations
-% SZS status Timeout for RNG026-6.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- cx is 97
- cy is 96
- cz is 98
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 95
- product_of_inverses is 75
- prove_right_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-Last chance: 1246139002.01
-Last chance: all is indexed 1246139022.02
-Last chance: failed over 100 goal 1246139022.02
-FAILURE in 0 iterations
-% SZS status Timeout for RNG027-7.p
-Order
- == is 100
- _ is 99
- add is 91
- additive_identity is 92
- additive_inverse is 86
- additive_inverse_additive_inverse is 83
- associativity_for_addition is 79
- associator is 94
- commutativity_for_addition is 80
- commutator is 76
- distribute1 is 82
- distribute2 is 81
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 90
- left_additive_inverse is 85
- left_alternative is 77
- left_multiplicative_zero is 88
- multiply is 96
- product_of_inverses is 75
- prove_left_moufang is 93
- right_additive_identity is 89
- right_additive_inverse is 84
- right_alternative is 78
- right_multiplicative_zero is 87
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-Last chance: 1246139292.16
-Last chance: all is indexed 1246139312.16
-Last chance: failed over 100 goal 1246139312.16
-FAILURE in 0 iterations
-% SZS status Timeout for RNG028-9.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 96
- product_of_inverses is 75
- prove_middle_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-Last chance: 1246139582.69
-Last chance: all is indexed 1246139602.7
-Last chance: failed over 100 goal 1246139602.7
-FAILURE in 0 iterations
-% SZS status Timeout for RNG029-7.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_fourthed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Last chance: 1246139872.91
-Last chance: all is indexed 1246139892.92
-Last chance: failed over 100 goal 1246139892.92
-FAILURE in 0 iterations
-% SZS status Timeout for RNG035-7.p
-Order
- == is 100
- _ is 99
- a is 98
- absorbtion is 88
- add is 95
- associativity_of_add is 92
- b is 97
- c is 90
- commutativity_of_add is 93
- d is 89
- negate is 96
- prove_huntingtons_axiom is 94
- robbins_axiom is 91
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
- Id : 8, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-Last chance: 1246140169.53
-Last chance: all is indexed 1246140189.53
-Last chance: failed over 100 goal 1246140189.53
-FAILURE in 0 iterations
-% SZS status Timeout for ROB006-1.p
-Order
- == is 100
- _ is 99
- absorbtion is 90
- add is 98
- associativity_of_add is 95
- c is 92
- commutativity_of_add is 96
- d is 91
- negate is 94
- prove_idempotence is 97
- robbins_axiom is 93
-Facts
- Id : 4, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
- Id : 6, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
- Id : 8, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-Last chance: 1246140468.26
-Last chance: all is indexed 1246140488.26
-Last chance: failed over 100 goal 1246140489.49
-FAILURE in 0 iterations
-% SZS status Timeout for ROB006-2.p
+++ /dev/null
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 77
- additive_id2 is 76
- additive_identity is 82
- additive_inverse1 is 84
- additive_inverse2 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- distributivity3 is 88
- distributivity4 is 87
- inverse is 86
- multiplicative_id1 is 79
- multiplicative_id2 is 78
- multiplicative_identity is 85
- multiplicative_inverse1 is 81
- multiplicative_inverse2 is 80
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
- Id : 14, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
- Id : 16, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
- Id : 18, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
- Id : 20, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
- Id : 22, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
- Id : 24, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
- Id : 26, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
- Id : 28, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
- Id : 30, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Timeout !
-FAILURE in 253 iterations
-% SZS status Timeout for BOO007-2.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 93
- additive_id1 is 87
- additive_identity is 88
- additive_inverse1 is 83
- b is 97
- c is 96
- commutativity_of_add is 92
- commutativity_of_multiply is 91
- distributivity1 is 90
- distributivity2 is 89
- inverse is 84
- multiplicative_id1 is 85
- multiplicative_identity is 86
- multiplicative_inverse1 is 82
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
- Id : 8, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
- Id : 10, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
- Id : 12, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
- Id : 14, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
- Id : 16, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
- Id : 18, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Timeout !
-FAILURE in 258 iterations
-% SZS status Timeout for BOO007-4.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 95
- additive_inverse is 83
- associativity_of_add is 80
- associativity_of_multiply is 79
- b is 97
- c is 96
- distributivity is 92
- inverse is 89
- l1 is 91
- l2 is 87
- l3 is 90
- l4 is 86
- multiplicative_inverse is 81
- multiply is 94
- n0 is 82
- n1 is 84
- property3 is 88
- property3_dual is 85
- prove_multiply_add_property is 93
-Facts
- Id : 4, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
- Id : 6, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
- Id : 8, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
- Id : 10, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
- Id : 12, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
- Id : 14, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
- Id : 16, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
- Id : 18, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
- Id : 20, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
- Id : 22, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
- Id : 24, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Goal
- Id : 2, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-Timeout !
-FAILURE in 221 iterations
-% SZS status Timeout for BOO031-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- b is 96
- c is 94
- d is 93
- e is 92
- f is 91
- g is 90
- inverse is 97
- left_inverse is 85
- multiply is 95
- prove_single_axiom is 89
- right_inverse is 84
- ternary_multiply_1 is 87
- ternary_multiply_2 is 86
-Facts
- Id : 4, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
- Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
- Id : 8, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
- Id : 10, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
- Id : 12, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-Goal
- Id : 2, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-Found proof, 2.355821s
-% SZS status Unsatisfiable for BOO034-1.p
-% SZS output start CNFRefutation for BOO034-1.p
-Id : 8, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
-Id : 6, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-Id : 12, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
-Id : 10, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
-Id : 4, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-Id : 75, {_}: multiply ?212 ?213 ?214 =<= multiply ?212 ?213 (multiply ?215 (multiply ?212 ?213 ?214) ?214) [215, 214, 213, 212] by Super 4 with 6 at 2
-Id : 84, {_}: multiply ?257 ?258 ?259 =<= multiply ?257 ?258 (multiply ?257 ?258 ?259) [259, 258, 257] by Super 75 with 8 at 3,3
-Id : 115, {_}: multiply (multiply ?285 ?286 ?288) ?289 (multiply ?285 ?286 ?287) =?= multiply ?285 ?286 (multiply ?288 ?289 (multiply ?285 ?286 ?287)) [287, 289, 288, 286, 285] by Super 4 with 84 at 3,2
-Id : 298, {_}: multiply ?735 ?736 (multiply ?737 ?738 ?739) =<= multiply ?735 ?736 (multiply ?737 ?738 (multiply ?735 ?736 ?739)) [739, 738, 737, 736, 735] by Demod 115 with 4 at 2
-Id : 184, {_}: multiply ?446 ?447 ?448 =<= multiply ?446 ?447 (multiply ?448 (multiply ?446 ?447 ?448) ?449) [449, 448, 447, 446] by Super 4 with 8 at 2
-Id : 189, {_}: multiply ?470 ?471 (inverse ?471) =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Super 184 with 12 at 2,3,3
-Id : 225, {_}: ?470 =<= multiply ?470 ?471 (multiply (inverse ?471) ?470 ?472) [472, 471, 470] by Demod 189 with 12 at 2
-Id : 321, {_}: multiply (inverse ?865) ?864 (multiply ?864 ?865 ?866) =>= multiply (inverse ?865) ?864 ?864 [866, 864, 865] by Super 298 with 225 at 3,3
-Id : 387, {_}: multiply (inverse ?963) ?964 (multiply ?964 ?963 ?965) =>= ?964 [965, 964, 963] by Demod 321 with 6 at 3
-Id : 389, {_}: multiply (inverse ?974) ?973 ?974 =>= ?973 [973, 974] by Super 387 with 6 at 3,2
-Id : 437, {_}: ?1071 =<= inverse (inverse ?1071) [1071] by Super 12 with 389 at 2
-Id : 462, {_}: multiply ?1119 (inverse ?1119) ?1120 =>= ?1120 [1120, 1119] by Super 10 with 437 at 1,2
-Id : 116, {_}: multiply (multiply ?291 ?292 ?293) ?294 (multiply ?291 ?292 ?295) =?= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Super 4 with 84 at 1,2
-Id : 12671, {_}: multiply ?19232 ?19233 (multiply ?19234 ?19235 ?19236) =<= multiply ?19232 ?19233 (multiply (multiply ?19232 ?19233 ?19234) ?19235 ?19236) [19236, 19235, 19234, 19233, 19232] by Demod 116 with 4 at 2
-Id : 80, {_}: multiply ?236 ?237 (inverse ?237) =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Super 75 with 12 at 2,3,3
-Id : 105, {_}: ?236 =<= multiply ?236 ?237 (multiply ?238 ?236 (inverse ?237)) [238, 237, 236] by Demod 80 with 12 at 2
-Id : 996, {_}: ?2202 =<= multiply ?2202 (inverse ?2203) (multiply ?2204 ?2202 ?2203) [2204, 2203, 2202] by Super 105 with 437 at 3,3,3
-Id : 1012, {_}: ?2262 =<= multiply ?2262 (inverse (multiply ?2261 ?2263 (inverse ?2262))) ?2263 [2263, 2261, 2262] by Super 996 with 105 at 3,3
-Id : 459, {_}: ?1109 =<= multiply ?1109 (inverse ?1108) (multiply ?1108 ?1109 ?1110) [1110, 1108, 1109] by Super 225 with 437 at 1,3,3
-Id : 1017, {_}: inverse ?2283 =<= multiply (inverse ?2283) (inverse (multiply ?2283 ?2285 ?2284)) ?2285 [2284, 2285, 2283] by Super 996 with 459 at 3,3
-Id : 1909, {_}: ?3987 =<= multiply ?3987 (inverse (inverse ?3985)) (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Super 1012 with 1017 at 1,2,3
-Id : 1996, {_}: ?3987 =<= multiply ?3987 ?3985 (inverse (multiply ?3985 (inverse ?3987) ?3986)) [3986, 3985, 3987] by Demod 1909 with 437 at 2,3
-Id : 2510, {_}: ?5132 =<= multiply ?5132 (multiply ?5132 (inverse ?5131) ?5133) ?5131 [5133, 5131, 5132] by Super 105 with 1996 at 3,3
-Id : 2812, {_}: multiply ?5719 (inverse (inverse ?5721)) ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Super 105 with 2510 at 3,3
-Id : 2874, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 (inverse (inverse ?5721)) ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2812 with 437 at 2,2
-Id : 2875, {_}: multiply ?5719 ?5721 ?5720 =<= multiply (multiply ?5719 ?5721 ?5720) ?5721 ?5719 [5720, 5721, 5719] by Demod 2874 with 437 at 2,1,3
-Id : 12777, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =?= multiply ?19864 ?19863 (multiply ?19864 ?19863 ?19862) [19862, 19863, 19864] by Super 12671 with 2875 at 3,3
-Id : 12993, {_}: multiply ?20226 ?20227 (multiply ?20228 ?20227 ?20226) =>= multiply ?20226 ?20227 ?20228 [20228, 20227, 20226] by Demod 12777 with 84 at 3
-Id : 19, {_}: multiply ?58 ?59 ?61 =<= multiply ?58 ?59 (multiply ?60 (multiply ?58 ?59 ?61) ?61) [60, 61, 59, 58] by Super 4 with 6 at 2
-Id : 463, {_}: multiply ?1122 ?1123 (inverse ?1122) =>= ?1123 [1123, 1122] by Super 389 with 437 at 1,2
-Id : 607, {_}: multiply ?1371 ?1372 (inverse ?1371) =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1372, 1371] by Super 19 with 463 at 2,3,3
-Id : 625, {_}: ?1372 =<= multiply ?1371 ?1372 (multiply ?1373 ?1372 (inverse ?1371)) [1373, 1371, 1372] by Demod 607 with 463 at 2
-Id : 460, {_}: ?1113 =<= multiply ?1113 (inverse ?1112) (multiply ?1114 ?1113 ?1112) [1114, 1112, 1113] by Super 105 with 437 at 3,3,3
-Id : 1018, {_}: inverse ?2287 =<= multiply (inverse ?2287) (inverse (multiply ?2288 ?2289 ?2287)) ?2289 [2289, 2288, 2287] by Super 996 with 460 at 3,3
-Id : 2078, {_}: ?4356 =<= multiply ?4356 (inverse (inverse ?4354)) (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Super 1012 with 1018 at 1,2,3
-Id : 2124, {_}: ?4356 =<= multiply ?4356 ?4354 (inverse (multiply ?4355 (inverse ?4356) ?4354)) [4355, 4354, 4356] by Demod 2078 with 437 at 2,3
-Id : 3650, {_}: ?7215 =<= multiply ?7215 (multiply ?7216 (inverse ?7214) ?7215) ?7214 [7214, 7216, 7215] by Super 105 with 2124 at 3,3
-Id : 4032, {_}: multiply ?7968 (inverse (inverse ?7969)) ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Super 625 with 3650 at 3,3
-Id : 4103, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 (inverse (inverse ?7969)) ?7967) ?7967 [7967, 7969, 7968] by Demod 4032 with 437 at 2,2
-Id : 4104, {_}: multiply ?7968 ?7969 ?7967 =<= multiply ?7969 (multiply ?7968 ?7969 ?7967) ?7967 [7967, 7969, 7968] by Demod 4103 with 437 at 2,2,3
-Id : 13062, {_}: multiply ?20502 (multiply ?20501 ?20503 ?20502) (multiply ?20501 ?20503 ?20502) =>= multiply ?20502 (multiply ?20501 ?20503 ?20502) ?20503 [20503, 20501, 20502] by Super 12993 with 4104 at 3,2
-Id : 13612, {_}: multiply ?21322 ?21323 ?21324 =<= multiply ?21324 (multiply ?21322 ?21323 ?21324) ?21323 [21324, 21323, 21322] by Demod 13062 with 6 at 2
-Id : 12903, {_}: multiply ?19864 ?19863 (multiply ?19862 ?19863 ?19864) =>= multiply ?19864 ?19863 ?19862 [19862, 19863, 19864] by Demod 12777 with 84 at 3
-Id : 13625, {_}: multiply ?21368 ?21369 (multiply ?21367 ?21369 ?21368) =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Super 13612 with 12903 at 2,3
-Id : 13783, {_}: multiply ?21368 ?21369 ?21367 =<= multiply (multiply ?21367 ?21369 ?21368) (multiply ?21368 ?21369 ?21367) ?21369 [21367, 21369, 21368] by Demod 13625 with 12903 at 2
-Id : 34254, {_}: multiply (multiply ?56219 ?56220 ?56221) ?56222 ?56219 =<= multiply ?56219 ?56220 (multiply ?56221 ?56222 (multiply ?56223 ?56219 (inverse ?56220))) [56223, 56222, 56221, 56220, 56219] by Super 4 with 105 at 3,2
-Id : 34779, {_}: multiply (multiply ?57676 ?57677 ?57678) ?57678 ?57676 =>= multiply ?57676 ?57677 ?57678 [57678, 57677, 57676] by Super 34254 with 8 at 3,3
-Id : 34856, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =?= multiply ?57993 (multiply ?57992 ?57993 ?57994) ?57994 [57994, 57993, 57992] by Super 34779 with 4104 at 1,2
-Id : 35127, {_}: multiply (multiply ?57992 ?57993 ?57994) ?57994 ?57993 =>= multiply ?57992 ?57993 ?57994 [57994, 57993, 57992] by Demod 34856 with 4104 at 3
-Id : 36341, {_}: multiply (multiply ?60132 ?60133 ?60134) ?60134 ?60133 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Super 13783 with 35127 at 2,3
-Id : 36698, {_}: multiply ?60132 ?60133 ?60134 =<= multiply (multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134)) (multiply ?60132 ?60133 ?60134) ?60134 [60134, 60133, 60132] by Demod 36341 with 35127 at 2
-Id : 36699, {_}: multiply ?60132 ?60133 ?60134 =<= multiply ?60133 ?60134 (multiply ?60132 ?60133 ?60134) [60134, 60133, 60132] by Demod 36698 with 35127 at 3
-Id : 136, {_}: multiply ?291 ?292 (multiply ?293 ?294 ?295) =<= multiply ?291 ?292 (multiply (multiply ?291 ?292 ?293) ?294 ?295) [295, 294, 293, 292, 291] by Demod 116 with 4 at 2
-Id : 2796, {_}: multiply ?5648 (inverse (inverse ?5650)) ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Super 625 with 2510 at 3,3
-Id : 2887, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 (inverse (inverse ?5650)) ?5649) ?5648 [5649, 5650, 5648] by Demod 2796 with 437 at 2,2
-Id : 2888, {_}: multiply ?5648 ?5650 ?5649 =<= multiply ?5650 (multiply ?5648 ?5650 ?5649) ?5648 [5649, 5650, 5648] by Demod 2887 with 437 at 2,2,3
-Id : 34851, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =?= multiply ?57973 (multiply ?57974 ?57973 ?57972) ?57974 [57972, 57973, 57974] by Super 34779 with 2888 at 1,2
-Id : 35118, {_}: multiply (multiply ?57974 ?57973 ?57972) ?57974 ?57973 =>= multiply ?57974 ?57973 ?57972 [57972, 57973, 57974] by Demod 34851 with 2888 at 3
-Id : 35773, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =?= multiply ?59268 ?59269 (multiply ?59268 ?59269 ?59270) [59270, 59269, 59268] by Super 136 with 35118 at 3,3
-Id : 36062, {_}: multiply ?59268 ?59269 (multiply ?59270 ?59268 ?59269) =>= multiply ?59268 ?59269 ?59270 [59270, 59269, 59268] by Demod 35773 with 84 at 3
-Id : 37434, {_}: multiply ?60132 ?60133 ?60134 =?= multiply ?60133 ?60134 ?60132 [60134, 60133, 60132] by Demod 36699 with 36062 at 3
-Id : 25, {_}: multiply ?84 ?85 ?86 =<= multiply ?84 ?85 (multiply ?86 (multiply ?84 ?85 ?86) ?87) [87, 86, 85, 84] by Super 4 with 8 at 2
-Id : 317, {_}: multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?848) =?= multiply ?845 (multiply ?846 ?847 ?845) (multiply ?846 ?847 ?845) [848, 847, 846, 845] by Super 298 with 25 at 3,3
-Id : 24761, {_}: multiply ?36657 (multiply ?36658 ?36659 ?36657) (multiply ?36658 ?36659 ?36660) =>= multiply ?36658 ?36659 ?36657 [36660, 36659, 36658, 36657] by Demod 317 with 6 at 3
-Id : 24766, {_}: multiply ?36681 (multiply ?36682 ?36683 ?36681) ?36682 =>= multiply ?36682 ?36683 ?36681 [36683, 36682, 36681] by Super 24761 with 12 at 3,2
-Id : 37848, {_}: multiply ?63783 ?63784 (multiply ?63783 ?63785 ?63784) =>= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Super 24766 with 37434 at 2
-Id : 37799, {_}: multiply ?63587 ?63589 (multiply ?63587 ?63588 ?63589) =>= multiply ?63587 ?63589 ?63588 [63588, 63589, 63587] by Super 12903 with 37434 at 3,2
-Id : 41410, {_}: multiply ?63783 ?63784 ?63785 =?= multiply ?63783 ?63785 ?63784 [63785, 63784, 63783] by Demod 37848 with 37799 at 2
-Id : 42482, {_}: b === b [] by Demod 42481 with 12 at 2
-Id : 42481, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 42480 with 41410 at 3,1,3,2
-Id : 42480, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 42479 with 41410 at 1,3,2
-Id : 42479, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 42478 with 41410 at 2,2
-Id : 42478, {_}: multiply b (multiply d (multiply g f e) c) (inverse (multiply d (multiply g e f) c)) =>= b [] by Demod 38490 with 41410 at 2
-Id : 38490, {_}: multiply b (inverse (multiply d (multiply g e f) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38489 with 37434 at 2,1,2,2
-Id : 38489, {_}: multiply b (inverse (multiply d (multiply f g e) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 38488 with 37434 at 2,1,2,2
-Id : 38488, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d (multiply g f e) c) =>= b [] by Demod 595 with 37434 at 1,2,2
-Id : 595, {_}: multiply b (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 53 with 462 at 1,2
-Id : 53, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 2 with 4 at 1,2,2
-Id : 2, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
-% SZS output end CNFRefutation for BOO034-1.p
-Order
- == is 100
- _ is 99
- a is 97
- add is 96
- b is 98
- dn1 is 93
- huntinton_1 is 95
- inverse is 94
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-Found proof, 0.372303s
-% SZS status Unsatisfiable for BOO072-1.p
-% SZS output start CNFRefutation for BOO072-1.p
-Id : 5, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 4, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 17, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?80)) ?81)) ?80)) ?82)) (inverse ?80))) ?80) =>= inverse ?80 [82, 81, 80] by Super 5 with 4 at 2,1,2
-Id : 22, {_}: inverse (add (inverse (add ?111 (inverse ?111))) ?111) =>= inverse ?111 [111] by Super 17 with 4 at 1,1,1,1,2
-Id : 36, {_}: inverse (add (inverse ?135) (inverse (add ?135 (inverse (add (inverse ?135) (inverse (add ?135 ?136))))))) =>= ?135 [136, 135] by Super 4 with 22 at 1,1,2
-Id : 57, {_}: inverse (add (inverse (add (inverse (add ?192 ?193)) ?190)) (inverse (add ?192 ?190))) =>= ?190 [190, 193, 192] by Super 4 with 36 at 2,1,2,1,2
-Id : 131, {_}: inverse (add (inverse (add (inverse (add ?400 ?401)) ?402)) (inverse (add ?400 ?402))) =>= ?402 [402, 401, 400] by Super 4 with 36 at 2,1,2,1,2
-Id : 141, {_}: inverse (add (inverse (add ?444 ?446)) (inverse (add (inverse ?444) ?446))) =>= ?446 [446, 444] by Super 131 with 36 at 1,1,1,1,2
-Id : 175, {_}: inverse (add ?545 (inverse (add ?544 (inverse (add (inverse ?544) ?545))))) =>= inverse (add (inverse ?544) ?545) [544, 545] by Super 57 with 141 at 1,1,2
-Id : 341, {_}: inverse (add (inverse ?894) (inverse (add ?894 (inverse (add (inverse ?894) (inverse ?894)))))) =>= ?894 [894] by Super 36 with 175 at 2,1,2,1,2
-Id : 390, {_}: inverse (add (inverse ?894) (inverse ?894)) =>= ?894 [894] by Demod 341 with 175 at 2
-Id : 176, {_}: inverse (add (inverse (add ?547 ?548)) (inverse (add (inverse ?547) ?548))) =>= ?548 [548, 547] by Super 131 with 36 at 1,1,1,1,2
-Id : 61, {_}: inverse (add (inverse ?208) (inverse (add ?208 (inverse (add (inverse ?208) (inverse (add ?208 ?209))))))) =>= ?208 [209, 208] by Super 4 with 22 at 1,1,2
-Id : 70, {_}: inverse (add (inverse ?244) (inverse (add ?244 ?244))) =>= ?244 [244] by Super 61 with 36 at 2,1,2,1,2
-Id : 189, {_}: inverse (add (inverse (add ?598 (inverse (add ?598 ?598)))) ?598) =>= inverse (add ?598 ?598) [598] by Super 176 with 70 at 2,1,2
-Id : 209, {_}: inverse (add (inverse (add ?635 ?635)) (inverse (add ?635 ?635))) =>= ?635 [635] by Super 57 with 189 at 1,1,2
-Id : 418, {_}: add ?635 ?635 =>= ?635 [635] by Demod 209 with 390 at 2
-Id : 427, {_}: inverse (inverse ?894) =>= ?894 [894] by Demod 390 with 418 at 1,2
-Id : 434, {_}: inverse (add (inverse (add (inverse ?1049) ?1050)) (inverse (add ?1049 ?1050))) =>= ?1050 [1050, 1049] by Super 141 with 427 at 1,1,2,1,2
-Id : 1002, {_}: inverse (add ?1872 (inverse (add (inverse ?1871) (inverse (add ?1871 ?1872))))) =>= inverse (add ?1871 ?1872) [1871, 1872] by Super 57 with 434 at 1,1,2
-Id : 2935, {_}: inverse (inverse (add ?4531 ?4530)) =<= add ?4530 (inverse (add (inverse ?4531) (inverse (add ?4531 ?4530)))) [4530, 4531] by Super 427 with 1002 at 1,2
-Id : 3025, {_}: add ?4531 ?4530 =<= add ?4530 (inverse (add (inverse ?4531) (inverse (add ?4531 ?4530)))) [4530, 4531] by Demod 2935 with 427 at 2
-Id : 5776, {_}: inverse (add ?7863 (inverse (add (inverse (add ?7864 ?7865)) (inverse (add ?7864 ?7863))))) =>= inverse (add ?7864 ?7863) [7865, 7864, 7863] by Super 131 with 57 at 1,1,2
-Id : 441, {_}: inverse (inverse ?1072) =>= ?1072 [1072] by Demod 390 with 418 at 1,2
-Id : 447, {_}: inverse (inverse (add (inverse ?1092) ?1091)) =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Super 441 with 175 at 1,2
-Id : 459, {_}: add (inverse ?1092) ?1091 =<= add ?1091 (inverse (add ?1092 (inverse (add (inverse ?1092) ?1091)))) [1091, 1092] by Demod 447 with 427 at 2
-Id : 5835, {_}: inverse (add (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104)))) (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) =>= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Super 5776 with 459 at 1,2,1,2
-Id : 5988, {_}: inverse (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104)))) =<= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Demod 5835 with 418 at 1,2
-Id : 5989, {_}: add (inverse ?8103) (inverse (add ?8103 ?8104)) =<= inverse (add ?8103 (inverse (add (inverse ?8103) (inverse (add ?8103 ?8104))))) [8104, 8103] by Demod 5988 with 427 at 2
-Id : 6002, {_}: inverse (add (inverse ?135) (add (inverse ?135) (inverse (add ?135 ?136)))) =>= ?135 [136, 135] by Demod 36 with 5989 at 2,1,2
-Id : 8, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?28)) ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Super 5 with 4 at 2,1,2
-Id : 428, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?28 ?27)) ?28)) ?30)) (inverse ?28))) ?28) =>= inverse ?28 [30, 27, 28] by Demod 8 with 427 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 251, {_}: inverse (add ?739 (inverse (add ?739 (inverse (add ?739 ?739))))) =>= inverse (add ?739 ?739) [739] by Super 57 with 209 at 1,1,2
-Id : 419, {_}: inverse (add ?739 (inverse (add ?739 (inverse ?739)))) =>= inverse (add ?739 ?739) [739] by Demod 251 with 418 at 1,2,1,2,1,2
-Id : 420, {_}: inverse (add ?739 (inverse (add ?739 (inverse ?739)))) =>= inverse ?739 [739] by Demod 419 with 418 at 1,3
-Id : 448, {_}: inverse (inverse ?1094) =<= add ?1094 (inverse (add ?1094 (inverse ?1094))) [1094] by Super 441 with 420 at 1,2
-Id : 460, {_}: ?1094 =<= add ?1094 (inverse (add ?1094 (inverse ?1094))) [1094] by Demod 448 with 427 at 2
-Id : 509, {_}: inverse (add (inverse (add (inverse ?1198) (inverse (inverse ?1198)))) (inverse (add ?1198 (inverse (inverse ?1198))))) =>= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Super 175 with 460 at 1,2,1,2,1,2
-Id : 522, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse (add ?1198 (inverse (inverse ?1198))))) =>= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 509 with 427 at 2,1,1,1,2
-Id : 523, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse (add ?1198 ?1198))) =?= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 522 with 427 at 2,1,2,1,2
-Id : 524, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =<= inverse (add (inverse ?1198) (inverse (add (inverse ?1198) (inverse (inverse ?1198))))) [1198] by Demod 523 with 418 at 1,2,1,2
-Id : 525, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =>= inverse (inverse ?1198) [1198] by Demod 524 with 460 at 1,3
-Id : 526, {_}: inverse (add (inverse (add (inverse ?1198) ?1198)) (inverse ?1198)) =>= ?1198 [1198] by Demod 525 with 427 at 3
-Id : 564, {_}: inverse ?1294 =<= add (inverse (add (inverse ?1294) ?1294)) (inverse ?1294) [1294] by Super 427 with 526 at 1,2
-Id : 633, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?1388)) ?1389)) (inverse (inverse ?1388)))) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Super 428 with 564 at 1,1,1,1,1,1,1,2
-Id : 653, {_}: inverse (add (inverse (add (inverse (add ?1388 ?1389)) (inverse (inverse ?1388)))) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Demod 633 with 427 at 1,1,1,1,1,1,2
-Id : 654, {_}: inverse (add (inverse (add (inverse (add ?1388 ?1389)) ?1388)) (inverse ?1388)) =>= inverse (inverse ?1388) [1389, 1388] by Demod 653 with 427 at 2,1,1,1,2
-Id : 1550, {_}: inverse (add (inverse (add (inverse (add ?2636 ?2637)) ?2636)) (inverse ?2636)) =>= ?2636 [2637, 2636] by Demod 654 with 427 at 3
-Id : 1579, {_}: inverse (add ?2725 (inverse (inverse (add ?2724 ?2725)))) =>= inverse (add ?2724 ?2725) [2724, 2725] by Super 1550 with 57 at 1,1,2
-Id : 1654, {_}: inverse (add ?2725 (add ?2724 ?2725)) =>= inverse (add ?2724 ?2725) [2724, 2725] by Demod 1579 with 427 at 2,1,2
-Id : 1668, {_}: inverse (inverse (add ?2771 ?2770)) =<= add ?2770 (add ?2771 ?2770) [2770, 2771] by Super 427 with 1654 at 1,2
-Id : 1719, {_}: add ?2771 ?2770 =<= add ?2770 (add ?2771 ?2770) [2770, 2771] by Demod 1668 with 427 at 2
-Id : 1694, {_}: inverse (add ?2869 (add ?2870 ?2869)) =>= inverse (add ?2870 ?2869) [2870, 2869] by Demod 1579 with 427 at 2,1,2
-Id : 1011, {_}: inverse ?1910 =<= add (inverse (add (inverse ?1909) ?1910)) (inverse (add ?1909 ?1910)) [1909, 1910] by Super 427 with 434 at 1,2
-Id : 1703, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =<= inverse (add (inverse (add (inverse ?2891) ?2890)) (inverse (add ?2891 ?2890))) [2890, 2891] by Super 1694 with 1011 at 2,1,2
-Id : 1752, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =>= inverse (inverse ?2890) [2890, 2891] by Demod 1703 with 1011 at 1,3
-Id : 1753, {_}: inverse (add (inverse (add ?2891 ?2890)) (inverse ?2890)) =>= ?2890 [2890, 2891] by Demod 1752 with 427 at 3
-Id : 1836, {_}: inverse ?3039 =<= add (inverse (add ?3038 ?3039)) (inverse ?3039) [3038, 3039] by Super 427 with 1753 at 1,2
-Id : 1990, {_}: inverse (add (inverse (inverse ?3259)) (inverse (add ?3260 (inverse ?3259)))) =>= inverse ?3259 [3260, 3259] by Super 57 with 1836 at 1,1,1,2
-Id : 2039, {_}: inverse (add ?3259 (inverse (add ?3260 (inverse ?3259)))) =>= inverse ?3259 [3260, 3259] by Demod 1990 with 427 at 1,1,2
-Id : 2119, {_}: inverse (inverse ?3394) =<= add ?3394 (inverse (add ?3395 (inverse ?3394))) [3395, 3394] by Super 427 with 2039 at 1,2
-Id : 2221, {_}: ?3394 =<= add ?3394 (inverse (add ?3395 (inverse ?3394))) [3395, 3394] by Demod 2119 with 427 at 2
-Id : 2575, {_}: add ?4058 (inverse (add ?4059 (inverse ?4058))) =?= add (inverse (add ?4059 (inverse ?4058))) ?4058 [4059, 4058] by Super 1719 with 2221 at 2,3
-Id : 2687, {_}: ?4204 =<= add (inverse (add ?4205 (inverse ?4204))) ?4204 [4205, 4204] by Demod 2575 with 2221 at 2
-Id : 5192, {_}: add ?7211 (inverse (add (inverse ?7212) (inverse (add ?7212 ?7213)))) =<= add ?7212 (add ?7211 (inverse (add (inverse ?7212) (inverse (add ?7212 ?7213))))) [7213, 7212, 7211] by Super 2687 with 4 at 1,3
-Id : 2141, {_}: add (inverse ?3482) (inverse (add ?3481 (inverse (inverse ?3482)))) =<= add (inverse (add ?3481 (inverse (inverse ?3482)))) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Super 459 with 2039 at 2,1,2,3
-Id : 2187, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 (inverse (inverse ?3482)))) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Demod 2141 with 427 at 2,1,2,2
-Id : 2188, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 ?3482)) (inverse (add ?3482 (inverse (inverse ?3482)))) [3481, 3482] by Demod 2187 with 427 at 2,1,1,3
-Id : 2189, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =<= add (inverse (add ?3481 ?3482)) (inverse (add ?3482 ?3482)) [3481, 3482] by Demod 2188 with 427 at 2,1,2,3
-Id : 2190, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =?= add (inverse (add ?3481 ?3482)) (inverse ?3482) [3481, 3482] by Demod 2189 with 418 at 1,2,3
-Id : 2191, {_}: add (inverse ?3482) (inverse (add ?3481 ?3482)) =>= inverse ?3482 [3481, 3482] by Demod 2190 with 1836 at 3
-Id : 5228, {_}: add (inverse (inverse (add ?7359 ?7360))) (inverse (add (inverse ?7359) (inverse (add ?7359 ?7360)))) =>= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Super 5192 with 2191 at 2,3
-Id : 5491, {_}: inverse (inverse (add ?7359 ?7360)) =<= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Demod 5228 with 2191 at 2
-Id : 5492, {_}: add ?7359 ?7360 =<= add ?7359 (inverse (inverse (add ?7359 ?7360))) [7360, 7359] by Demod 5491 with 427 at 2
-Id : 5493, {_}: add ?7359 ?7360 =<= add ?7359 (add ?7359 ?7360) [7360, 7359] by Demod 5492 with 427 at 2,3
-Id : 6003, {_}: inverse (add (inverse ?135) (inverse (add ?135 ?136))) =>= ?135 [136, 135] by Demod 6002 with 5493 at 1,2
-Id : 6005, {_}: add ?4531 ?4530 =?= add ?4530 ?4531 [4530, 4531] by Demod 3025 with 6003 at 2,3
-Id : 6260, {_}: add a b === add a b [] by Demod 2 with 6005 at 2
-Id : 2, {_}: add b a =>= add a b [] by huntinton_1
-% SZS output end CNFRefutation for BOO072-1.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 96
- b is 97
- c is 95
- dn1 is 92
- huntinton_2 is 94
- inverse is 93
-Facts
- Id : 4, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-Timeout !
-FAILURE in 151 iterations
-% SZS status Timeout for BOO073-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- nand is 95
- prove_meredith_2_basis_2 is 94
- sh_1 is 93
-Facts
- Id : 4, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-Timeout !
-FAILURE in 131 iterations
-% SZS status Timeout for BOO076-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 376 iterations
-% SZS status Timeout for COL003-12.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 26 iterations
-% SZS status Timeout for COL003-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
- w is 92
- w_definition is 91
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 374 iterations
-% SZS status Timeout for COL003-20.p
-Order
- == is 100
- _ is 99
- apply is 96
- fixed_pt is 97
- k is 92
- k_definition is 91
- prove_strong_fixed_point is 95
- s is 94
- s_definition is 93
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
- Id : 6, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 425 iterations
-% SZS status Timeout for COL006-6.p
-Order
- == is 100
- _ is 99
- apply is 97
- combinator is 98
- o is 95
- o_definition is 94
- prove_fixed_point is 96
- q1 is 93
- q1_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
- Id : 6, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-Goal
- Id : 2, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 13 iterations
-% SZS status Timeout for COL011-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 27 iterations
-% SZS status Timeout for COL037-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 93
- m_definition is 92
- prove_fixed_point is 96
- v is 91
- v_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
- Id : 8, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 35 iterations
-% SZS status Timeout for COL038-1.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- h is 92
- h_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 388 iterations
-% SZS status Timeout for COL043-3.p
-Order
- == is 100
- _ is 99
- apply is 96
- b is 94
- b_definition is 93
- fixed_pt is 97
- n is 92
- n_definition is 91
- prove_strong_fixed_point is 95
- strong_fixed_point is 98
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
- Id : 6, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
- Id : 8, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-Goal
- Id : 2, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-Timeout !
-FAILURE in 339 iterations
-% SZS status Timeout for COL044-8.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- m is 91
- m_definition is 90
- prove_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-Timeout !
-FAILURE in 26 iterations
-% SZS status Timeout for COL046-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 95
- b_definition is 94
- f is 98
- m is 91
- m_definition is 90
- prove_strong_fixed_point is 96
- w is 93
- w_definition is 92
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
- Id : 8, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 26 iterations
-% SZS status Timeout for COL049-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- c is 91
- c_definition is 90
- f is 98
- i is 89
- i_definition is 88
- prove_strong_fixed_point is 96
- s is 95
- s_definition is 94
-Facts
- Id : 4, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
- Id : 8, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
- Id : 10, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Goal
- Id : 2, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-Timeout !
-FAILURE in 28 iterations
-% SZS status Timeout for COL057-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-Timeout !
-FAILURE in 44 iterations
-% SZS status Timeout for COL060-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_q1_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-Timeout !
-FAILURE in 44 iterations
-% SZS status Timeout for COL061-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_f_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-Timeout !
-FAILURE in 43 iterations
-% SZS status Timeout for COL063-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 93
- b_definition is 92
- f is 98
- g is 96
- h is 95
- prove_v_combinator is 94
- t is 91
- t_definition is 90
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-Timeout !
-FAILURE in 43 iterations
-% SZS status Timeout for COL064-1.p
-Order
- == is 100
- _ is 99
- apply is 97
- b is 92
- b_definition is 91
- f is 98
- g is 96
- h is 95
- i is 94
- prove_g_combinator is 93
- t is 90
- t_definition is 89
-Facts
- Id : 4, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
- Id : 6, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-Goal
- Id : 2, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-Timeout !
-FAILURE in 41 iterations
-% SZS status Timeout for COL065-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- group_axiom is 92
- inverse is 93
- multiply is 95
- prove_associativity is 94
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-Found proof, 2.278024s
-% SZS status Unsatisfiable for GRP014-1.p
-% SZS output start CNFRefutation for GRP014-1.p
-Id : 4, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Id : 5, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
-Id : 8, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (inverse (multiply (inverse ?26) (multiply (inverse (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?27))) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 31, 26, 30, 27, 29] by Super 5 with 4 at 1,1,2,2
-Id : 7, {_}: multiply ?22 (inverse (multiply (multiply (inverse (multiply (inverse ?23) ?20)) ?24) (inverse (multiply ?23 ?24)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?19) (multiply (inverse (inverse ?22)) ?20))) ?21) (inverse (multiply ?19 ?21))) [21, 19, 24, 20, 23, 22] by Super 5 with 4 at 2,1,1,1,1,2,2
-Id : 65, {_}: multiply (inverse ?586) (multiply ?586 (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587, 586] by Super 4 with 7 at 2,2
-Id : 66, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?596) (multiply (inverse (inverse ?593)) (multiply (inverse ?593) ?598)))) ?597) (inverse (multiply ?596 ?597))) =>= ?598 [597, 598, 593, 596] by Super 4 with 7 at 2
-Id : 285, {_}: multiply (inverse ?2327) (multiply ?2327 ?2328) =?= multiply (inverse (inverse ?2329)) (multiply (inverse ?2329) ?2328) [2329, 2328, 2327] by Super 65 with 66 at 2,2,2
-Id : 188, {_}: multiply (inverse ?1696) (multiply ?1696 ?1694) =?= multiply (inverse (inverse ?1693)) (multiply (inverse ?1693) ?1694) [1693, 1694, 1696] by Super 65 with 66 at 2,2,2
-Id : 299, {_}: multiply (inverse ?2421) (multiply ?2421 ?2422) =?= multiply (inverse ?2420) (multiply ?2420 ?2422) [2420, 2422, 2421] by Super 285 with 188 at 3
-Id : 395, {_}: multiply (inverse ?2916) (multiply ?2916 (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915, 2916] by Super 65 with 299 at 1,1,1,1,2,2,2
-Id : 549, {_}: multiply ?3835 (inverse (multiply (multiply (inverse (multiply (inverse ?3836) (multiply ?3836 ?3837))) ?3838) (inverse (multiply (inverse ?3835) ?3838)))) =>= ?3837 [3838, 3837, 3836, 3835] by Super 4 with 299 at 1,1,1,1,2,2
-Id : 2606, {_}: multiply ?16468 (inverse (multiply (multiply (inverse (multiply (inverse ?16469) (multiply ?16469 ?16470))) (multiply ?16468 ?16471)) (inverse (multiply (inverse ?16472) (multiply ?16472 ?16471))))) =>= ?16470 [16472, 16471, 16470, 16469, 16468] by Super 549 with 299 at 1,2,1,2,2
-Id : 2691, {_}: multiply (multiply (inverse ?17193) (multiply ?17193 ?17194)) (inverse (multiply ?17191 (inverse (multiply (inverse ?17195) (multiply ?17195 (inverse (multiply (multiply (inverse (multiply (inverse ?17190) ?17191)) ?17192) (inverse (multiply ?17190 ?17192))))))))) =>= ?17194 [17192, 17190, 17195, 17191, 17194, 17193] by Super 2606 with 65 at 1,1,2,2
-Id : 2733, {_}: multiply (multiply (inverse ?17193) (multiply ?17193 ?17194)) (inverse (multiply ?17191 (inverse ?17191))) =>= ?17194 [17191, 17194, 17193] by Demod 2691 with 65 at 1,2,1,2,2
-Id : 2764, {_}: multiply (inverse (multiply (inverse ?17455) (multiply ?17455 ?17456))) ?17456 =?= multiply (inverse (multiply (inverse ?17457) (multiply ?17457 ?17458))) ?17458 [17458, 17457, 17456, 17455] by Super 395 with 2733 at 2,2
-Id : 2997, {_}: multiply (inverse (inverse (multiply (inverse ?18879) (multiply ?18879 (inverse (multiply (multiply (inverse (multiply (inverse ?18882) ?18883)) ?18884) (inverse (multiply ?18882 ?18884)))))))) (multiply (inverse (multiply (inverse ?18880) (multiply ?18880 ?18881))) ?18881) =>= ?18883 [18881, 18880, 18884, 18883, 18882, 18879] by Super 65 with 2764 at 2,2
-Id : 3188, {_}: multiply (inverse (inverse ?18883)) (multiply (inverse (multiply (inverse ?18880) (multiply ?18880 ?18881))) ?18881) =>= ?18883 [18881, 18880, 18883] by Demod 2997 with 65 at 1,1,1,2
-Id : 137, {_}: multiply (inverse ?1284) (multiply ?1284 (inverse (multiply (multiply (inverse (multiply (inverse ?1285) ?1286)) ?1287) (inverse (multiply ?1285 ?1287))))) =>= ?1286 [1287, 1286, 1285, 1284] by Super 4 with 7 at 2,2
-Id : 156, {_}: multiply (inverse ?1443) (multiply ?1443 (multiply ?1439 (inverse (multiply (multiply (inverse (multiply (inverse ?1440) ?1441)) ?1442) (inverse (multiply ?1440 ?1442)))))) =>= multiply (inverse (inverse ?1439)) ?1441 [1442, 1441, 1440, 1439, 1443] by Super 137 with 7 at 2,2,2
-Id : 3268, {_}: multiply (inverse (inverse (inverse ?20656))) ?20656 =?= multiply (inverse (inverse (inverse (multiply (inverse ?20657) (multiply ?20657 (inverse (multiply (multiply (inverse (multiply (inverse ?20658) ?20659)) ?20660) (inverse (multiply ?20658 ?20660))))))))) ?20659 [20660, 20659, 20658, 20657, 20656] by Super 156 with 3188 at 2,2
-Id : 3359, {_}: multiply (inverse (inverse (inverse ?20656))) ?20656 =?= multiply (inverse (inverse (inverse ?20659))) ?20659 [20659, 20656] by Demod 3268 with 65 at 1,1,1,1,3
-Id : 3543, {_}: multiply (inverse (inverse ?21963)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?21961)))) (multiply (inverse (inverse (inverse ?21962))) ?21962))) ?21961) =>= ?21963 [21962, 21961, 21963] by Super 3188 with 3359 at 2,1,1,2,2
-Id : 379, {_}: multiply ?2799 (inverse (multiply (multiply (inverse ?2798) (multiply ?2798 ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2798, 2799] by Super 4 with 299 at 1,1,2,2
-Id : 190, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1706) (multiply (inverse (inverse ?1707)) (multiply (inverse ?1707) ?1708)))) ?1709) (inverse (multiply ?1706 ?1709))) =>= ?1708 [1709, 1708, 1707, 1706] by Super 4 with 7 at 2
-Id : 198, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1768) (multiply (inverse (inverse ?1769)) (multiply (inverse ?1769) ?1770)))) ?1771) (inverse (multiply ?1768 ?1771))))) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1771, 1770, 1769, 1768, 1772] by Super 190 with 66 at 1,2,2,1,1,1,1,2
-Id : 223, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1772) (multiply (inverse ?1770) (multiply ?1770 ?1773)))) ?1774) (inverse (multiply ?1772 ?1774))) =>= ?1773 [1774, 1773, 1770, 1772] by Demod 198 with 66 at 1,1,2,1,1,1,1,2
-Id : 635, {_}: multiply (inverse ?4438) (multiply ?4438 (multiply ?4439 (inverse (multiply (multiply (inverse (multiply (inverse ?4440) ?4441)) ?4442) (inverse (multiply ?4440 ?4442)))))) =>= multiply (inverse (inverse ?4439)) ?4441 [4442, 4441, 4440, 4439, 4438] by Super 137 with 7 at 2,2,2
-Id : 668, {_}: multiply (inverse ?4724) (multiply ?4724 (multiply ?4725 ?4723)) =?= multiply (inverse (inverse ?4725)) (multiply (inverse ?4722) (multiply ?4722 ?4723)) [4722, 4723, 4725, 4724] by Super 635 with 223 at 2,2,2,2
-Id : 761, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5332) (multiply ?5332 (multiply ?5333 ?5334)))) ?5336) (inverse (multiply (inverse ?5333) ?5336))) =>= ?5334 [5336, 5334, 5333, 5332] by Super 223 with 668 at 1,1,1,1,2
-Id : 2971, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18698) (multiply ?18698 ?18699))) ?18699) (inverse (multiply (inverse ?18700) (multiply ?18700 ?18701)))) =>= ?18701 [18701, 18700, 18699, 18698] by Super 761 with 2764 at 1,1,2
-Id : 3407, {_}: multiply (multiply (inverse (inverse (inverse (inverse ?21175)))) (multiply (inverse (inverse (inverse ?21176))) ?21176)) (inverse (multiply ?21177 (inverse ?21177))) =>= ?21175 [21177, 21176, 21175] by Super 2733 with 3359 at 2,1,2
-Id : 3267, {_}: multiply (inverse ?20652) (multiply ?20652 (multiply ?20653 (inverse (multiply (multiply (inverse ?20649) ?20654) (inverse (multiply (inverse ?20649) ?20654)))))) =?= multiply (inverse (inverse ?20653)) (multiply (inverse (multiply (inverse ?20650) (multiply ?20650 ?20651))) ?20651) [20651, 20650, 20654, 20649, 20653, 20652] by Super 156 with 3188 at 1,1,1,1,2,2,2,2
-Id : 5050, {_}: multiply (inverse ?30421) (multiply ?30421 (multiply ?30422 (inverse (multiply (multiply (inverse ?30423) ?30424) (inverse (multiply (inverse ?30423) ?30424)))))) =>= ?30422 [30424, 30423, 30422, 30421] by Demod 3267 with 3188 at 3
-Id : 5058, {_}: multiply (inverse ?30488) (multiply ?30488 (multiply ?30489 (inverse (multiply (multiply (inverse ?30490) (inverse (multiply (multiply (inverse (multiply (inverse ?30485) (multiply (inverse (inverse ?30490)) ?30486))) ?30487) (inverse (multiply ?30485 ?30487))))) (inverse ?30486))))) =>= ?30489 [30487, 30486, 30485, 30490, 30489, 30488] by Super 5050 with 4 at 1,2,1,2,2,2,2
-Id : 5182, {_}: multiply (inverse ?30488) (multiply ?30488 (multiply ?30489 (inverse (multiply ?30486 (inverse ?30486))))) =>= ?30489 [30486, 30489, 30488] by Demod 5058 with 4 at 1,1,2,2,2,2
-Id : 5242, {_}: multiply ?31236 (inverse (multiply ?31238 (inverse ?31238))) =?= multiply ?31236 (inverse (multiply ?31237 (inverse ?31237))) [31237, 31238, 31236] by Super 3407 with 5182 at 1,2
-Id : 5880, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?34514) (multiply ?34514 ?34515))) ?34515) (inverse (multiply (inverse ?34511) (multiply ?34511 (inverse (multiply ?34513 (inverse ?34513))))))) =?= inverse (multiply ?34512 (inverse ?34512)) [34512, 34513, 34511, 34515, 34514] by Super 2971 with 5242 at 2,1,2,1,2
-Id : 5941, {_}: inverse (multiply ?34513 (inverse ?34513)) =?= inverse (multiply ?34512 (inverse ?34512)) [34512, 34513] by Demod 5880 with 2971 at 2
-Id : 6233, {_}: multiply (inverse (inverse (multiply ?36082 (inverse ?36082)))) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?36083)))) (multiply (inverse (inverse (inverse ?36084))) ?36084))) ?36083) =?= multiply ?36081 (inverse ?36081) [36081, 36084, 36083, 36082] by Super 3543 with 5941 at 1,1,2
-Id : 6294, {_}: multiply ?36082 (inverse ?36082) =?= multiply ?36081 (inverse ?36081) [36081, 36082] by Demod 6233 with 3543 at 2
-Id : 6354, {_}: multiply (multiply (inverse ?36480) (multiply ?36481 (inverse ?36481))) (inverse (multiply ?36482 (inverse ?36482))) =>= inverse ?36480 [36482, 36481, 36480] by Super 2733 with 6294 at 2,1,2
-Id : 6918, {_}: multiply ?39301 (inverse (multiply (multiply (inverse ?39302) (multiply ?39302 (inverse (multiply ?39300 (inverse ?39300))))) (inverse (multiply ?39299 (inverse ?39299))))) =>= inverse (inverse ?39301) [39299, 39300, 39302, 39301] by Super 379 with 6354 at 2,1,2,1,2,2
-Id : 6993, {_}: multiply ?39301 (inverse (inverse (multiply ?39300 (inverse ?39300)))) =>= inverse (inverse ?39301) [39300, 39301] by Demod 6918 with 2733 at 1,2,2
-Id : 7034, {_}: multiply (inverse (inverse ?39791)) (multiply (inverse (multiply (inverse ?39789) (inverse (inverse ?39789)))) (inverse (inverse (multiply ?39790 (inverse ?39790))))) =>= ?39791 [39790, 39789, 39791] by Super 3188 with 6993 at 2,1,1,2,2
-Id : 7801, {_}: multiply (inverse (inverse ?42915)) (inverse (inverse (inverse (multiply (inverse ?42916) (inverse (inverse ?42916)))))) =>= ?42915 [42916, 42915] by Demod 7034 with 6993 at 2,2
-Id : 7116, {_}: multiply ?40237 (inverse ?40237) =?= inverse (inverse (inverse (multiply ?40236 (inverse ?40236)))) [40236, 40237] by Super 6294 with 6993 at 3
-Id : 7831, {_}: multiply (inverse (inverse ?43066)) (multiply ?43065 (inverse ?43065)) =>= ?43066 [43065, 43066] by Super 7801 with 7116 at 2,2
-Id : 7980, {_}: multiply ?43590 (inverse (multiply ?43591 (inverse ?43591))) =>= inverse (inverse ?43590) [43591, 43590] by Super 2733 with 7831 at 1,2
-Id : 8167, {_}: multiply (inverse (inverse ?44390)) (inverse (inverse (inverse (multiply (inverse (inverse (inverse (inverse (inverse (multiply ?44389 (inverse ?44389))))))) (multiply (inverse (inverse (inverse ?44391))) ?44391))))) =>= ?44390 [44391, 44389, 44390] by Super 3543 with 7980 at 2,2
-Id : 8053, {_}: inverse (inverse (multiply (inverse (inverse (inverse (inverse ?21175)))) (multiply (inverse (inverse (inverse ?21176))) ?21176))) =>= ?21175 [21176, 21175] by Demod 3407 with 7980 at 2
-Id : 8222, {_}: multiply (inverse (inverse ?44390)) (inverse (inverse (multiply ?44389 (inverse ?44389)))) =>= ?44390 [44389, 44390] by Demod 8167 with 8053 at 1,2,2
-Id : 8223, {_}: inverse (inverse (inverse (inverse ?44390))) =>= ?44390 [44390] by Demod 8222 with 6993 at 2
-Id : 905, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6097) (multiply ?6097 (multiply ?6098 ?6099)))) ?6100) (inverse (multiply (inverse ?6098) ?6100))) =>= ?6099 [6100, 6099, 6098, 6097] by Super 223 with 668 at 1,1,1,1,2
-Id : 926, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6262) (multiply ?6262 (multiply (inverse ?6261) (multiply ?6261 ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260, 6261, 6262] by Super 905 with 299 at 2,2,1,1,1,1,2
-Id : 8054, {_}: multiply (inverse ?30488) (multiply ?30488 (inverse (inverse ?30489))) =>= ?30489 [30489, 30488] by Demod 5182 with 7980 at 2,2,2
-Id : 8447, {_}: multiply (inverse ?45106) (multiply ?45106 ?45105) =>= inverse (inverse ?45105) [45105, 45106] by Super 8054 with 8223 at 2,2,2
-Id : 8864, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?6261) (multiply ?6261 ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260, 6261] by Demod 926 with 8447 at 1,1,1,1,2
-Id : 8865, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?6260))))) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260] by Demod 8864 with 8447 at 1,1,1,1,1,1,2
-Id : 8898, {_}: inverse (multiply (multiply (inverse ?6260) ?6263) (inverse (multiply (inverse (inverse ?6259)) ?6263))) =>= multiply ?6259 ?6260 [6259, 6263, 6260] by Demod 8865 with 8223 at 1,1,1,2
-Id : 8350, {_}: multiply ?44637 (inverse (multiply (inverse (inverse (inverse ?44636))) ?44636)) =>= inverse (inverse ?44637) [44636, 44637] by Super 7980 with 8223 at 2,1,2,2
-Id : 9047, {_}: inverse (inverse (inverse (multiply (inverse ?46455) ?46454))) =>= multiply (inverse ?46454) ?46455 [46454, 46455] by Super 8898 with 8350 at 1,2
-Id : 9341, {_}: inverse (multiply (inverse ?47101) ?47100) =>= multiply (inverse ?47100) ?47101 [47100, 47101] by Super 8223 with 9047 at 1,2
-Id : 9509, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?27)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 8 with 9341 at 1,1,1,2,1,2,1,2,2
-Id : 9510, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?30) (multiply (inverse ?29) ?31)))) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9509 with 9341 at 1,1,1,1,2,1,2,1,2,2
-Id : 9511, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?29) ?31)) ?30)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9510 with 9341 at 2,1,1,1,1,2,1,2,1,2,2
-Id : 9512, {_}: multiply ?29 (inverse (multiply ?27 (inverse (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28) (inverse (multiply ?26 ?28)))))))) =>= ?31 [28, 26, 31, 30, 27, 29] by Demod 9511 with 9341 at 1,2,1,1,1,1,2,1,2,1,2,2
-Id : 8876, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2915) (multiply ?2915 ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914, 2915] by Demod 395 with 8447 at 2
-Id : 8877, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8876 with 8447 at 1,1,1,1,1,1,2
-Id : 9058, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?46500))) ?46499))))) =>= multiply (inverse (inverse (inverse ?46499))) ?46500 [46499, 46500] by Super 8877 with 8350 at 1,1,1,2
-Id : 9242, {_}: inverse (multiply (inverse (inverse (inverse ?46500))) ?46499) =>= multiply (inverse (inverse (inverse ?46499))) ?46500 [46499, 46500] by Demod 9058 with 8223 at 2
-Id : 9696, {_}: multiply (inverse ?46499) (inverse (inverse ?46500)) =?= multiply (inverse (inverse (inverse ?46499))) ?46500 [46500, 46499] by Demod 9242 with 9341 at 2
-Id : 9788, {_}: multiply (inverse ?48461) (inverse (inverse (multiply (inverse (inverse ?48461)) ?48462))) =>= inverse (inverse ?48462) [48462, 48461] by Super 8447 with 9696 at 2
-Id : 9936, {_}: multiply (inverse ?48461) (inverse (multiply (inverse ?48462) (inverse ?48461))) =>= inverse (inverse ?48462) [48462, 48461] by Demod 9788 with 9341 at 1,2,2
-Id : 9937, {_}: multiply (inverse ?48461) (multiply (inverse (inverse ?48461)) ?48462) =>= inverse (inverse ?48462) [48462, 48461] by Demod 9936 with 9341 at 2,2
-Id : 8881, {_}: multiply ?2799 (inverse (multiply (inverse (inverse ?2797)) (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797))))) =>= ?2801 [2801, 2800, 2797, 2799] by Demod 379 with 8447 at 1,1,2,2
-Id : 9499, {_}: multiply ?2799 (multiply (inverse (inverse (multiply ?2800 (multiply (multiply (inverse ?2800) (multiply (inverse ?2799) ?2801)) ?2797)))) (inverse ?2797)) =>= ?2801 [2797, 2801, 2800, 2799] by Demod 8881 with 9341 at 2,2
-Id : 397, {_}: multiply (inverse ?2927) (multiply ?2927 (inverse (multiply (multiply (inverse ?2926) (multiply ?2926 ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925, 2926, 2927] by Super 65 with 299 at 1,1,2,2,2
-Id : 8862, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2926) (multiply ?2926 ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925, 2926] by Demod 397 with 8447 at 2
-Id : 8863, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2925)) (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))))) =>= ?2929 [2929, 2928, 2925] by Demod 8862 with 8447 at 1,1,1,1,2
-Id : 9311, {_}: multiply (inverse (inverse (multiply ?2928 (multiply (multiply (inverse ?2928) ?2929) ?2925)))) (inverse ?2925) =>= ?2929 [2925, 2929, 2928] by Demod 8863 with 9047 at 2
-Id : 9517, {_}: multiply ?2799 (multiply (inverse ?2799) ?2801) =>= ?2801 [2801, 2799] by Demod 9499 with 9311 at 2,2
-Id : 9938, {_}: ?48462 =<= inverse (inverse ?48462) [48462] by Demod 9937 with 9517 at 2
-Id : 10374, {_}: inverse (multiply ?49383 ?49384) =<= multiply (inverse ?49384) (inverse ?49383) [49384, 49383] by Super 9341 with 9938 at 1,1,2
-Id : 10391, {_}: inverse (multiply ?49456 (inverse ?49455)) =>= multiply ?49455 (inverse ?49456) [49455, 49456] by Super 10374 with 9938 at 1,3
-Id : 10496, {_}: multiply ?29 (multiply (multiply ?30 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28) (inverse (multiply ?26 ?28))))) (inverse ?27)) =>= ?31 [28, 26, 31, 27, 30, 29] by Demod 9512 with 10391 at 2,2
-Id : 10497, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?31) ?29) ?30)) ?26) ?28)))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 10496 with 10391 at 2,1,2,2
-Id : 10262, {_}: inverse (multiply ?49016 ?49017) =<= multiply (inverse ?49017) (inverse ?49016) [49017, 49016] by Super 9341 with 9938 at 1,1,2
-Id : 10628, {_}: multiply ?49899 (inverse (multiply ?49900 ?49899)) =>= inverse ?49900 [49900, 49899] by Super 9517 with 10262 at 2,2
-Id : 10356, {_}: multiply ?49320 (inverse (multiply ?49319 ?49320)) =>= inverse ?49319 [49319, 49320] by Super 9517 with 10262 at 2,2
-Id : 10637, {_}: multiply (inverse (multiply ?49929 ?49930)) (inverse (inverse ?49929)) =>= inverse ?49930 [49930, 49929] by Super 10628 with 10356 at 1,2,2
-Id : 10710, {_}: inverse (multiply (inverse ?49929) (multiply ?49929 ?49930)) =>= inverse ?49930 [49930, 49929] by Demod 10637 with 10262 at 2
-Id : 10949, {_}: multiply (inverse (multiply ?50486 ?50487)) ?50486 =>= inverse ?50487 [50487, 50486] by Demod 10710 with 9341 at 2
-Id : 8870, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?587) ?588)) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 588, 587] by Demod 65 with 8447 at 2
-Id : 9498, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?588) ?587) ?589) (inverse (multiply ?587 ?589))))) =>= ?588 [589, 587, 588] by Demod 8870 with 9341 at 1,1,1,1,1,2
-Id : 10246, {_}: inverse (multiply (multiply (multiply (inverse ?588) ?587) ?589) (inverse (multiply ?587 ?589))) =>= ?588 [589, 587, 588] by Demod 9498 with 9938 at 2
-Id : 10500, {_}: multiply (multiply ?587 ?589) (inverse (multiply (multiply (inverse ?588) ?587) ?589)) =>= ?588 [588, 589, 587] by Demod 10246 with 10391 at 2
-Id : 10962, {_}: multiply (inverse ?50540) (multiply ?50538 ?50539) =<= inverse (inverse (multiply (multiply (inverse ?50540) ?50538) ?50539)) [50539, 50538, 50540] by Super 10949 with 10500 at 1,1,2
-Id : 11025, {_}: multiply (inverse ?50540) (multiply ?50538 ?50539) =<= multiply (multiply (inverse ?50540) ?50538) ?50539 [50539, 50538, 50540] by Demod 10962 with 9938 at 3
-Id : 11420, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?31) ?29) ?30) ?26)) ?28)))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 10497 with 11025 at 1,1,2,2,1,2,2
-Id : 11421, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?31) ?29) ?30) ?26) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11420 with 11025 at 1,2,2,1,2,2
-Id : 11422, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?31) (multiply ?29 ?30)) ?26) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11421 with 11025 at 1,1,2,1,2,2,1,2,2
-Id : 11423, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?31) (multiply (multiply ?29 ?30) ?26)) ?28))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11422 with 11025 at 1,2,1,2,2,1,2,2
-Id : 11424, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (inverse (multiply (inverse ?27) (multiply (inverse ?31) (multiply (multiply (multiply ?29 ?30) ?26) ?28)))))) (inverse ?27)) =>= ?31 [31, 27, 28, 26, 30, 29] by Demod 11423 with 11025 at 2,1,2,2,1,2,2
-Id : 11441, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (inverse (multiply (inverse ?31) (multiply (multiply (multiply ?29 ?30) ?26) ?28))) ?27))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11424 with 9341 at 2,2,1,2,2
-Id : 11442, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (multiply (inverse (multiply (multiply (multiply ?29 ?30) ?26) ?28)) ?31) ?27))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11441 with 9341 at 1,2,2,1,2,2
-Id : 11443, {_}: multiply ?29 (multiply (multiply ?30 (multiply (multiply ?26 ?28) (multiply (inverse (multiply (multiply (multiply ?29 ?30) ?26) ?28)) (multiply ?31 ?27)))) (inverse ?27)) =>= ?31 [27, 31, 28, 26, 30, 29] by Demod 11442 with 11025 at 2,2,1,2,2
-Id : 3545, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= inverse (multiply (inverse (multiply (inverse ?21970) (multiply ?21970 ?21971))) ?21971) [21971, 21970, 21969] by Super 3188 with 3359 at 2
-Id : 8885, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= inverse (multiply (inverse (inverse (inverse ?21971))) ?21971) [21971, 21969] by Demod 3545 with 8447 at 1,1,1,3
-Id : 9513, {_}: multiply (inverse (inverse (inverse ?21969))) ?21969 =?= multiply (inverse ?21971) (inverse (inverse ?21971)) [21971, 21969] by Demod 8885 with 9341 at 3
-Id : 10244, {_}: multiply (inverse ?21969) ?21969 =?= multiply (inverse ?21971) (inverse (inverse ?21971)) [21971, 21969] by Demod 9513 with 9938 at 1,2
-Id : 10245, {_}: multiply (inverse ?21969) ?21969 =?= multiply (inverse ?21971) ?21971 [21971, 21969] by Demod 10244 with 9938 at 2,3
-Id : 10259, {_}: multiply (inverse ?49007) ?49007 =?= multiply ?49006 (inverse ?49006) [49006, 49007] by Super 10245 with 9938 at 1,3
-Id : 12679, {_}: multiply ?53137 (multiply (multiply ?53138 (multiply (multiply ?53139 ?53140) (multiply ?53136 (inverse ?53136)))) (inverse ?53140)) =>= multiply (multiply ?53137 ?53138) ?53139 [53136, 53140, 53139, 53138, 53137] by Super 11443 with 10259 at 2,2,1,2,2
-Id : 8358, {_}: multiply ?44663 (multiply ?44664 (inverse ?44664)) =>= inverse (inverse ?44663) [44664, 44663] by Super 7831 with 8223 at 1,2
-Id : 10234, {_}: multiply ?44663 (multiply ?44664 (inverse ?44664)) =>= ?44663 [44664, 44663] by Demod 8358 with 9938 at 3
-Id : 12924, {_}: multiply ?53137 (multiply (multiply ?53138 (multiply ?53139 ?53140)) (inverse ?53140)) =>= multiply (multiply ?53137 ?53138) ?53139 [53140, 53139, 53138, 53137] by Demod 12679 with 10234 at 2,1,2,2
-Id : 10222, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2914))) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 8877 with 9938 at 2
-Id : 10223, {_}: inverse (multiply (multiply (inverse ?2914) ?2917) (inverse (multiply ?2913 ?2917))) =>= multiply ?2913 ?2914 [2913, 2917, 2914] by Demod 10222 with 9938 at 1,1,1,2
-Id : 10502, {_}: multiply (multiply ?2913 ?2917) (inverse (multiply (inverse ?2914) ?2917)) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 10223 with 10391 at 2
-Id : 10503, {_}: multiply (multiply ?2913 ?2917) (multiply (inverse ?2917) ?2914) =>= multiply ?2913 ?2914 [2914, 2917, 2913] by Demod 10502 with 9341 at 2,2
-Id : 10711, {_}: multiply (inverse (multiply ?49929 ?49930)) ?49929 =>= inverse ?49930 [49930, 49929] by Demod 10710 with 9341 at 2
-Id : 10940, {_}: multiply (multiply ?50443 (multiply ?50441 ?50442)) (inverse ?50442) =>= multiply ?50443 ?50441 [50442, 50441, 50443] by Super 10503 with 10711 at 2,2
-Id : 22401, {_}: multiply ?53137 (multiply ?53138 ?53139) =?= multiply (multiply ?53137 ?53138) ?53139 [53139, 53138, 53137] by Demod 12924 with 10940 at 2,2
-Id : 22896, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 2 with 22401 at 3
-Id : 2, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for GRP014-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_commutator is 86
- b is 97
- c is 96
- commutator is 95
- identity is 92
- inverse is 90
- left_identity is 91
- left_inverse is 89
- multiply is 94
- name is 87
- prove_center is 93
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
- Id : 12, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-Goal
- Id : 2, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-Timeout !
-FAILURE in 254 iterations
-% SZS status Timeout for GRP024-5.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- identity is 93
- intersection is 85
- intersection_associative is 79
- intersection_commutative is 81
- intersection_idempotent is 84
- intersection_union_absorbtion is 76
- inverse is 91
- inverse_involution is 87
- inverse_of_identity is 88
- inverse_product_lemma is 86
- left_identity is 92
- left_inverse is 90
- multiply is 95
- multiply_intersection1 is 74
- multiply_intersection2 is 72
- multiply_union1 is 75
- multiply_union2 is 73
- negative_part is 96
- positive_part is 97
- prove_product is 94
- union is 83
- union_associative is 78
- union_commutative is 80
- union_idempotent is 82
- union_intersection_absorbtion is 77
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
- Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
- Id : 14, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
- Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
- Id : 18, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
- Id : 20, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
- Id : 22, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
- Id : 24, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
- Id : 26, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
- Id : 28, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
- Id : 30, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
- Id : 32, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
- Id : 34, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
- Id : 36, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
- Id : 38, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
- Id : 40, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
- Id : 42, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-Goal
- Id : 2, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-Found proof, 2.362992s
-% SZS status Unsatisfiable for GRP114-1.p
-% SZS output start CNFRefutation for GRP114-1.p
-Id : 16, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-Id : 24, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
-Id : 34, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-Id : 28, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
-Id : 26, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
-Id : 267, {_}: multiply (union ?680 ?681) ?682 =<= union (multiply ?680 ?682) (multiply ?681 ?682) [682, 681, 680] by multiply_union2 ?680 ?681 ?682
-Id : 30, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
-Id : 230, {_}: multiply ?593 (intersection ?594 ?595) =<= intersection (multiply ?593 ?594) (multiply ?593 ?595) [595, 594, 593] by multiply_intersection1 ?593 ?594 ?595
-Id : 42, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
-Id : 20, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
-Id : 303, {_}: multiply (intersection ?770 ?771) ?772 =<= intersection (multiply ?770 ?772) (multiply ?771 ?772) [772, 771, 770] by multiply_intersection2 ?770 ?771 ?772
-Id : 14, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
-Id : 22, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
-Id : 40, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
-Id : 10, {_}: inverse identity =>= identity [] by inverse_of_identity
-Id : 32, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-Id : 12, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-Id : 79, {_}: inverse (multiply ?142 ?143) =<= multiply (inverse ?143) (inverse ?142) [143, 142] by inverse_product_lemma ?142 ?143
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 47, {_}: multiply (multiply ?68 ?69) ?70 =?= multiply ?68 (multiply ?69 ?70) [70, 69, 68] by associativity ?68 ?69 ?70
-Id : 56, {_}: multiply identity ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Super 47 with 6 at 1,2
-Id : 8878, {_}: ?10861 =<= multiply (inverse ?10862) (multiply ?10862 ?10861) [10862, 10861] by Demod 56 with 4 at 2
-Id : 81, {_}: inverse (multiply (inverse ?147) ?148) =>= multiply (inverse ?148) ?147 [148, 147] by Super 79 with 12 at 2,3
-Id : 80, {_}: inverse (multiply identity ?145) =<= multiply (inverse ?145) identity [145] by Super 79 with 10 at 2,3
-Id : 450, {_}: inverse ?990 =<= multiply (inverse ?990) identity [990] by Demod 80 with 4 at 1,2
-Id : 452, {_}: inverse (inverse ?993) =<= multiply ?993 identity [993] by Super 450 with 12 at 1,3
-Id : 467, {_}: ?993 =<= multiply ?993 identity [993] by Demod 452 with 12 at 2
-Id : 472, {_}: multiply ?1004 (union ?1005 identity) =?= union (multiply ?1004 ?1005) ?1004 [1005, 1004] by Super 32 with 467 at 2,3
-Id : 3150, {_}: multiply ?4224 (positive_part ?4225) =<= union (multiply ?4224 ?4225) ?4224 [4225, 4224] by Demod 472 with 40 at 2,2
-Id : 3152, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= union identity (inverse ?4229) [4229] by Super 3150 with 6 at 1,3
-Id : 336, {_}: union identity ?835 =>= positive_part ?835 [835] by Super 22 with 40 at 3
-Id : 3189, {_}: multiply (inverse ?4229) (positive_part ?4229) =>= positive_part (inverse ?4229) [4229] by Demod 3152 with 336 at 3
-Id : 3219, {_}: inverse (positive_part (inverse ?4304)) =<= multiply (inverse (positive_part ?4304)) ?4304 [4304] by Super 81 with 3189 at 1,2
-Id : 8893, {_}: ?10899 =<= multiply (inverse (inverse (positive_part ?10899))) (inverse (positive_part (inverse ?10899))) [10899] by Super 8878 with 3219 at 2,3
-Id : 8928, {_}: ?10899 =<= inverse (multiply (positive_part (inverse ?10899)) (inverse (positive_part ?10899))) [10899] by Demod 8893 with 14 at 3
-Id : 83, {_}: inverse (multiply ?153 (inverse ?152)) =>= multiply ?152 (inverse ?153) [152, 153] by Super 79 with 12 at 1,3
-Id : 8929, {_}: ?10899 =<= multiply (positive_part ?10899) (inverse (positive_part (inverse ?10899))) [10899] by Demod 8928 with 83 at 3
-Id : 310, {_}: multiply (intersection (inverse ?798) ?797) ?798 =>= intersection identity (multiply ?797 ?798) [797, 798] by Super 303 with 6 at 1,3
-Id : 355, {_}: intersection identity ?867 =>= negative_part ?867 [867] by Super 20 with 42 at 3
-Id : 15914, {_}: multiply (intersection (inverse ?16735) ?16736) ?16735 =>= negative_part (multiply ?16736 ?16735) [16736, 16735] by Demod 310 with 355 at 3
-Id : 15939, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part (multiply identity ?16817) [16817] by Super 15914 with 42 at 1,2
-Id : 15984, {_}: multiply (negative_part (inverse ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15939 with 4 at 1,3
-Id : 237, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= intersection identity (multiply (inverse ?620) ?621) [621, 620] by Super 230 with 6 at 1,3
-Id : 9377, {_}: multiply (inverse ?620) (intersection ?620 ?621) =>= negative_part (multiply (inverse ?620) ?621) [621, 620] by Demod 237 with 355 at 3
-Id : 387, {_}: intersection (positive_part ?915) ?915 =>= ?915 [915] by Super 30 with 336 at 1,2
-Id : 274, {_}: multiply (union (inverse ?708) ?707) ?708 =>= union identity (multiply ?707 ?708) [707, 708] by Super 267 with 6 at 1,3
-Id : 9854, {_}: multiply (union (inverse ?12356) ?12357) ?12356 =>= positive_part (multiply ?12357 ?12356) [12357, 12356] by Demod 274 with 336 at 3
-Id : 384, {_}: union identity (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Super 26 with 336 at 1,3
-Id : 394, {_}: positive_part (union ?906 ?907) =>= union (positive_part ?906) ?907 [907, 906] by Demod 384 with 336 at 2
-Id : 339, {_}: union ?842 (union ?843 identity) =>= positive_part (union ?842 ?843) [843, 842] by Super 26 with 40 at 3
-Id : 350, {_}: union ?842 (positive_part ?843) =<= positive_part (union ?842 ?843) [843, 842] by Demod 339 with 40 at 2,2
-Id : 667, {_}: union ?906 (positive_part ?907) =?= union (positive_part ?906) ?907 [907, 906] by Demod 394 with 350 at 2
-Id : 414, {_}: union (negative_part ?942) ?942 =>= ?942 [942] by Super 28 with 355 at 1,2
-Id : 479, {_}: multiply ?1021 (intersection ?1022 identity) =?= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Super 34 with 467 at 2,3
-Id : 2571, {_}: multiply ?3618 (negative_part ?3619) =<= intersection (multiply ?3618 ?3619) ?3618 [3619, 3618] by Demod 479 with 42 at 2,2
-Id : 2573, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= intersection identity (inverse ?3623) [3623] by Super 2571 with 6 at 1,3
-Id : 2624, {_}: multiply (inverse ?3692) (negative_part ?3692) =>= negative_part (inverse ?3692) [3692] by Demod 2573 with 355 at 3
-Id : 358, {_}: intersection ?874 (intersection ?875 identity) =>= negative_part (intersection ?874 ?875) [875, 874] by Super 24 with 42 at 3
-Id : 603, {_}: intersection ?1157 (negative_part ?1158) =<= negative_part (intersection ?1157 ?1158) [1158, 1157] by Demod 358 with 42 at 2,2
-Id : 613, {_}: intersection ?1189 (negative_part identity) =>= negative_part (negative_part ?1189) [1189] by Super 603 with 42 at 1,3
-Id : 354, {_}: negative_part identity =>= identity [] by Super 16 with 42 at 2
-Id : 624, {_}: intersection ?1189 identity =<= negative_part (negative_part ?1189) [1189] by Demod 613 with 354 at 2,2
-Id : 625, {_}: negative_part ?1189 =<= negative_part (negative_part ?1189) [1189] by Demod 624 with 42 at 2
-Id : 2630, {_}: multiply (inverse (negative_part ?3706)) (negative_part ?3706) =>= negative_part (inverse (negative_part ?3706)) [3706] by Super 2624 with 625 at 2,2
-Id : 2650, {_}: identity =<= negative_part (inverse (negative_part ?3706)) [3706] by Demod 2630 with 6 at 2
-Id : 2720, {_}: union identity (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Super 414 with 2650 at 1,2
-Id : 2757, {_}: positive_part (inverse (negative_part ?3792)) =>= inverse (negative_part ?3792) [3792] by Demod 2720 with 336 at 2
-Id : 2867, {_}: union (inverse (negative_part ?3906)) (positive_part ?3907) =>= union (inverse (negative_part ?3906)) ?3907 [3907, 3906] by Super 667 with 2757 at 1,3
-Id : 9877, {_}: multiply (union (inverse (negative_part ?12432)) ?12433) (negative_part ?12432) =>= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12433, 12432] by Super 9854 with 2867 at 1,2
-Id : 9834, {_}: multiply (union (inverse ?708) ?707) ?708 =>= positive_part (multiply ?707 ?708) [707, 708] by Demod 274 with 336 at 3
-Id : 9911, {_}: positive_part (multiply ?12433 (negative_part ?12432)) =<= positive_part (multiply (positive_part ?12433) (negative_part ?12432)) [12432, 12433] by Demod 9877 with 9834 at 2
-Id : 492, {_}: multiply ?1021 (negative_part ?1022) =<= intersection (multiply ?1021 ?1022) ?1021 [1022, 1021] by Demod 479 with 42 at 2,2
-Id : 9880, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part (multiply identity ?12441) [12441] by Super 9854 with 40 at 1,2
-Id : 9914, {_}: multiply (positive_part (inverse ?12441)) ?12441 =>= positive_part ?12441 [12441] by Demod 9880 with 4 at 1,3
-Id : 9937, {_}: multiply (positive_part (inverse ?12495)) (negative_part ?12495) =>= intersection (positive_part ?12495) (positive_part (inverse ?12495)) [12495] by Super 492 with 9914 at 1,3
-Id : 10764, {_}: positive_part (multiply (inverse ?13313) (negative_part ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Super 9911 with 9937 at 1,3
-Id : 2601, {_}: multiply (inverse ?3623) (negative_part ?3623) =>= negative_part (inverse ?3623) [3623] by Demod 2573 with 355 at 3
-Id : 10802, {_}: positive_part (negative_part (inverse ?13313)) =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10764 with 2601 at 1,2
-Id : 334, {_}: positive_part (intersection ?832 identity) =>= identity [832] by Super 28 with 40 at 2
-Id : 507, {_}: positive_part (negative_part ?832) =>= identity [832] by Demod 334 with 42 at 1,2
-Id : 10803, {_}: identity =<= positive_part (intersection (positive_part ?13313) (positive_part (inverse ?13313))) [13313] by Demod 10802 with 507 at 2
-Id : 51479, {_}: intersection identity (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Super 387 with 10803 at 1,2
-Id : 51786, {_}: negative_part (intersection (positive_part ?50477) (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51479 with 355 at 2
-Id : 369, {_}: intersection ?874 (negative_part ?875) =<= negative_part (intersection ?874 ?875) [875, 874] by Demod 358 with 42 at 2,2
-Id : 51787, {_}: intersection (positive_part ?50477) (negative_part (positive_part (inverse ?50477))) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51786 with 369 at 2
-Id : 51788, {_}: intersection (negative_part (positive_part (inverse ?50477))) (positive_part ?50477) =>= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51787 with 20 at 2
-Id : 411, {_}: intersection identity (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Super 24 with 355 at 1,3
-Id : 421, {_}: negative_part (intersection ?933 ?934) =>= intersection (negative_part ?933) ?934 [934, 933] by Demod 411 with 355 at 2
-Id : 795, {_}: intersection ?1452 (negative_part ?1453) =?= intersection (negative_part ?1452) ?1453 [1453, 1452] by Demod 421 with 369 at 2
-Id : 353, {_}: negative_part (union ?864 identity) =>= identity [864] by Super 30 with 42 at 2
-Id : 371, {_}: negative_part (positive_part ?864) =>= identity [864] by Demod 353 with 40 at 1,2
-Id : 797, {_}: intersection (positive_part ?1457) (negative_part ?1458) =>= intersection identity ?1458 [1458, 1457] by Super 795 with 371 at 1,3
-Id : 834, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= intersection identity ?1458 [1457, 1458] by Demod 797 with 20 at 2
-Id : 835, {_}: intersection (negative_part ?1458) (positive_part ?1457) =>= negative_part ?1458 [1457, 1458] by Demod 834 with 355 at 3
-Id : 51789, {_}: negative_part (positive_part (inverse ?50477)) =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51788 with 835 at 2
-Id : 51790, {_}: identity =<= intersection (positive_part ?50477) (positive_part (inverse ?50477)) [50477] by Demod 51789 with 371 at 2
-Id : 52162, {_}: multiply (inverse (positive_part ?50853)) identity =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Super 9377 with 51790 at 2,2
-Id : 52250, {_}: inverse (positive_part ?50853) =<= negative_part (multiply (inverse (positive_part ?50853)) (positive_part (inverse ?50853))) [50853] by Demod 52162 with 467 at 2
-Id : 65, {_}: ?103 =<= multiply (inverse ?102) (multiply ?102 ?103) [102, 103] by Demod 56 with 4 at 2
-Id : 9942, {_}: multiply (positive_part (inverse ?12505)) ?12505 =>= positive_part ?12505 [12505] by Demod 9880 with 4 at 1,3
-Id : 9944, {_}: multiply (positive_part ?12508) (inverse ?12508) =>= positive_part (inverse ?12508) [12508] by Super 9942 with 12 at 1,1,2
-Id : 10037, {_}: inverse ?12562 =<= multiply (inverse (positive_part ?12562)) (positive_part (inverse ?12562)) [12562] by Super 65 with 9944 at 2,3
-Id : 52251, {_}: inverse (positive_part ?50853) =<= negative_part (inverse ?50853) [50853] by Demod 52250 with 10037 at 1,3
-Id : 52520, {_}: multiply (inverse (positive_part ?16817)) ?16817 =>= negative_part ?16817 [16817] by Demod 15984 with 52251 at 1,2
-Id : 52551, {_}: inverse (positive_part (inverse ?16817)) =>= negative_part ?16817 [16817] by Demod 52520 with 3219 at 2
-Id : 52560, {_}: ?10899 =<= multiply (positive_part ?10899) (negative_part ?10899) [10899] by Demod 8929 with 52551 at 2,3
-Id : 52939, {_}: a === a [] by Demod 2 with 52560 at 2
-Id : 2, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
-% SZS output end CNFRefutation for GRP114-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 87
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 89
- least_upper_bound is 95
- left_identity is 90
- left_inverse is 88
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 91
- prove_distrun is 93
- symmetry_of_glb is 86
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-Timeout !
-FAILURE in 345 iterations
-% SZS status Timeout for GRP164-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 84
- associativity_of_lub is 83
- glb_absorbtion is 79
- greatest_lower_bound is 88
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 93
- inverse is 91
- lat4_1 is 74
- lat4_2 is 73
- lat4_3 is 72
- lat4_4 is 71
- least_upper_bound is 86
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- negative_part is 96
- positive_part is 97
- prove_lat4 is 94
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
- Id : 36, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
- Id : 38, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
- Id : 40, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-Goal
- Id : 2, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-Found proof, 4.088951s
-% SZS status Unsatisfiable for GRP167-1.p
-% SZS output start CNFRefutation for GRP167-1.p
-Id : 202, {_}: multiply ?551 (greatest_lower_bound ?552 ?553) =<= greatest_lower_bound (multiply ?551 ?552) (multiply ?551 ?553) [553, 552, 551] by monotony_glb1 ?551 ?552 ?553
-Id : 22, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 24, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 171, {_}: multiply ?475 (least_upper_bound ?476 ?477) =<= least_upper_bound (multiply ?475 ?476) (multiply ?475 ?477) [477, 476, 475] by monotony_lub1 ?475 ?476 ?477
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 384, {_}: greatest_lower_bound ?977 (least_upper_bound ?978 ?979) =<= least_upper_bound (greatest_lower_bound ?977 ?978) (greatest_lower_bound ?977 ?979) [979, 978, 977] by lat4_4 ?977 ?978 ?979
-Id : 34, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 236, {_}: multiply (least_upper_bound ?630 ?631) ?632 =<= least_upper_bound (multiply ?630 ?632) (multiply ?631 ?632) [632, 631, 630] by monotony_lub2 ?630 ?631 ?632
-Id : 36, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 269, {_}: multiply (greatest_lower_bound ?712 ?713) ?714 =<= greatest_lower_bound (multiply ?712 ?714) (multiply ?713 ?714) [714, 713, 712] by monotony_glb2 ?712 ?713 ?714
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 45, {_}: multiply (multiply ?70 ?71) ?72 =?= multiply ?70 (multiply ?71 ?72) [72, 71, 70] by associativity ?70 ?71 ?72
-Id : 54, {_}: multiply identity ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Super 45 with 6 at 1,2
-Id : 63, {_}: ?105 =<= multiply (inverse ?104) (multiply ?104 ?105) [104, 105] by Demod 54 with 4 at 2
-Id : 275, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= greatest_lower_bound identity (multiply ?735 ?736) [735, 736] by Super 269 with 6 at 1,3
-Id : 314, {_}: greatest_lower_bound identity ?795 =>= negative_part ?795 [795] by Super 10 with 36 at 3
-Id : 16387, {_}: multiply (greatest_lower_bound (inverse ?19768) ?19769) ?19768 =>= negative_part (multiply ?19769 ?19768) [19769, 19768] by Demod 275 with 314 at 3
-Id : 16411, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part (multiply identity ?19845) [19845] by Super 16387 with 36 at 1,2
-Id : 16448, {_}: multiply (negative_part (inverse ?19845)) ?19845 =>= negative_part ?19845 [19845] by Demod 16411 with 4 at 1,3
-Id : 16459, {_}: ?19856 =<= multiply (inverse (negative_part (inverse ?19856))) (negative_part ?19856) [19856] by Super 63 with 16448 at 2,3
-Id : 242, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= least_upper_bound identity (multiply ?653 ?654) [653, 654] by Super 236 with 6 at 1,3
-Id : 298, {_}: least_upper_bound identity ?767 =>= positive_part ?767 [767] by Super 12 with 34 at 3
-Id : 14211, {_}: multiply (least_upper_bound (inverse ?17599) ?17600) ?17599 =>= positive_part (multiply ?17600 ?17599) [17600, 17599] by Demod 242 with 298 at 3
-Id : 14234, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part (multiply identity ?17673) [17673] by Super 14211 with 34 at 1,2
-Id : 14264, {_}: multiply (positive_part (inverse ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14234 with 4 at 1,3
-Id : 14196, {_}: multiply (least_upper_bound (inverse ?654) ?653) ?654 =>= positive_part (multiply ?653 ?654) [653, 654] by Demod 242 with 298 at 3
-Id : 393, {_}: greatest_lower_bound ?1016 (least_upper_bound ?1017 identity) =<= least_upper_bound (greatest_lower_bound ?1016 ?1017) (negative_part ?1016) [1017, 1016] by Super 384 with 36 at 2,3
-Id : 17840, {_}: greatest_lower_bound ?21384 (positive_part ?21385) =<= least_upper_bound (greatest_lower_bound ?21384 ?21385) (negative_part ?21384) [21385, 21384] by Demod 393 with 34 at 2,2
-Id : 17869, {_}: greatest_lower_bound ?21489 (positive_part ?21490) =<= least_upper_bound (greatest_lower_bound ?21490 ?21489) (negative_part ?21489) [21490, 21489] by Super 17840 with 10 at 1,3
-Id : 16471, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19889)) ?19890) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Super 32 with 16448 at 1,3
-Id : 480, {_}: greatest_lower_bound identity (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Super 14 with 314 at 1,3
-Id : 492, {_}: negative_part (greatest_lower_bound ?1137 ?1138) =>= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 480 with 314 at 2
-Id : 317, {_}: greatest_lower_bound ?802 (greatest_lower_bound ?803 identity) =>= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Super 14 with 36 at 3
-Id : 326, {_}: greatest_lower_bound ?802 (negative_part ?803) =<= negative_part (greatest_lower_bound ?802 ?803) [803, 802] by Demod 317 with 36 at 2,2
-Id : 770, {_}: greatest_lower_bound ?1137 (negative_part ?1138) =?= greatest_lower_bound (negative_part ?1137) ?1138 [1138, 1137] by Demod 492 with 326 at 2
-Id : 16499, {_}: multiply (greatest_lower_bound (inverse ?19889) (negative_part ?19890)) ?19889 =>= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19890, 19889] by Demod 16471 with 770 at 1,2
-Id : 16372, {_}: multiply (greatest_lower_bound (inverse ?736) ?735) ?736 =>= negative_part (multiply ?735 ?736) [735, 736] by Demod 275 with 314 at 3
-Id : 16500, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (negative_part ?19889) (multiply ?19890 ?19889) [19889, 19890] by Demod 16499 with 16372 at 2
-Id : 16501, {_}: negative_part (multiply (negative_part ?19890) ?19889) =<= greatest_lower_bound (multiply ?19890 ?19889) (negative_part ?19889) [19889, 19890] by Demod 16500 with 10 at 3
-Id : 47, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= multiply ?77 identity [78, 77] by Super 45 with 6 at 2,3
-Id : 4534, {_}: multiply (multiply ?6403 (inverse ?6404)) ?6404 =>= multiply ?6403 identity [6404, 6403] by Super 45 with 6 at 2,3
-Id : 4537, {_}: multiply identity ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Super 4534 with 6 at 1,2
-Id : 4552, {_}: ?6410 =<= multiply (inverse (inverse ?6410)) identity [6410] by Demod 4537 with 4 at 2
-Id : 46, {_}: multiply (multiply ?74 identity) ?75 =>= multiply ?74 ?75 [75, 74] by Super 45 with 4 at 2,3
-Id : 4557, {_}: multiply ?6432 ?6433 =<= multiply (inverse (inverse ?6432)) ?6433 [6433, 6432] by Super 46 with 4552 at 1,2
-Id : 4577, {_}: ?6410 =<= multiply ?6410 identity [6410] by Demod 4552 with 4557 at 3
-Id : 4578, {_}: multiply (multiply ?77 (inverse ?78)) ?78 =>= ?77 [78, 77] by Demod 47 with 4577 at 3
-Id : 4593, {_}: inverse (inverse ?6519) =<= multiply ?6519 identity [6519] by Super 4577 with 4557 at 3
-Id : 4599, {_}: inverse (inverse ?6519) =>= ?6519 [6519] by Demod 4593 with 4577 at 3
-Id : 4627, {_}: multiply (multiply ?6536 ?6535) (inverse ?6535) =>= ?6536 [6535, 6536] by Super 4578 with 4599 at 2,1,2
-Id : 62767, {_}: inverse ?65768 =<= multiply (inverse (multiply ?65769 ?65768)) ?65769 [65769, 65768] by Super 63 with 4627 at 2,3
-Id : 177, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= least_upper_bound identity (multiply (inverse ?498) ?499) [499, 498] by Super 171 with 6 at 1,3
-Id : 4718, {_}: multiply (inverse ?6711) (least_upper_bound ?6711 ?6712) =>= positive_part (multiply (inverse ?6711) ?6712) [6712, 6711] by Demod 177 with 298 at 3
-Id : 4741, {_}: multiply (inverse ?6778) (positive_part ?6778) =?= positive_part (multiply (inverse ?6778) identity) [6778] by Super 4718 with 34 at 2,2
-Id : 4789, {_}: multiply (inverse ?6833) (positive_part ?6833) =>= positive_part (inverse ?6833) [6833] by Demod 4741 with 4577 at 1,3
-Id : 4801, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part (inverse (inverse ?6862)) [6862] by Super 4789 with 4599 at 1,2
-Id : 4820, {_}: multiply ?6862 (positive_part (inverse ?6862)) =>= positive_part ?6862 [6862] by Demod 4801 with 4599 at 1,3
-Id : 62784, {_}: inverse (positive_part (inverse ?65816)) =<= multiply (inverse (positive_part ?65816)) ?65816 [65816] by Super 62767 with 4820 at 1,1,3
-Id : 63204, {_}: negative_part (multiply (negative_part (inverse (positive_part ?66345))) ?66345) =>= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Super 16501 with 62784 at 1,3
-Id : 303, {_}: greatest_lower_bound ?780 (positive_part ?780) =>= ?780 [780] by Super 24 with 34 at 2,2
-Id : 535, {_}: greatest_lower_bound (positive_part ?1185) ?1185 =>= ?1185 [1185] by Super 10 with 303 at 3
-Id : 301, {_}: least_upper_bound ?774 (least_upper_bound ?775 identity) =>= positive_part (least_upper_bound ?774 ?775) [775, 774] by Super 16 with 34 at 3
-Id : 566, {_}: least_upper_bound ?1228 (positive_part ?1229) =<= positive_part (least_upper_bound ?1228 ?1229) [1229, 1228] by Demod 301 with 34 at 2,2
-Id : 576, {_}: least_upper_bound ?1260 (positive_part identity) =>= positive_part (positive_part ?1260) [1260] by Super 566 with 34 at 1,3
-Id : 297, {_}: positive_part identity =>= identity [] by Super 18 with 34 at 2
-Id : 590, {_}: least_upper_bound ?1260 identity =<= positive_part (positive_part ?1260) [1260] by Demod 576 with 297 at 2,2
-Id : 591, {_}: positive_part ?1260 =<= positive_part (positive_part ?1260) [1260] by Demod 590 with 34 at 2
-Id : 4798, {_}: multiply (inverse (positive_part ?6856)) (positive_part ?6856) =>= positive_part (inverse (positive_part ?6856)) [6856] by Super 4789 with 591 at 2,2
-Id : 4815, {_}: identity =<= positive_part (inverse (positive_part ?6856)) [6856] by Demod 4798 with 6 at 2
-Id : 4901, {_}: greatest_lower_bound identity (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Super 535 with 4815 at 1,2
-Id : 4948, {_}: negative_part (inverse (positive_part ?6968)) =>= inverse (positive_part ?6968) [6968] by Demod 4901 with 314 at 2
-Id : 63301, {_}: negative_part (multiply (inverse (positive_part ?66345)) ?66345) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63204 with 4948 at 1,1,2
-Id : 63302, {_}: negative_part (inverse (positive_part (inverse ?66345))) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63301 with 62784 at 1,2
-Id : 63303, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) (negative_part ?66345) [66345] by Demod 63302 with 4948 at 2
-Id : 5093, {_}: greatest_lower_bound (inverse (positive_part ?7140)) (negative_part ?7141) =>= greatest_lower_bound (inverse (positive_part ?7140)) ?7141 [7141, 7140] by Super 770 with 4948 at 1,3
-Id : 63304, {_}: inverse (positive_part (inverse ?66345)) =<= greatest_lower_bound (inverse (positive_part (inverse ?66345))) ?66345 [66345] by Demod 63303 with 5093 at 3
-Id : 63811, {_}: greatest_lower_bound ?66966 (positive_part (inverse (positive_part (inverse ?66966)))) =>= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Super 17869 with 63304 at 1,3
-Id : 64079, {_}: greatest_lower_bound ?66966 identity =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 63811 with 4815 at 2,2
-Id : 64080, {_}: negative_part ?66966 =<= least_upper_bound (inverse (positive_part (inverse ?66966))) (negative_part ?66966) [66966] by Demod 64079 with 36 at 2
-Id : 81148, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (positive_part (inverse ?80770))) [80770] by Super 14196 with 64080 at 1,2
-Id : 4706, {_}: multiply (inverse ?498) (least_upper_bound ?498 ?499) =>= positive_part (multiply (inverse ?498) ?499) [499, 498] by Demod 177 with 298 at 3
-Id : 444, {_}: least_upper_bound identity (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Super 16 with 298 at 1,3
-Id : 455, {_}: positive_part (least_upper_bound ?1100 ?1101) =>= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 444 with 298 at 2
-Id : 310, {_}: least_upper_bound ?774 (positive_part ?775) =<= positive_part (least_upper_bound ?774 ?775) [775, 774] by Demod 301 with 34 at 2,2
-Id : 677, {_}: least_upper_bound ?1100 (positive_part ?1101) =?= least_upper_bound (positive_part ?1100) ?1101 [1101, 1100] by Demod 455 with 310 at 2
-Id : 483, {_}: least_upper_bound identity (negative_part ?1146) =>= identity [1146] by Super 22 with 314 at 2,2
-Id : 491, {_}: positive_part (negative_part ?1146) =>= identity [1146] by Demod 483 with 298 at 2
-Id : 4791, {_}: multiply (inverse (negative_part ?6836)) identity =>= positive_part (inverse (negative_part ?6836)) [6836] by Super 4789 with 491 at 2,2
-Id : 4812, {_}: inverse (negative_part ?6836) =<= positive_part (inverse (negative_part ?6836)) [6836] by Demod 4791 with 4577 at 2
-Id : 4834, {_}: least_upper_bound (inverse (negative_part ?6900)) (positive_part ?6901) =>= least_upper_bound (inverse (negative_part ?6900)) ?6901 [6901, 6900] by Super 677 with 4812 at 1,3
-Id : 6361, {_}: multiply (inverse (inverse (negative_part ?8525))) (least_upper_bound (inverse (negative_part ?8525)) ?8526) =>= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Super 4706 with 4834 at 2,2
-Id : 6399, {_}: positive_part (multiply (inverse (inverse (negative_part ?8525))) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6361 with 4706 at 2
-Id : 6400, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (inverse (inverse (negative_part ?8525))) (positive_part ?8526)) [8526, 8525] by Demod 6399 with 4599 at 1,1,2
-Id : 6401, {_}: positive_part (multiply (negative_part ?8525) ?8526) =<= positive_part (multiply (negative_part ?8525) (positive_part ?8526)) [8526, 8525] by Demod 6400 with 4599 at 1,1,3
-Id : 81268, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =<= positive_part (multiply (negative_part ?80770) (inverse ?80770)) [80770] by Demod 81148 with 6401 at 3
-Id : 16474, {_}: multiply (negative_part (inverse ?19896)) ?19896 =>= negative_part ?19896 [19896] by Demod 16411 with 4 at 1,3
-Id : 16476, {_}: multiply (negative_part ?19899) (inverse ?19899) =>= negative_part (inverse ?19899) [19899] by Super 16474 with 4599 at 1,1,2
-Id : 81269, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= positive_part (negative_part (inverse ?80770)) [80770] by Demod 81268 with 16476 at 1,3
-Id : 81270, {_}: multiply (negative_part ?80770) (positive_part (inverse ?80770)) =>= identity [80770] by Demod 81269 with 491 at 3
-Id : 81595, {_}: positive_part (inverse ?81005) =<= multiply (inverse (negative_part ?81005)) identity [81005] by Super 63 with 81270 at 2,3
-Id : 81710, {_}: positive_part (inverse ?81005) =>= inverse (negative_part ?81005) [81005] by Demod 81595 with 4577 at 3
-Id : 81898, {_}: multiply (inverse (negative_part ?17673)) ?17673 =>= positive_part ?17673 [17673] by Demod 14264 with 81710 at 1,2
-Id : 208, {_}: multiply (inverse ?574) (greatest_lower_bound ?574 ?575) =>= greatest_lower_bound identity (multiply (inverse ?574) ?575) [575, 574] by Super 202 with 6 at 1,3
-Id : 13514, {_}: multiply (inverse ?16653) (greatest_lower_bound ?16653 ?16654) =>= negative_part (multiply (inverse ?16653) ?16654) [16654, 16653] by Demod 208 with 314 at 3
-Id : 13540, {_}: multiply (inverse ?16729) (negative_part ?16729) =?= negative_part (multiply (inverse ?16729) identity) [16729] by Super 13514 with 36 at 2,2
-Id : 13620, {_}: multiply (inverse ?16816) (negative_part ?16816) =>= negative_part (inverse ?16816) [16816] by Demod 13540 with 4577 at 1,3
-Id : 13647, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part (inverse (inverse ?16885)) [16885] by Super 13620 with 4599 at 1,2
-Id : 13709, {_}: multiply ?16885 (negative_part (inverse ?16885)) =>= negative_part ?16885 [16885] by Demod 13647 with 4599 at 1,3
-Id : 62788, {_}: inverse (negative_part (inverse ?65826)) =<= multiply (inverse (negative_part ?65826)) ?65826 [65826] by Super 62767 with 13709 at 1,1,3
-Id : 81922, {_}: inverse (negative_part (inverse ?17673)) =>= positive_part ?17673 [17673] by Demod 81898 with 62788 at 2
-Id : 81929, {_}: ?19856 =<= multiply (positive_part ?19856) (negative_part ?19856) [19856] by Demod 16459 with 81922 at 1,3
-Id : 82398, {_}: a === a [] by Demod 2 with 81929 at 3
-Id : 2, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 84
- associativity_of_lub is 83
- b is 97
- c is 96
- glb_absorbtion is 79
- greatest_lower_bound is 94
- idempotence_of_gld is 81
- idempotence_of_lub is 82
- identity is 92
- inverse is 90
- least_upper_bound is 86
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 80
- monotony_glb1 is 77
- monotony_glb2 is 75
- monotony_lub1 is 78
- monotony_lub2 is 76
- multiply is 95
- p09b_1 is 74
- p09b_2 is 73
- p09b_3 is 72
- p09b_4 is 71
- prove_p09b is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 85
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
- Id : 36, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
- Id : 38, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
- Id : 40, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-Goal
- Id : 2, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-Timeout !
-FAILURE in 993 iterations
-% SZS status Timeout for GRP178-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- c is 72
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 94
- p12x_1 is 75
- p12x_2 is 74
- p12x_3 is 73
- p12x_4 is 71
- p12x_5 is 70
- p12x_6 is 69
- p12x_7 is 68
- prove_p12x is 96
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p12x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
- Id : 40, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
- Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
- Id : 44, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
- Id : 46, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-Goal
- Id : 2, {_}: a =>= b [] by prove_p12x
-Found proof, 6.988612s
-% SZS status Unsatisfiable for GRP181-4.p
-% SZS output start CNFRefutation for GRP181-4.p
-Id : 42, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-Id : 30, {_}: multiply (least_upper_bound ?42 ?43) ?44 =<= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 40, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
-Id : 32, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 14, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 16, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 12, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 44, {_}: inverse (greatest_lower_bound ?58 ?59) =<= least_upper_bound (inverse ?58) (inverse ?59) [59, 58] by p12x_6 ?58 ?59
-Id : 375, {_}: inverse (greatest_lower_bound ?877 ?878) =<= least_upper_bound (inverse ?877) (inverse ?878) [878, 877] by p12x_6 ?877 ?878
-Id : 398, {_}: inverse (least_upper_bound ?920 ?921) =<= greatest_lower_bound (inverse ?920) (inverse ?921) [921, 920] by p12x_7 ?920 ?921
-Id : 10, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 208, {_}: multiply ?553 (greatest_lower_bound ?554 ?555) =<= greatest_lower_bound (multiply ?553 ?554) (multiply ?553 ?555) [555, 554, 553] by monotony_glb1 ?553 ?554 ?555
-Id : 8, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 38, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
-Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 34, {_}: inverse identity =>= identity [] by p12x_1
-Id : 324, {_}: inverse (multiply ?822 ?823) =<= multiply (inverse ?823) (inverse ?822) [823, 822] by p12x_3 ?822 ?823
-Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 51, {_}: multiply (multiply ?72 ?73) ?74 =?= multiply ?72 (multiply ?73 ?74) [74, 73, 72] by associativity ?72 ?73 ?74
-Id : 53, {_}: multiply (multiply ?79 (inverse ?80)) ?80 =>= multiply ?79 identity [80, 79] by Super 51 with 6 at 2,3
-Id : 325, {_}: inverse (multiply identity ?825) =<= multiply (inverse ?825) identity [825] by Super 324 with 34 at 2,3
-Id : 428, {_}: inverse ?975 =<= multiply (inverse ?975) identity [975] by Demod 325 with 4 at 1,2
-Id : 430, {_}: inverse (inverse ?978) =<= multiply ?978 identity [978] by Super 428 with 36 at 1,3
-Id : 441, {_}: ?978 =<= multiply ?978 identity [978] by Demod 430 with 36 at 2
-Id : 20385, {_}: multiply (multiply ?15306 (inverse ?15307)) ?15307 =>= ?15306 [15307, 15306] by Demod 53 with 441 at 3
-Id : 20408, {_}: multiply (inverse (multiply ?15383 ?15382)) ?15383 =>= inverse ?15382 [15382, 15383] by Super 20385 with 38 at 1,2
-Id : 307, {_}: multiply ?771 (inverse ?771) =>= identity [771] by Super 6 with 36 at 1,2
-Id : 598, {_}: multiply (multiply ?1178 ?1177) (inverse ?1177) =>= multiply ?1178 identity [1177, 1178] by Super 8 with 307 at 2,3
-Id : 32025, {_}: multiply (multiply ?27293 ?27294) (inverse ?27294) =>= ?27293 [27294, 27293] by Demod 598 with 441 at 3
-Id : 210, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound (multiply (inverse ?561) ?560) identity [560, 561] by Super 208 with 6 at 2,3
-Id : 229, {_}: multiply (inverse ?561) (greatest_lower_bound ?560 ?561) =>= greatest_lower_bound identity (multiply (inverse ?561) ?560) [560, 561] by Demod 210 with 10 at 3
-Id : 401, {_}: inverse (least_upper_bound identity ?928) =>= greatest_lower_bound identity (inverse ?928) [928] by Super 398 with 34 at 1,3
-Id : 534, {_}: inverse (multiply (least_upper_bound identity ?1106) ?1107) =<= multiply (inverse ?1107) (greatest_lower_bound identity (inverse ?1106)) [1107, 1106] by Super 38 with 401 at 2,3
-Id : 25730, {_}: inverse (multiply (least_upper_bound identity ?21145) (inverse ?21145)) =>= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Super 229 with 534 at 2
-Id : 328, {_}: inverse (multiply ?833 (inverse ?832)) =>= multiply ?832 (inverse ?833) [832, 833] by Super 324 with 36 at 1,3
-Id : 25792, {_}: multiply ?21145 (inverse (least_upper_bound identity ?21145)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Demod 25730 with 328 at 2
-Id : 25793, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =?= greatest_lower_bound identity (multiply (inverse (inverse ?21145)) identity) [21145] by Demod 25792 with 401 at 2,2
-Id : 25794, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =>= greatest_lower_bound identity (inverse (inverse ?21145)) [21145] by Demod 25793 with 441 at 2,3
-Id : 25795, {_}: multiply ?21145 (greatest_lower_bound identity (inverse ?21145)) =>= greatest_lower_bound identity ?21145 [21145] by Demod 25794 with 36 at 2,3
-Id : 32085, {_}: multiply (greatest_lower_bound identity ?27496) (inverse (greatest_lower_bound identity (inverse ?27496))) =>= ?27496 [27496] by Super 32025 with 25795 at 1,2
-Id : 377, {_}: inverse (greatest_lower_bound ?883 (inverse ?882)) =>= least_upper_bound (inverse ?883) ?882 [882, 883] by Super 375 with 36 at 2,3
-Id : 32119, {_}: multiply (greatest_lower_bound identity ?27496) (least_upper_bound (inverse identity) ?27496) =>= ?27496 [27496] by Demod 32085 with 377 at 2,2
-Id : 82952, {_}: multiply (greatest_lower_bound identity ?64096) (least_upper_bound identity ?64096) =>= ?64096 [64096] by Demod 32119 with 34 at 1,2,2
-Id : 376, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound (inverse ?880) identity [880] by Super 375 with 34 at 2,3
-Id : 388, {_}: inverse (greatest_lower_bound ?880 identity) =>= least_upper_bound identity (inverse ?880) [880] by Demod 376 with 12 at 3
-Id : 509, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (inverse ?1077) (least_upper_bound identity (inverse ?1076)) [1076, 1077] by Super 44 with 388 at 2,3
-Id : 519, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound (least_upper_bound identity (inverse ?1076)) (inverse ?1077) [1076, 1077] by Demod 509 with 12 at 3
-Id : 520, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =<= least_upper_bound identity (least_upper_bound (inverse ?1076) (inverse ?1077)) [1076, 1077] by Demod 519 with 16 at 3
-Id : 521, {_}: inverse (greatest_lower_bound ?1077 (greatest_lower_bound ?1076 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 520 with 44 at 2,3
-Id : 512, {_}: inverse (greatest_lower_bound ?1083 identity) =>= least_upper_bound identity (inverse ?1083) [1083] by Demod 376 with 12 at 3
-Id : 516, {_}: inverse (greatest_lower_bound ?1090 (greatest_lower_bound ?1091 identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound ?1090 ?1091)) [1091, 1090] by Super 512 with 14 at 1,2
-Id : 2139, {_}: least_upper_bound identity (inverse (greatest_lower_bound ?1077 ?1076)) =?= least_upper_bound identity (inverse (greatest_lower_bound ?1076 ?1077)) [1076, 1077] by Demod 521 with 516 at 2
-Id : 28172, {_}: multiply (greatest_lower_bound ?24454 ?24455) (inverse ?24454) =>= greatest_lower_bound identity (multiply ?24455 (inverse ?24454)) [24455, 24454] by Super 32 with 307 at 1,3
-Id : 337, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 40 with 10 at 2
-Id : 338, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 337 with 10 at 3
-Id : 28217, {_}: multiply (greatest_lower_bound c b) (inverse c) =>= greatest_lower_bound identity (multiply a (inverse c)) [] by Super 28172 with 338 at 1,2
-Id : 595, {_}: multiply (greatest_lower_bound ?1168 ?1169) (inverse ?1168) =>= greatest_lower_bound identity (multiply ?1169 (inverse ?1168)) [1169, 1168] by Super 32 with 307 at 1,3
-Id : 28364, {_}: greatest_lower_bound identity (multiply b (inverse c)) =<= greatest_lower_bound identity (multiply a (inverse c)) [] by Demod 28217 with 595 at 2
-Id : 28527, {_}: least_upper_bound identity (inverse (greatest_lower_bound (multiply a (inverse c)) identity)) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Super 2139 with 28364 at 1,2,3
-Id : 28562, {_}: least_upper_bound identity (inverse (greatest_lower_bound identity (multiply a (inverse c)))) =>= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28527 with 2139 at 2
-Id : 378, {_}: inverse (greatest_lower_bound identity ?885) =>= least_upper_bound identity (inverse ?885) [885] by Super 375 with 34 at 1,3
-Id : 28563, {_}: least_upper_bound identity (least_upper_bound identity (inverse (multiply a (inverse c)))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28562 with 378 at 2,2
-Id : 112, {_}: least_upper_bound ?298 (least_upper_bound ?298 ?299) =>= least_upper_bound ?298 ?299 [299, 298] by Super 16 with 18 at 1,3
-Id : 28564, {_}: least_upper_bound identity (inverse (multiply a (inverse c))) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28563 with 112 at 2
-Id : 28565, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (inverse (greatest_lower_bound identity (multiply b (inverse c)))) [] by Demod 28564 with 328 at 2,2
-Id : 28566, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (least_upper_bound identity (inverse (multiply b (inverse c)))) [] by Demod 28565 with 378 at 2,3
-Id : 28567, {_}: least_upper_bound identity (multiply c (inverse a)) =<= least_upper_bound identity (inverse (multiply b (inverse c))) [] by Demod 28566 with 112 at 3
-Id : 28568, {_}: least_upper_bound identity (multiply c (inverse a)) =>= least_upper_bound identity (multiply c (inverse b)) [] by Demod 28567 with 328 at 2,3
-Id : 82970, {_}: multiply (greatest_lower_bound identity (multiply c (inverse a))) (least_upper_bound identity (multiply c (inverse b))) =>= multiply c (inverse a) [] by Super 82952 with 28568 at 2,2
-Id : 29872, {_}: multiply (least_upper_bound ?25739 ?25740) (inverse ?25739) =>= least_upper_bound identity (multiply ?25740 (inverse ?25739)) [25740, 25739] by Super 30 with 307 at 1,3
-Id : 353, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 42 with 12 at 2
-Id : 354, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 353 with 12 at 3
-Id : 29917, {_}: multiply (least_upper_bound c b) (inverse c) =>= least_upper_bound identity (multiply a (inverse c)) [] by Super 29872 with 354 at 1,2
-Id : 605, {_}: multiply (least_upper_bound ?1196 ?1197) (inverse ?1196) =>= least_upper_bound identity (multiply ?1197 (inverse ?1196)) [1197, 1196] by Super 30 with 307 at 1,3
-Id : 30072, {_}: least_upper_bound identity (multiply b (inverse c)) =<= least_upper_bound identity (multiply a (inverse c)) [] by Demod 29917 with 605 at 2
-Id : 30292, {_}: inverse (least_upper_bound identity (multiply b (inverse c))) =>= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Super 401 with 30072 at 1,2
-Id : 30345, {_}: greatest_lower_bound identity (inverse (multiply b (inverse c))) =<= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Demod 30292 with 401 at 2
-Id : 30346, {_}: greatest_lower_bound identity (multiply c (inverse b)) =<= greatest_lower_bound identity (inverse (multiply a (inverse c))) [] by Demod 30345 with 328 at 2,2
-Id : 30347, {_}: greatest_lower_bound identity (multiply c (inverse b)) =<= greatest_lower_bound identity (multiply c (inverse a)) [] by Demod 30346 with 328 at 2,3
-Id : 83131, {_}: multiply (greatest_lower_bound identity (multiply c (inverse b))) (least_upper_bound identity (multiply c (inverse b))) =>= multiply c (inverse a) [] by Demod 82970 with 30347 at 1,2
-Id : 32120, {_}: multiply (greatest_lower_bound identity ?27496) (least_upper_bound identity ?27496) =>= ?27496 [27496] by Demod 32119 with 34 at 1,2,2
-Id : 83132, {_}: multiply c (inverse b) =<= multiply c (inverse a) [] by Demod 83131 with 32120 at 2
-Id : 83209, {_}: multiply (inverse (multiply c (inverse b))) c =>= inverse (inverse a) [] by Super 20408 with 83132 at 1,1,2
-Id : 83212, {_}: inverse (inverse b) =<= inverse (inverse a) [] by Demod 83209 with 20408 at 2
-Id : 83213, {_}: b =<= inverse (inverse a) [] by Demod 83212 with 36 at 2
-Id : 83214, {_}: b =<= a [] by Demod 83213 with 36 at 3
-Id : 83672, {_}: b === b [] by Demod 2 with 83214 at 2
-Id : 2, {_}: a =>= b [] by prove_p12x
-% SZS output end CNFRefutation for GRP181-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 94
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 95
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 92
- p20x_1 is 76
- p20x_3 is 75
- prove_20x is 93
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p20x_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-Timeout !
-FAILURE in 339 iterations
-% SZS status Timeout for GRP183-4.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21 is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-Timeout !
-FAILURE in 344 iterations
-% SZS status Timeout for GRP184-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 86
- associativity_of_lub is 85
- glb_absorbtion is 81
- greatest_lower_bound is 95
- idempotence_of_gld is 83
- idempotence_of_lub is 84
- identity is 97
- inverse is 94
- least_upper_bound is 96
- left_identity is 91
- left_inverse is 90
- lub_absorbtion is 82
- monotony_glb1 is 79
- monotony_glb2 is 77
- monotony_lub1 is 80
- monotony_lub2 is 78
- multiply is 93
- prove_p21x is 92
- symmetry_of_glb is 88
- symmetry_of_lub is 87
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-Timeout !
-FAILURE in 343 iterations
-% SZS status Timeout for GRP184-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 89
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 88
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 91
- least_upper_bound is 94
- left_identity is 92
- left_inverse is 90
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p22a_1 is 75
- p22a_2 is 74
- p22a_3 is 73
- prove_p22a is 93
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p22a_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-Timeout !
-FAILURE in 339 iterations
-% SZS status Timeout for GRP185-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 93
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 90
- least_upper_bound is 94
- left_identity is 91
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p22b is 92
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-Timeout !
-FAILURE in 352 iterations
-% SZS status Timeout for GRP185-3.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Timeout !
-FAILURE in 343 iterations
-% SZS status Timeout for GRP186-1.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 88
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 92
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 95
- inverse is 93
- least_upper_bound is 94
- left_identity is 90
- left_inverse is 89
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p23_1 is 75
- p23_2 is 74
- p23_3 is 73
- prove_p23 is 91
- symmetry_of_glb is 87
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}: inverse identity =>= identity [] by p23_1
- Id : 36, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
- Id : 38, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-Goal
- Id : 2, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-Timeout !
-FAILURE in 341 iterations
-% SZS status Timeout for GRP186-2.p
-Order
- == is 100
- _ is 99
- a is 98
- associativity is 90
- associativity_of_glb is 85
- associativity_of_lub is 84
- b is 97
- glb_absorbtion is 80
- greatest_lower_bound is 89
- idempotence_of_gld is 82
- idempotence_of_lub is 83
- identity is 94
- inverse is 92
- least_upper_bound is 87
- left_identity is 93
- left_inverse is 91
- lub_absorbtion is 81
- monotony_glb1 is 78
- monotony_glb2 is 76
- monotony_lub1 is 79
- monotony_lub2 is 77
- multiply is 96
- p33_1 is 75
- prove_p33 is 95
- symmetry_of_glb is 88
- symmetry_of_lub is 86
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
- Id : 8, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
- Id : 10, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
- Id : 12, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
- Id : 14, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
- Id : 16, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
- Id : 18, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
- Id : 20, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
- Id : 22, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
- Id : 24, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
- Id : 26, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
- Id : 28, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
- Id : 30, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
- Id : 32, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
- Id : 34, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_p33
-Timeout !
-FAILURE in 534 iterations
-% SZS status Timeout for GRP187-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 95
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang1 is 82
- multiply is 96
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang2 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-Timeout !
-FAILURE in 276 iterations
-% SZS status Timeout for GRP200-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- c is 96
- identity is 93
- left_division is 90
- left_division_multiply is 88
- left_identity is 92
- left_inverse is 83
- moufang3 is 82
- multiply is 95
- multiply_left_division is 89
- multiply_right_division is 86
- prove_moufang1 is 94
- right_division is 87
- right_division_multiply is 85
- right_identity is 91
- right_inverse is 84
-Facts
- Id : 4, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
- Id : 6, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
- Id : 8, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
- Id : 10, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
- Id : 12, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
- Id : 14, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
- Id : 16, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
- Id : 18, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
- Id : 20, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-Goal
- Id : 2, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-Timeout !
-FAILURE in 260 iterations
-% SZS status Timeout for GRP202-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Timeout !
-FAILURE in 62 iterations
-% SZS status Timeout for GRP404-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Timeout !
-FAILURE in 62 iterations
-% SZS status Timeout for GRP405-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Timeout !
-FAILURE in 52 iterations
-% SZS status Timeout for GRP422-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Timeout !
-FAILURE in 52 iterations
-% SZS status Timeout for GRP423-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- inverse is 93
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Timeout !
-FAILURE in 72 iterations
-% SZS status Timeout for GRP444-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- divide is 93
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Found proof, 0.089757s
-% SZS status Unsatisfiable for GRP452-1.p
-% SZS output start CNFRefutation for GRP452-1.p
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
-Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 265, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 270, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 265 with 40 at 2,1,1,3
-Id : 286, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 270 with 8 at 1,1,2
-Id : 306, {_}: divide (divide (inverse (inverse ?778)) ?779) (inverse ?779) =>= ?778 [779, 778] by Super 63 with 286 at 1,2
-Id : 319, {_}: multiply (divide (inverse (inverse ?778)) ?779) ?779 =>= ?778 [779, 778] by Demod 306 with 33 at 2
-Id : 682, {_}: ?1380 =<= inverse (inverse (inverse (inverse ?1380))) [1380] by Super 36 with 319 at 2
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 269, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 265 with 33 at 2,1,1,3
-Id : 285, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 269 with 33 at 2
-Id : 743, {_}: ?1513 =<= inverse (inverse (inverse (inverse ?1513))) [1513] by Super 36 with 319 at 2
-Id : 138, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 1731, {_}: multiply ?3407 (divide (inverse ?3408) ?3409) =<= inverse (inverse (divide (inverse (divide ?3408 ?3407)) ?3409)) [3409, 3408, 3407] by Super 743 with 138 at 1,1,3
-Id : 1810, {_}: multiply ?3532 (divide (inverse ?3532) ?3533) =>= inverse (inverse (inverse ?3533)) [3533, 3532] by Super 1731 with 40 at 1,1,3
-Id : 735, {_}: multiply ?1490 (inverse (inverse (inverse ?1489))) =>= divide ?1490 ?1489 [1489, 1490] by Super 33 with 682 at 2,3
-Id : 742, {_}: multiply (divide ?1510 ?1511) ?1511 =>= inverse (inverse ?1510) [1511, 1510] by Super 319 with 682 at 1,1,2
-Id : 867, {_}: inverse (inverse ?1672) =<= divide (divide ?1672 (inverse (inverse (inverse ?1673)))) ?1673 [1673, 1672] by Super 735 with 742 at 2
-Id : 1192, {_}: inverse (inverse ?2233) =<= divide (multiply ?2233 (inverse (inverse ?2234))) ?2234 [2234, 2233] by Demod 867 with 33 at 1,3
-Id : 55, {_}: multiply (inverse (inverse (divide ?138 ?138))) ?139 =>= inverse (inverse ?139) [139, 138] by Super 36 with 40 at 1,2
-Id : 1206, {_}: inverse (inverse (inverse (inverse (divide ?2285 ?2285)))) =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Super 1192 with 55 at 1,3
-Id : 1239, {_}: divide ?2285 ?2285 =?= divide (inverse (inverse (inverse (inverse ?2286)))) ?2286 [2286, 2285] by Demod 1206 with 682 at 2
-Id : 1240, {_}: divide ?2285 ?2285 =?= divide ?2286 ?2286 [2286, 2285] by Demod 1239 with 682 at 1,3
-Id : 1820, {_}: multiply ?3573 (divide ?3572 ?3572) =?= inverse (inverse (inverse (inverse ?3573))) [3572, 3573] by Super 1810 with 1240 at 2,2
-Id : 1859, {_}: multiply ?3573 (divide ?3572 ?3572) =>= ?3573 [3572, 3573] by Demod 1820 with 682 at 3
-Id : 1899, {_}: multiply (inverse (divide ?3678 ?3679)) (divide ?3677 ?3677) =>= inverse (inverse (multiply ?3679 (inverse ?3678))) [3677, 3679, 3678] by Super 285 with 1859 at 2,1,1,3
-Id : 1926, {_}: inverse (divide ?3678 ?3679) =<= inverse (inverse (multiply ?3679 (inverse ?3678))) [3679, 3678] by Demod 1899 with 1859 at 2
-Id : 1927, {_}: inverse (divide ?3678 ?3679) =<= divide (inverse (inverse ?3679)) ?3678 [3679, 3678] by Demod 1926 with 286 at 3
-Id : 1948, {_}: inverse ?121 =<= inverse (divide ?121 (divide ?120 ?120)) [120, 121] by Demod 50 with 1927 at 3
-Id : 1882, {_}: divide ?3627 (divide ?3626 ?3626) =>= inverse (inverse ?3627) [3626, 3627] by Super 742 with 1859 at 2
-Id : 2237, {_}: inverse ?121 =<= inverse (inverse (inverse ?121)) [121] by Demod 1948 with 1882 at 1,3
-Id : 2241, {_}: ?1380 =<= inverse (inverse ?1380) [1380] by Demod 682 with 2237 at 3
-Id : 2403, {_}: a2 === a2 [] by Demod 85 with 2241 at 2
-Id : 85, {_}: inverse (inverse a2) =>= a2 [] by Demod 2 with 47 at 2
-Id : 2, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP452-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 91
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 92
-Facts
- Id : 4, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
- Id : 6, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
- Id : 8, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 0.810429s
-% SZS status Unsatisfiable for GRP453-1.p
-% SZS output start CNFRefutation for GRP453-1.p
-Id : 6, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 39, {_}: inverse ?93 =<= divide (divide ?94 ?94) ?93 [94, 93] by inverse ?93 ?94
-Id : 8, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 4, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 34, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 4 with 8 at 1,2
-Id : 35, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 34 with 8 at 1,2,2,1,1,2
-Id : 40, {_}: inverse ?97 =<= divide (inverse (divide ?96 ?96)) ?97 [96, 97] by Super 39 with 8 at 1,3
-Id : 52, {_}: divide (inverse (divide (divide ?127 ?127) (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128, 127] by Super 35 with 40 at 2,2,1,1,2
-Id : 62, {_}: divide (inverse (inverse (divide ?128 (inverse ?126)))) ?126 =>= ?128 [126, 128] by Demod 52 with 8 at 1,1,2
-Id : 33, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 6 with 8 at 2,3
-Id : 63, {_}: divide (inverse (inverse (multiply ?128 ?126))) ?126 =>= ?128 [126, 128] by Demod 62 with 33 at 1,1,1,2
-Id : 264, {_}: divide (inverse (divide ?664 ?665)) ?666 =<= inverse (inverse (multiply ?665 (divide (inverse ?664) ?666))) [666, 665, 664] by Super 35 with 63 at 2,1,1,2
-Id : 269, {_}: divide (inverse (divide (divide ?687 ?687) ?688)) ?689 =>= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688, 687] by Super 264 with 40 at 2,1,1,3
-Id : 285, {_}: divide (inverse (inverse ?688)) ?689 =<= inverse (inverse (multiply ?688 (inverse ?689))) [689, 688] by Demod 269 with 8 at 1,1,2
-Id : 307, {_}: divide (inverse (inverse ?786)) ?787 =<= inverse (inverse (multiply ?786 (inverse ?787))) [787, 786] by Demod 269 with 8 at 1,1,2
-Id : 36, {_}: multiply (divide ?82 ?82) ?83 =>= inverse (inverse ?83) [83, 82] by Super 33 with 8 at 3
-Id : 310, {_}: divide (inverse (inverse (divide ?798 ?798))) ?799 =>= inverse (inverse (inverse (inverse (inverse ?799)))) [799, 798] by Super 307 with 36 at 1,1,3
-Id : 50, {_}: inverse ?121 =<= divide (inverse (inverse (divide ?120 ?120))) ?121 [120, 121] by Super 8 with 40 at 1,3
-Id : 325, {_}: inverse ?799 =<= inverse (inverse (inverse (inverse (inverse ?799)))) [799] by Demod 310 with 50 at 2
-Id : 332, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= divide ?837 (inverse ?836) [836, 837] by Super 33 with 325 at 2,3
-Id : 354, {_}: multiply ?837 (inverse (inverse (inverse (inverse ?836)))) =>= multiply ?837 ?836 [836, 837] by Demod 332 with 33 at 3
-Id : 364, {_}: divide (inverse (inverse ?880)) (inverse (inverse (inverse ?881))) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Super 285 with 354 at 1,1,3
-Id : 423, {_}: multiply (inverse (inverse ?880)) (inverse (inverse ?881)) =>= inverse (inverse (multiply ?880 ?881)) [881, 880] by Demod 364 with 33 at 2
-Id : 448, {_}: divide (inverse (inverse (inverse (inverse ?1012)))) (inverse ?1013) =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Super 285 with 423 at 1,1,3
-Id : 470, {_}: multiply (inverse (inverse (inverse (inverse ?1012)))) ?1013 =>= inverse (inverse (inverse (inverse (multiply ?1012 ?1013)))) [1013, 1012] by Demod 448 with 33 at 2
-Id : 499, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1108 ?1109))))))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Super 63 with 470 at 1,1,1,2
-Id : 519, {_}: divide (inverse (inverse (multiply ?1108 ?1109))) ?1109 =>= inverse (inverse (inverse (inverse ?1108))) [1109, 1108] by Demod 499 with 325 at 1,2
-Id : 520, {_}: ?1108 =<= inverse (inverse (inverse (inverse ?1108))) [1108] by Demod 519 with 63 at 2
-Id : 268, {_}: divide (inverse (divide ?684 ?685)) (inverse ?683) =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Super 264 with 33 at 2,1,1,3
-Id : 284, {_}: multiply (inverse (divide ?684 ?685)) ?683 =<= inverse (inverse (multiply ?685 (multiply (inverse ?684) ?683))) [683, 685, 684] by Demod 268 with 33 at 2
-Id : 1304, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =<= inverse (inverse (multiply (inverse (divide ?2414 ?2415)) ?2416)) [2416, 2414, 2415] by Super 520 with 284 at 1,1,3
-Id : 565, {_}: multiply ?1187 (inverse (inverse (inverse ?1186))) =>= divide ?1187 ?1186 [1186, 1187] by Super 33 with 520 at 2,3
-Id : 590, {_}: divide (inverse (inverse ?1228)) (inverse (inverse ?1229)) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Super 285 with 565 at 1,1,3
-Id : 687, {_}: multiply (inverse (inverse ?1369)) (inverse ?1370) =>= inverse (inverse (divide ?1369 ?1370)) [1370, 1369] by Demod 590 with 33 at 2
-Id : 781, {_}: multiply ?1560 (inverse ?1561) =<= inverse (inverse (divide (inverse (inverse ?1560)) ?1561)) [1561, 1560] by Super 687 with 520 at 1,2
-Id : 791, {_}: multiply ?1599 (inverse (inverse ?1598)) =<= inverse (inverse (multiply (inverse (inverse ?1599)) ?1598)) [1598, 1599] by Super 781 with 33 at 1,1,3
-Id : 2425, {_}: multiply ?4605 (multiply (inverse ?4606) ?4607) =<= inverse (inverse (multiply (inverse (divide ?4606 ?4605)) ?4607)) [4607, 4606, 4605] by Super 520 with 284 at 1,1,3
-Id : 652, {_}: multiply (inverse (inverse ?1228)) (inverse ?1229) =>= inverse (inverse (divide ?1228 ?1229)) [1229, 1228] by Demod 590 with 33 at 2
-Id : 676, {_}: divide (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) (inverse ?1337) =>= inverse (inverse ?1336) [1337, 1336] by Super 63 with 652 at 1,1,1,2
-Id : 716, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1336 ?1337))))) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 676 with 33 at 2
-Id : 734, {_}: multiply (divide ?1438 ?1439) ?1439 =>= inverse (inverse ?1438) [1439, 1438] by Demod 716 with 520 at 1,2
-Id : 741, {_}: multiply (inverse ?1461) ?1461 =?= inverse (inverse (inverse (inverse (divide ?1460 ?1460)))) [1460, 1461] by Super 734 with 50 at 1,2
-Id : 756, {_}: multiply (inverse ?1461) ?1461 =?= divide ?1460 ?1460 [1460, 1461] by Demod 741 with 520 at 3
-Id : 2438, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =?= inverse (inverse (multiply (inverse (multiply (inverse ?4658) ?4658)) ?4660)) [4658, 4660, 4659] by Super 2425 with 756 at 1,1,1,1,3
-Id : 41, {_}: inverse ?100 =<= divide (multiply (inverse ?99) ?99) ?100 [99, 100] by Super 39 with 33 at 1,3
-Id : 65, {_}: multiply (inverse (multiply (inverse ?159) ?159)) ?160 =>= inverse (inverse ?160) [160, 159] by Super 36 with 41 at 1,2
-Id : 2490, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =>= inverse (inverse (inverse (inverse ?4660))) [4660, 4659] by Demod 2438 with 65 at 1,1,3
-Id : 2491, {_}: multiply ?4659 (multiply (inverse ?4659) ?4660) =>= ?4660 [4660, 4659] by Demod 2490 with 520 at 3
-Id : 738, {_}: multiply (multiply ?1452 ?1451) (inverse ?1451) =>= inverse (inverse ?1452) [1451, 1452] by Super 734 with 33 at 1,2
-Id : 2508, {_}: multiply ?4731 (inverse (multiply (inverse ?4730) ?4731)) =>= inverse (inverse ?4730) [4730, 4731] by Super 738 with 2491 at 1,2
-Id : 2677, {_}: multiply ?4949 (inverse (inverse ?4948)) =<= inverse (multiply (inverse ?4948) (inverse ?4949)) [4948, 4949] by Super 2491 with 2508 at 2,2
-Id : 2810, {_}: multiply ?5205 (inverse (inverse (inverse ?5204))) =<= inverse (multiply ?5204 (inverse (inverse (inverse ?5205)))) [5204, 5205] by Super 791 with 2677 at 1,3
-Id : 2855, {_}: divide ?5205 ?5204 =<= inverse (multiply ?5204 (inverse (inverse (inverse ?5205)))) [5204, 5205] by Demod 2810 with 565 at 2
-Id : 2856, {_}: divide ?5205 ?5204 =<= inverse (divide ?5204 ?5205) [5204, 5205] by Demod 2855 with 565 at 1,3
-Id : 2935, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =<= inverse (inverse (multiply (divide ?2415 ?2414) ?2416)) [2416, 2414, 2415] by Demod 1304 with 2856 at 1,1,1,3
-Id : 70, {_}: inverse ?177 =<= divide (inverse (inverse (multiply (inverse ?176) ?176))) ?177 [176, 177] by Super 40 with 41 at 1,1,3
-Id : 696, {_}: multiply ?1405 (inverse ?1406) =<= inverse (inverse (divide (inverse (inverse ?1405)) ?1406)) [1406, 1405] by Super 687 with 520 at 1,2
-Id : 2929, {_}: multiply ?1405 (inverse ?1406) =<= inverse (divide ?1406 (inverse (inverse ?1405))) [1406, 1405] by Demod 696 with 2856 at 1,3
-Id : 2930, {_}: multiply ?1405 (inverse ?1406) =<= divide (inverse (inverse ?1405)) ?1406 [1406, 1405] by Demod 2929 with 2856 at 3
-Id : 2938, {_}: inverse ?177 =<= multiply (multiply (inverse ?176) ?176) (inverse ?177) [176, 177] by Demod 70 with 2930 at 3
-Id : 45, {_}: multiply (divide ?108 ?108) ?109 =>= inverse (inverse ?109) [109, 108] by Super 33 with 8 at 3
-Id : 47, {_}: multiply (multiply (inverse ?114) ?114) ?115 =>= inverse (inverse ?115) [115, 114] by Super 45 with 33 at 1,2
-Id : 2941, {_}: inverse ?177 =<= inverse (inverse (inverse ?177)) [177] by Demod 2938 with 47 at 3
-Id : 2943, {_}: ?1108 =<= inverse (inverse ?1108) [1108] by Demod 520 with 2941 at 3
-Id : 2962, {_}: multiply ?2415 (multiply (inverse ?2414) ?2416) =>= multiply (divide ?2415 ?2414) ?2416 [2416, 2414, 2415] by Demod 2935 with 2943 at 3
-Id : 717, {_}: multiply (divide ?1336 ?1337) ?1337 =>= inverse (inverse ?1336) [1337, 1336] by Demod 716 with 520 at 1,2
-Id : 2957, {_}: multiply (divide ?1336 ?1337) ?1337 =>= ?1336 [1337, 1336] by Demod 717 with 2943 at 3
-Id : 2946, {_}: multiply ?4731 (inverse (multiply (inverse ?4730) ?4731)) =>= ?4730 [4730, 4731] by Demod 2508 with 2943 at 3
-Id : 2963, {_}: multiply ?1405 (inverse ?1406) =>= divide ?1405 ?1406 [1406, 1405] by Demod 2930 with 2943 at 1,3
-Id : 2983, {_}: divide ?4731 (multiply (inverse ?4730) ?4731) =>= ?4730 [4730, 4731] by Demod 2946 with 2963 at 2
-Id : 3087, {_}: divide ?5518 (multiply (divide ?5519 ?5520) ?5518) =>= divide ?5520 ?5519 [5520, 5519, 5518] by Super 2983 with 2856 at 1,2,2
-Id : 3092, {_}: divide ?5541 (multiply ?5540 ?5541) =?= divide (multiply (inverse ?5540) ?5542) ?5542 [5542, 5540, 5541] by Super 3087 with 2983 at 1,2,2
-Id : 2958, {_}: multiply (multiply ?1452 ?1451) (inverse ?1451) =>= ?1452 [1451, 1452] by Demod 738 with 2943 at 3
-Id : 2979, {_}: divide (multiply ?1452 ?1451) ?1451 =>= ?1452 [1451, 1452] by Demod 2958 with 2963 at 2
-Id : 3136, {_}: divide ?5541 (multiply ?5540 ?5541) =>= inverse ?5540 [5540, 5541] by Demod 3092 with 2979 at 3
-Id : 3184, {_}: multiply (inverse ?5645) (multiply ?5645 ?5644) =>= ?5644 [5644, 5645] by Super 2957 with 3136 at 1,2
-Id : 4178, {_}: multiply ?6966 ?6967 =<= multiply (divide ?6966 ?6968) (multiply ?6968 ?6967) [6968, 6967, 6966] by Super 2962 with 3184 at 2,2
-Id : 309, {_}: divide (inverse (inverse ?796)) (inverse (multiply ?794 (inverse ?795))) =>= inverse (inverse (multiply ?796 (divide (inverse (inverse ?794)) ?795))) [795, 794, 796] by Super 307 with 285 at 2,1,1,3
-Id : 323, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =<= inverse (inverse (multiply ?796 (divide (inverse (inverse ?794)) ?795))) [795, 794, 796] by Demod 309 with 33 at 2
-Id : 137, {_}: divide (inverse (divide ?349 ?348)) ?350 =<= inverse (inverse (multiply ?348 (divide (inverse ?349) ?350))) [350, 348, 349] by Super 35 with 63 at 2,1,1,2
-Id : 324, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =>= divide (inverse (divide (inverse ?794) ?796)) ?795 [795, 794, 796] by Demod 323 with 137 at 3
-Id : 2912, {_}: multiply (inverse (inverse ?796)) (multiply ?794 (inverse ?795)) =>= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 324 with 2856 at 1,3
-Id : 3003, {_}: multiply ?796 (multiply ?794 (inverse ?795)) =>= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 2912 with 2943 at 1,2
-Id : 3004, {_}: multiply ?796 (divide ?794 ?795) =<= divide (divide ?796 (inverse ?794)) ?795 [795, 794, 796] by Demod 3003 with 2963 at 2,2
-Id : 606, {_}: multiply ?1276 (inverse (inverse (inverse ?1277))) =>= divide ?1276 ?1277 [1277, 1276] by Super 33 with 520 at 2,3
-Id : 611, {_}: multiply ?1298 (inverse (divide (inverse (inverse ?1296)) ?1297)) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1297, 1296, 1298] by Super 606 with 285 at 1,2,2
-Id : 2932, {_}: multiply ?1298 (divide ?1297 (inverse (inverse ?1296))) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 611 with 2856 at 2,2
-Id : 2936, {_}: multiply ?1298 (multiply ?1297 (inverse ?1296)) =>= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 2932 with 33 at 2,2
-Id : 2965, {_}: multiply ?1298 (divide ?1297 ?1296) =<= divide ?1298 (multiply ?1296 (inverse ?1297)) [1296, 1297, 1298] by Demod 2936 with 2963 at 2,2
-Id : 2966, {_}: multiply ?1298 (divide ?1297 ?1296) =>= divide ?1298 (divide ?1296 ?1297) [1296, 1297, 1298] by Demod 2965 with 2963 at 2,3
-Id : 3005, {_}: divide ?796 (divide ?795 ?794) =<= divide (divide ?796 (inverse ?794)) ?795 [794, 795, 796] by Demod 3004 with 2966 at 2
-Id : 3006, {_}: divide ?796 (divide ?795 ?794) =?= divide (multiply ?796 ?794) ?795 [794, 795, 796] by Demod 3005 with 33 at 1,3
-Id : 4201, {_}: multiply (multiply ?7065 ?7066) ?7067 =<= multiply (divide ?7065 (divide ?7068 ?7066)) (multiply ?7068 ?7067) [7068, 7067, 7066, 7065] by Super 4178 with 3006 at 1,3
-Id : 3248, {_}: multiply ?5734 ?5733 =<= multiply (divide ?5734 ?5732) (multiply ?5732 ?5733) [5732, 5733, 5734] by Super 2962 with 3184 at 2,2
-Id : 4188, {_}: multiply ?7012 (multiply ?7011 ?7010) =<= multiply (divide ?7012 (divide ?7009 ?7011)) (multiply ?7009 ?7010) [7009, 7010, 7011, 7012] by Super 4178 with 3248 at 2,3
-Id : 12339, {_}: multiply (multiply ?7065 ?7066) ?7067 =?= multiply ?7065 (multiply ?7066 ?7067) [7067, 7066, 7065] by Demod 4201 with 4188 at 3
-Id : 12708, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 12339 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP453-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Timeout !
-FAILURE in 180 iterations
-% SZS status Timeout for GRP471-1.p
-Order
- == is 100
- _ is 99
- a3 is 98
- b3 is 97
- c3 is 95
- divide is 93
- inverse is 92
- multiply is 96
- prove_these_axioms_3 is 94
- single_axiom is 91
-Facts
- Id : 4, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
- Id : 6, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-Goal
- Id : 2, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-Found proof, 9.696012s
-% SZS status Unsatisfiable for GRP477-1.p
-% SZS output start CNFRefutation for GRP477-1.p
-Id : 6, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 7, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 4, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 9, {_}: divide (inverse (divide (divide (divide ?26 ?27) (divide ?23 ?22)) ?25)) (divide ?27 ?26) =?= inverse (divide (divide (divide ?22 ?23) ?24) (divide ?25 ?24)) [24, 25, 22, 23, 27, 26] by Super 7 with 4 at 2,1,1,2
-Id : 8947, {_}: inverse (divide (divide (divide ?66899 ?66900) ?66901) (divide (divide ?66902 (divide ?66900 ?66899)) ?66901)) =>= ?66902 [66902, 66901, 66900, 66899] by Super 4 with 9 at 2
-Id : 9487, {_}: inverse (divide (divide (divide (inverse ?70062) ?70063) ?70064) (divide (divide ?70065 (multiply ?70063 ?70062)) ?70064)) =>= ?70065 [70065, 70064, 70063, 70062] by Super 8947 with 6 at 2,1,2,1,2
-Id : 13, {_}: divide (inverse (divide (divide (divide ?48 ?49) (inverse ?47)) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Super 4 with 6 at 2,1,1,2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?88 ?89) ?90) (multiply ?91 ?90))) (divide ?89 ?88) =>= ?91 [91, 90, 89, 88] by Demod 13 with 6 at 1,1,1,2
-Id : 27, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (divide (divide ?113 ?112) (inverse (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114)))) =>= ?117 [114, 112, 113, 117, 116, 115] by Super 23 with 4 at 1,1,1,1,2
-Id : 35, {_}: divide (inverse (divide (multiply ?115 ?116) (multiply ?117 ?116))) (multiply (divide ?113 ?112) (divide (divide (divide ?112 ?113) ?114) (divide ?115 ?114))) =>= ?117 [114, 112, 113, 117, 116, 115] by Demod 27 with 6 at 2,2
-Id : 9506, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?70226 ?70225) ?70227) (divide ?70222 ?70227))) (divide ?70225 ?70226)) ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222, 70227, 70225, 70226] by Super 9487 with 35 at 1,2,1,2
-Id : 9604, {_}: inverse (divide (divide ?70222 ?70228) (divide ?70224 ?70228)) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70224, 70228, 70222] by Demod 9506 with 4 at 1,1,1,2
-Id : 27713, {_}: divide (divide (inverse (divide (divide (divide ?169617 ?169618) (divide ?169619 ?169620)) ?169621)) (divide ?169618 ?169617)) (divide ?169619 ?169620) =>= ?169621 [169621, 169620, 169619, 169618, 169617] by Super 4 with 9 at 1,2
-Id : 27714, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) (divide (inverse (divide (divide (divide ?169623 ?169624) ?169625) (divide ?169626 ?169625))) (divide ?169624 ?169623))) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169625, 169624, 169623, 169628, 169627] by Super 27713 with 4 at 2,2
-Id : 28344, {_}: divide (divide (inverse (divide (divide (divide ?173215 ?173216) ?173217) ?173218)) (divide ?173216 ?173215)) ?173217 =>= ?173218 [173218, 173217, 173216, 173215] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28449, {_}: divide (divide (inverse (multiply (divide (divide ?174106 ?174107) ?174108) ?174105)) (divide ?174107 ?174106)) ?174108 =>= inverse ?174105 [174105, 174108, 174107, 174106] by Super 28344 with 6 at 1,1,1,2
-Id : 28803, {_}: multiply (divide (inverse (multiply (divide (divide ?175142 ?175143) (inverse ?175145)) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Super 6 with 28449 at 3
-Id : 29850, {_}: multiply (divide (inverse (multiply (multiply (divide ?180549 ?180550) ?180551) ?180552)) (divide ?180550 ?180549)) ?180551 =>= inverse ?180552 [180552, 180551, 180550, 180549] by Demod 28803 with 6 at 1,1,1,1,2
-Id : 33200, {_}: multiply (divide (inverse (multiply (multiply (divide (inverse ?199058) ?199059) ?199060) ?199061)) (multiply ?199059 ?199058)) ?199060 =>= inverse ?199061 [199061, 199060, 199059, 199058] by Super 29850 with 6 at 2,1,2
-Id : 33302, {_}: multiply (divide (inverse (multiply (multiply (multiply (inverse ?199942) ?199941) ?199943) ?199944)) (multiply (inverse ?199941) ?199942)) ?199943 =>= inverse ?199944 [199944, 199943, 199941, 199942] by Super 33200 with 6 at 1,1,1,1,1,2
-Id : 43, {_}: divide (inverse (divide (divide (divide (inverse ?171) ?172) ?173) (divide ?174 ?173))) (multiply ?172 ?171) =>= ?174 [174, 173, 172, 171] by Super 4 with 6 at 2,2
-Id : 48, {_}: divide (inverse (divide (divide ?205 ?206) (divide ?207 ?206))) (multiply (divide ?203 ?202) (divide (divide (divide ?202 ?203) ?204) (divide ?205 ?204))) =>= ?207 [204, 202, 203, 207, 206, 205] by Super 43 with 4 at 1,1,1,1,2
-Id : 8271, {_}: inverse (divide (divide (divide ?62998 ?62997) ?62999) (divide (divide ?63000 (divide ?62997 ?62998)) ?62999)) =>= ?63000 [63000, 62999, 62997, 62998] by Super 4 with 9 at 2
-Id : 8914, {_}: divide ?66588 (multiply (divide ?66589 ?66590) (divide (divide (divide ?66590 ?66589) ?66591) (divide (divide ?66585 ?66586) ?66591))) =>= divide ?66588 (divide ?66586 ?66585) [66586, 66585, 66591, 66590, 66589, 66588] by Super 48 with 8271 at 1,2
-Id : 28446, {_}: divide (divide (inverse (divide (divide (divide ?174083 ?174084) ?174085) (divide ?174082 ?174081))) (divide ?174084 ?174083)) ?174085 =?= multiply (divide ?174078 ?174079) (divide (divide (divide ?174079 ?174078) ?174080) (divide (divide ?174081 ?174082) ?174080)) [174080, 174079, 174078, 174081, 174082, 174085, 174084, 174083] by Super 28344 with 8914 at 1,1,1,2
-Id : 27948, {_}: divide (divide (inverse (divide (divide (divide ?169627 ?169628) ?169626) ?169629)) (divide ?169628 ?169627)) ?169626 =>= ?169629 [169629, 169626, 169628, 169627] by Demod 27714 with 4 at 2,1,1,1,1,2
-Id : 28598, {_}: divide ?174082 ?174081 =<= multiply (divide ?174078 ?174079) (divide (divide (divide ?174079 ?174078) ?174080) (divide (divide ?174081 ?174082) ?174080)) [174080, 174079, 174078, 174081, 174082] by Demod 28446 with 27948 at 2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?48 ?49) ?47) (multiply ?46 ?47))) (divide ?49 ?48) =>= ?46 [46, 47, 49, 48] by Demod 13 with 6 at 1,1,1,2
-Id : 22, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (divide (divide ?82 ?81) (inverse (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83)))) =>= ?86 [83, 81, 82, 86, 85, 84] by Super 4 with 18 at 1,1,1,1,2
-Id : 32, {_}: divide (inverse (divide (divide ?84 ?85) (divide ?86 ?85))) (multiply (divide ?82 ?81) (divide (multiply (divide ?81 ?82) ?83) (multiply ?84 ?83))) =>= ?86 [83, 81, 82, 86, 85, 84] by Demod 22 with 6 at 2,2
-Id : 8902, {_}: divide ?66500 (multiply (divide ?66501 ?66502) (divide (multiply (divide ?66502 ?66501) ?66503) (multiply (divide ?66497 ?66498) ?66503))) =>= divide ?66500 (divide ?66498 ?66497) [66498, 66497, 66503, 66502, 66501, 66500] by Super 32 with 8271 at 1,2
-Id : 28445, {_}: divide (divide (inverse (divide (divide (divide ?174074 ?174075) ?174076) (divide ?174073 ?174072))) (divide ?174075 ?174074)) ?174076 =?= multiply (divide ?174069 ?174070) (divide (multiply (divide ?174070 ?174069) ?174071) (multiply (divide ?174072 ?174073) ?174071)) [174071, 174070, 174069, 174072, 174073, 174076, 174075, 174074] by Super 28344 with 8902 at 1,1,1,2
-Id : 28597, {_}: divide ?174073 ?174072 =<= multiply (divide ?174069 ?174070) (divide (multiply (divide ?174070 ?174069) ?174071) (multiply (divide ?174072 ?174073) ?174071)) [174071, 174070, 174069, 174072, 174073] by Demod 28445 with 27948 at 2
-Id : 34240, {_}: divide (divide (inverse (divide ?204167 ?204168)) (divide ?204171 ?204170)) ?204172 =<= inverse (divide (multiply (divide ?204172 (divide ?204170 ?204171)) ?204169) (multiply (divide ?204168 ?204167) ?204169)) [204169, 204172, 204170, 204171, 204168, 204167] by Super 28449 with 28597 at 1,1,1,2
-Id : 34776, {_}: divide (divide (divide (inverse (divide ?206532 ?206533)) (divide ?206534 ?206535)) ?206536) (divide (divide ?206535 ?206534) ?206536) =>= divide ?206533 ?206532 [206536, 206535, 206534, 206533, 206532] by Super 18 with 34240 at 1,2
-Id : 52856, {_}: divide ?292676 ?292677 =<= multiply (divide (divide ?292676 ?292677) (inverse (divide ?292674 ?292675))) (divide ?292675 ?292674) [292675, 292674, 292677, 292676] by Super 28598 with 34776 at 2,3
-Id : 53526, {_}: divide ?296370 ?296371 =<= multiply (multiply (divide ?296370 ?296371) (divide ?296372 ?296373)) (divide ?296373 ?296372) [296373, 296372, 296371, 296370] by Demod 52856 with 6 at 1,3
-Id : 53629, {_}: divide (inverse (divide (divide (divide ?297219 ?297220) ?297221) (divide ?297222 ?297221))) (divide ?297220 ?297219) =?= multiply (multiply ?297222 (divide ?297223 ?297224)) (divide ?297224 ?297223) [297224, 297223, 297222, 297221, 297220, 297219] by Super 53526 with 4 at 1,1,3
-Id : 53865, {_}: ?297222 =<= multiply (multiply ?297222 (divide ?297223 ?297224)) (divide ?297224 ?297223) [297224, 297223, 297222] by Demod 53629 with 4 at 2
-Id : 28234, {_}: multiply (divide (inverse (divide (divide (divide ?172298 ?172299) (inverse ?172301)) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Super 6 with 27948 at 3
-Id : 28487, {_}: multiply (divide (inverse (divide (multiply (divide ?172298 ?172299) ?172301) ?172300)) (divide ?172299 ?172298)) ?172301 =>= ?172300 [172300, 172301, 172299, 172298] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 9011, {_}: inverse (divide (divide (divide ?67439 ?67440) (inverse ?67438)) (multiply (divide ?67441 (divide ?67440 ?67439)) ?67438)) =>= ?67441 [67441, 67438, 67440, 67439] by Super 8947 with 6 at 2,1,2
-Id : 9220, {_}: inverse (divide (multiply (divide ?68482 ?68483) ?68484) (multiply (divide ?68485 (divide ?68483 ?68482)) ?68484)) =>= ?68485 [68485, 68484, 68483, 68482] by Demod 9011 with 6 at 1,1,2
-Id : 9262, {_}: inverse (divide (multiply (divide (inverse ?68840) ?68841) ?68842) (multiply (divide ?68843 (multiply ?68841 ?68840)) ?68842)) =>= ?68843 [68843, 68842, 68841, 68840] by Super 9220 with 6 at 2,1,2,1,2
-Id : 34816, {_}: inverse (divide (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) (divide (divide ?206979 ?206978) ?206984)) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206978, 206979, 206984, 206980, 206981, 206982] by Super 9604 with 34240 at 3
-Id : 52845, {_}: inverse (divide ?292579 ?292578) =<= divide (divide (inverse (divide ?292580 ?292581)) (divide ?292581 ?292580)) (inverse (divide ?292578 ?292579)) [292581, 292580, 292578, 292579] by Super 34816 with 34776 at 1,2
-Id : 53105, {_}: inverse (divide ?292579 ?292578) =<= multiply (divide (inverse (divide ?292580 ?292581)) (divide ?292581 ?292580)) (divide ?292578 ?292579) [292581, 292580, 292578, 292579] by Demod 52845 with 6 at 3
-Id : 57037, {_}: inverse (divide (inverse (divide ?313195 ?313196)) (multiply (divide ?313199 (multiply (divide ?313198 ?313197) (divide ?313197 ?313198))) (divide ?313196 ?313195))) =>= ?313199 [313197, 313198, 313199, 313196, 313195] by Super 9262 with 53105 at 1,1,2
-Id : 12, {_}: divide (inverse (divide (divide (divide (inverse ?42) ?41) ?43) (divide ?44 ?43))) (multiply ?41 ?42) =>= ?44 [44, 43, 41, 42] by Super 4 with 6 at 2,2
-Id : 52731, {_}: divide (inverse (divide ?291529 ?291528)) (multiply (divide ?291530 ?291531) (divide ?291528 ?291529)) =>= divide ?291531 ?291530 [291531, 291530, 291528, 291529] by Super 12 with 34776 at 1,1,2
-Id : 57379, {_}: inverse (divide (multiply (divide ?313198 ?313197) (divide ?313197 ?313198)) ?313199) =>= ?313199 [313199, 313197, 313198] by Demod 57037 with 52731 at 1,2
-Id : 57732, {_}: multiply (divide ?315540 (divide ?315539 ?315538)) (divide ?315539 ?315538) =>= ?315540 [315538, 315539, 315540] by Super 28487 with 57379 at 1,1,2
-Id : 58290, {_}: divide ?318875 (divide ?318876 ?318877) =<= multiply ?318875 (divide ?318877 ?318876) [318877, 318876, 318875] by Super 53865 with 57732 at 1,3
-Id : 58885, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?321635) ?321636) ?321637) (divide ?321633 ?321634))) (multiply (inverse ?321636) ?321635)) ?321637 =>= inverse (divide ?321634 ?321633) [321634, 321633, 321637, 321636, 321635] by Super 33302 with 58290 at 1,1,1,2
-Id : 29397, {_}: multiply (divide (inverse (divide (multiply (divide ?178179 ?178180) ?178181) ?178182)) (divide ?178180 ?178179)) ?178181 =>= ?178182 [178182, 178181, 178180, 178179] by Demod 28234 with 6 at 1,1,1,1,2
-Id : 32339, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?194066) ?194067) ?194068) ?194069)) (multiply ?194067 ?194066)) ?194068 =>= ?194069 [194069, 194068, 194067, 194066] by Super 29397 with 6 at 2,1,2
-Id : 32439, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?194936) ?194935) ?194937) ?194938)) (multiply (inverse ?194935) ?194936)) ?194937 =>= ?194938 [194938, 194937, 194935, 194936] by Super 32339 with 6 at 1,1,1,1,1,2
-Id : 59201, {_}: divide ?321633 ?321634 =<= inverse (divide ?321634 ?321633) [321634, 321633] by Demod 58885 with 32439 at 2
-Id : 59708, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= inverse (divide (multiply ?70222 ?70223) (multiply ?70224 ?70223)) [70223, 70222, 70228, 70224] by Demod 9604 with 59201 at 2
-Id : 59709, {_}: divide (divide ?70224 ?70228) (divide ?70222 ?70228) =?= divide (multiply ?70224 ?70223) (multiply ?70222 ?70223) [70223, 70222, 70228, 70224] by Demod 59708 with 59201 at 3
-Id : 29064, {_}: multiply (divide (inverse (multiply (multiply (divide ?175142 ?175143) ?175145) ?175144)) (divide ?175143 ?175142)) ?175145 =>= inverse ?175144 [175144, 175145, 175143, 175142] by Demod 28803 with 6 at 1,1,1,1,2
-Id : 59905, {_}: divide ?323677 ?323678 =<= inverse (divide ?323678 ?323677) [323678, 323677] by Demod 58885 with 32439 at 2
-Id : 59980, {_}: divide (inverse ?324139) ?324140 =>= inverse (multiply ?324140 ?324139) [324140, 324139] by Super 59905 with 6 at 1,3
-Id : 60322, {_}: multiply (inverse (multiply (divide ?175143 ?175142) (multiply (multiply (divide ?175142 ?175143) ?175145) ?175144))) ?175145 =>= inverse ?175144 [175144, 175145, 175142, 175143] by Demod 29064 with 59980 at 1,2
-Id : 58656, {_}: inverse (divide (divide (divide ?313198 ?313197) (divide ?313198 ?313197)) ?313199) =>= ?313199 [313199, 313197, 313198] by Demod 57379 with 58290 at 1,1,2
-Id : 59766, {_}: divide ?313199 (divide (divide ?313198 ?313197) (divide ?313198 ?313197)) =>= ?313199 [313197, 313198, 313199] by Demod 58656 with 59201 at 2
-Id : 64277, {_}: divide (divide (divide ?332921 ?332922) (divide ?332921 ?332922)) ?332923 =>= inverse ?332923 [332923, 332922, 332921] by Super 59905 with 59766 at 1,3
-Id : 29, {_}: divide (inverse (divide (multiply (multiply ?127 ?126) ?128) (multiply ?129 ?128))) (divide (inverse ?126) ?127) =>= ?129 [129, 128, 126, 127] by Super 23 with 6 at 1,1,1,1,2
-Id : 95, {_}: divide (inverse (divide (multiply (divide (inverse ?431) ?432) ?433) (multiply ?434 ?433))) (multiply ?432 ?431) =>= ?434 [434, 433, 432, 431] by Super 23 with 6 at 2,2
-Id : 101, {_}: divide (inverse (divide (multiply (multiply (inverse ?472) ?471) ?473) (multiply ?474 ?473))) (multiply (inverse ?471) ?472) =>= ?474 [474, 473, 471, 472] by Super 95 with 6 at 1,1,1,1,2
-Id : 163, {_}: divide (inverse (divide (multiply (multiply (multiply (inverse ?755) ?754) (divide (multiply (multiply (inverse ?754) ?755) ?756) (multiply ?757 ?756))) ?758) (multiply ?759 ?758))) ?757 =>= ?759 [759, 758, 757, 756, 754, 755] by Super 29 with 101 at 2,2
-Id : 58602, {_}: divide (inverse (divide (multiply (divide (multiply (inverse ?755) ?754) (divide (multiply ?757 ?756) (multiply (multiply (inverse ?754) ?755) ?756))) ?758) (multiply ?759 ?758))) ?757 =>= ?759 [759, 758, 756, 757, 754, 755] by Demod 163 with 58290 at 1,1,1,1,2
-Id : 59646, {_}: divide (divide (multiply ?759 ?758) (multiply (divide (multiply (inverse ?755) ?754) (divide (multiply ?757 ?756) (multiply (multiply (inverse ?754) ?755) ?756))) ?758)) ?757 =>= ?759 [756, 757, 754, 755, 758, 759] by Demod 58602 with 59201 at 1,2
-Id : 64278, {_}: divide (divide (divide (divide (multiply ?332925 ?332926) (multiply (divide (multiply (inverse ?332927) ?332928) (divide (multiply ?332930 ?332929) (multiply (multiply (inverse ?332928) ?332927) ?332929))) ?332926)) ?332930) ?332925) ?332931 =>= inverse ?332931 [332931, 332929, 332930, 332928, 332927, 332926, 332925] by Super 64277 with 59646 at 2,1,2
-Id : 65204, {_}: divide (divide ?332925 ?332925) ?332931 =>= inverse ?332931 [332931, 332925] by Demod 64278 with 59646 at 1,1,2
-Id : 66466, {_}: multiply (divide ?338522 ?338522) ?338523 =>= inverse (inverse ?338523) [338523, 338522] by Super 6 with 65204 at 3
-Id : 60452, {_}: divide ?324438 (inverse ?324437) =<= inverse (inverse (multiply ?324438 ?324437)) [324437, 324438] by Super 59201 with 59980 at 1,3
-Id : 61190, {_}: multiply ?326165 ?326166 =<= inverse (inverse (multiply ?326165 ?326166)) [326166, 326165] by Demod 60452 with 6 at 2
-Id : 20, {_}: divide (inverse (divide (divide (divide (divide ?68 ?67) (inverse (divide (multiply (divide ?67 ?68) ?69) (multiply ?70 ?69)))) ?71) (divide ?72 ?71))) ?70 =>= ?72 [72, 71, 70, 69, 67, 68] by Super 4 with 18 at 2,2
-Id : 31, {_}: divide (inverse (divide (divide (multiply (divide ?68 ?67) (divide (multiply (divide ?67 ?68) ?69) (multiply ?70 ?69))) ?71) (divide ?72 ?71))) ?70 =>= ?72 [72, 71, 70, 69, 67, 68] by Demod 20 with 6 at 1,1,1,1,2
-Id : 188, {_}: multiply (inverse (divide (divide (multiply (divide ?884 ?885) (divide (multiply (divide ?885 ?884) ?886) (multiply (inverse ?889) ?886))) ?887) (divide ?888 ?887))) ?889 =>= ?888 [888, 887, 889, 886, 885, 884] by Super 6 with 31 at 3
-Id : 58606, {_}: multiply (inverse (divide (divide (divide (divide ?884 ?885) (divide (multiply (inverse ?889) ?886) (multiply (divide ?885 ?884) ?886))) ?887) (divide ?888 ?887))) ?889 =>= ?888 [888, 887, 886, 889, 885, 884] by Demod 188 with 58290 at 1,1,1,1,2
-Id : 59648, {_}: multiply (divide (divide ?888 ?887) (divide (divide (divide ?884 ?885) (divide (multiply (inverse ?889) ?886) (multiply (divide ?885 ?884) ?886))) ?887)) ?889 =>= ?888 [886, 889, 885, 884, 887, 888] by Demod 58606 with 59201 at 1,2
-Id : 61191, {_}: multiply (divide (divide ?326168 ?326169) (divide (divide (divide ?326170 ?326171) (divide (multiply (inverse ?326173) ?326172) (multiply (divide ?326171 ?326170) ?326172))) ?326169)) ?326173 =>= inverse (inverse ?326168) [326172, 326173, 326171, 326170, 326169, 326168] by Super 61190 with 59648 at 1,1,3
-Id : 61231, {_}: ?326168 =<= inverse (inverse ?326168) [326168] by Demod 61191 with 59648 at 2
-Id : 67123, {_}: multiply (divide ?338522 ?338522) ?338523 =>= ?338523 [338523, 338522] by Demod 66466 with 61231 at 3
-Id : 69503, {_}: multiply (inverse (multiply (divide ?344249 ?344249) (multiply ?344250 ?344251))) ?344250 =>= inverse ?344251 [344251, 344250, 344249] by Super 60322 with 67123 at 1,2,1,1,2
-Id : 70168, {_}: multiply (inverse (multiply ?344250 ?344251)) ?344250 =>= inverse ?344251 [344251, 344250] by Demod 69503 with 67123 at 1,1,2
-Id : 71425, {_}: divide (divide ?348688 ?348689) (divide (inverse (multiply ?348686 ?348687)) ?348689) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Super 59709 with 70168 at 2,3
-Id : 71942, {_}: divide (divide ?348688 ?348689) (inverse (multiply ?348689 (multiply ?348686 ?348687))) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Demod 71425 with 59980 at 2,2
-Id : 71943, {_}: multiply (divide ?348688 ?348689) (multiply ?348689 (multiply ?348686 ?348687)) =>= divide (multiply ?348688 ?348686) (inverse ?348687) [348687, 348686, 348689, 348688] by Demod 71942 with 6 at 2
-Id : 71944, {_}: multiply (divide ?348688 ?348689) (multiply ?348689 (multiply ?348686 ?348687)) =>= multiply (multiply ?348688 ?348686) ?348687 [348687, 348686, 348689, 348688] by Demod 71943 with 6 at 3
-Id : 26, {_}: divide (inverse (divide (multiply (divide (inverse ?107) ?108) ?109) (multiply ?110 ?109))) (multiply ?108 ?107) =>= ?110 [110, 109, 108, 107] by Super 23 with 6 at 2,2
-Id : 91, {_}: divide (inverse (divide (multiply (divide (multiply ?404 ?403) (inverse (divide (multiply (divide (inverse ?403) ?404) ?405) (multiply ?406 ?405)))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 406, 405, 403, 404] by Super 18 with 26 at 2,2
-Id : 103, {_}: divide (inverse (divide (multiply (multiply (multiply ?404 ?403) (divide (multiply (divide (inverse ?403) ?404) ?405) (multiply ?406 ?405))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 406, 405, 403, 404] by Demod 91 with 6 at 1,1,1,1,2
-Id : 58628, {_}: divide (inverse (divide (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (divide (inverse ?403) ?404) ?405))) ?407) (multiply ?408 ?407))) ?406 =>= ?408 [408, 407, 405, 406, 403, 404] by Demod 103 with 58290 at 1,1,1,1,2
-Id : 59659, {_}: divide (divide (multiply ?408 ?407) (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (divide (inverse ?403) ?404) ?405))) ?407)) ?406 =>= ?408 [405, 406, 403, 404, 407, 408] by Demod 58628 with 59201 at 1,2
-Id : 60280, {_}: divide (divide (multiply ?408 ?407) (multiply (divide (multiply ?404 ?403) (divide (multiply ?406 ?405) (multiply (inverse (multiply ?404 ?403)) ?405))) ?407)) ?406 =>= ?408 [405, 406, 403, 404, 407, 408] by Demod 59659 with 59980 at 1,2,2,1,2,1,2
-Id : 69677, {_}: multiply (divide ?345297 ?345297) ?345298 =>= ?345298 [345298, 345297] by Demod 66466 with 61231 at 3
-Id : 69694, {_}: multiply (multiply (inverse ?345392) ?345392) ?345393 =>= ?345393 [345393, 345392] by Super 69677 with 6 at 1,2
-Id : 70939, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (divide ?347988 (multiply (inverse (multiply ?347991 ?347992)) ?347988))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347988, 347992, 347991, 347990, 347989] by Super 60280 with 69694 at 1,2,1,2,1,2
-Id : 59713, {_}: divide (divide (divide ?63000 (divide ?62997 ?62998)) ?62999) (divide (divide ?62998 ?62997) ?62999) =>= ?63000 [62999, 62998, 62997, 63000] by Demod 8271 with 59201 at 2
-Id : 59961, {_}: divide (divide (divide ?324009 ?324010) (divide ?324009 ?324010)) ?324011 =>= inverse ?324011 [324011, 324010, 324009] by Super 59905 with 59766 at 1,3
-Id : 64211, {_}: divide (divide (divide ?332479 (inverse ?332478)) ?332480) (divide (divide ?332478 (divide (divide ?332476 ?332477) (divide ?332476 ?332477))) ?332480) =>= ?332479 [332477, 332476, 332480, 332478, 332479] by Super 59713 with 59961 at 2,1,1,2
-Id : 59760, {_}: divide (divide (divide ?206979 ?206978) ?206984) (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) =>= divide (divide (inverse (divide ?206978 ?206979)) (divide ?206980 ?206981)) ?206982 [206980, 206981, 206982, 206984, 206978, 206979] by Demod 34816 with 59201 at 2
-Id : 59761, {_}: divide (divide (divide ?206979 ?206978) ?206984) (divide (divide ?206982 (divide ?206981 ?206980)) ?206984) =>= divide (divide (divide ?206979 ?206978) (divide ?206980 ?206981)) ?206982 [206980, 206981, 206982, 206984, 206978, 206979] by Demod 59760 with 59201 at 1,1,3
-Id : 64644, {_}: divide (divide (divide ?332479 (inverse ?332478)) (divide (divide ?332476 ?332477) (divide ?332476 ?332477))) ?332478 =>= ?332479 [332477, 332476, 332478, 332479] by Demod 64211 with 59761 at 2
-Id : 64645, {_}: divide (divide ?332479 (inverse ?332478)) ?332478 =>= ?332479 [332478, 332479] by Demod 64644 with 59766 at 1,2
-Id : 64646, {_}: divide (multiply ?332479 ?332478) ?332478 =>= ?332479 [332478, 332479] by Demod 64645 with 6 at 1,2
-Id : 66156, {_}: divide ?337261 (multiply ?337260 ?337261) =>= inverse ?337260 [337260, 337261] by Super 59201 with 64646 at 1,3
-Id : 71006, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (inverse (inverse (multiply ?347991 ?347992)))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 70939 with 66156 at 2,1,2,1,2
-Id : 71007, {_}: divide (divide (multiply ?347989 ?347990) (multiply (multiply (multiply ?347991 ?347992) (inverse (multiply ?347991 ?347992))) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 71006 with 6 at 1,2,1,2
-Id : 61286, {_}: multiply ?326469 (inverse ?326468) =>= divide ?326469 ?326468 [326468, 326469] by Super 6 with 61231 at 2,3
-Id : 71008, {_}: divide (divide (multiply ?347989 ?347990) (multiply (divide (multiply ?347991 ?347992) (multiply ?347991 ?347992)) ?347990)) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347992, 347991, 347990, 347989] by Demod 71007 with 61286 at 1,2,1,2
-Id : 71009, {_}: divide (divide (multiply ?347989 ?347990) ?347990) (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347990, 347989] by Demod 71008 with 67123 at 2,1,2
-Id : 71010, {_}: divide ?347989 (multiply (inverse ?347987) ?347987) =>= ?347989 [347987, 347989] by Demod 71009 with 64646 at 1,2
-Id : 73616, {_}: divide (divide ?351709 ?351710) (divide (inverse ?351708) ?351710) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Super 59709 with 71010 at 3
-Id : 74280, {_}: divide (divide ?351709 ?351710) (inverse (multiply ?351710 ?351708)) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Demod 73616 with 59980 at 2,2
-Id : 74281, {_}: multiply (divide ?351709 ?351710) (multiply ?351710 ?351708) =>= multiply ?351709 ?351708 [351708, 351710, 351709] by Demod 74280 with 6 at 2
-Id : 89373, {_}: multiply ?348688 (multiply ?348686 ?348687) =?= multiply (multiply ?348688 ?348686) ?348687 [348687, 348686, 348688] by Demod 71944 with 74281 at 2
-Id : 89656, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 2 with 89373 at 2
-Id : 2, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP477-1.p
-Order
- == is 100
- _ is 99
- a2 is 95
- b2 is 98
- inverse is 97
- multiply is 96
- prove_these_axioms_2 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-Timeout !
-FAILURE in 41 iterations
-% SZS status Timeout for GRP506-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- inverse is 94
- multiply is 96
- prove_these_axioms_4 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-Timeout !
-FAILURE in 41 iterations
-% SZS status Timeout for GRP508-1.p
-Order
- == is 100
- _ is 99
- a is 98
- join is 95
- meet is 97
- prove_normal_axioms_1 is 96
- single_axiom is 94
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: meet a a =>= a [] by prove_normal_axioms_1
-Timeout !
-FAILURE in 12 iterations
-% SZS status Timeout for LAT080-1.p
-Order
- == is 100
- _ is 99
- a is 98
- b is 97
- join is 95
- meet is 96
- prove_normal_axioms_8 is 94
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-Goal
- Id : 2, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-Timeout !
-FAILURE in 12 iterations
-% SZS status Timeout for LAT087-1.p
-Order
- == is 100
- _ is 99
- a is 97
- b is 98
- join is 94
- meet is 96
- prove_wal_axioms_2 is 95
- single_axiom is 93
-Facts
- Id : 4, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-Goal
- Id : 2, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-Timeout !
-FAILURE in 14 iterations
-% SZS status Timeout for LAT093-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H7 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 141 iterations
-% SZS status Timeout for LAT138-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H2 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT140-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H34 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H28 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-Timeout !
-FAILURE in 143 iterations
-% SZS status Timeout for LAT146-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H34 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Timeout !
-FAILURE in 141 iterations
-% SZS status Timeout for LAT148-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H40 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT152-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT156-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H50 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H7 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-Timeout !
-FAILURE in 143 iterations
-% SZS status Timeout for LAT159-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H76 is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 94
- meet is 95
- prove_H6 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT164-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H77 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT165-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H77 is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H78 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT166-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H21_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT169-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 90
- absorption2 is 89
- associativity_of_join is 85
- associativity_of_meet is 86
- b is 97
- c is 96
- commutativity_of_join is 87
- commutativity_of_meet is 88
- equation_H49_dual is 84
- idempotence_of_join is 91
- idempotence_of_meet is 92
- join is 95
- meet is 94
- prove_H58 is 93
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-Timeout !
-FAILURE in 143 iterations
-% SZS status Timeout for LAT170-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H76_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 94
- meet is 93
- prove_H40 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT173-1.p
-Order
- == is 100
- _ is 99
- a is 98
- absorption1 is 89
- absorption2 is 88
- associativity_of_join is 84
- associativity_of_meet is 85
- b is 97
- c is 96
- commutativity_of_join is 86
- commutativity_of_meet is 87
- d is 95
- equation_H79_dual is 83
- idempotence_of_join is 90
- idempotence_of_meet is 91
- join is 93
- meet is 94
- prove_H32 is 92
-Facts
- Id : 4, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
- Id : 6, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
- Id : 8, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
- Id : 10, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
- Id : 12, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
- Id : 14, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
- Id : 16, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
- Id : 18, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
- Id : 20, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-Goal
- Id : 2, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-Timeout !
-FAILURE in 142 iterations
-% SZS status Timeout for LAT175-1.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_cubed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Timeout !
-FAILURE in 832 iterations
-% SZS status Timeout for RNG009-7.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Timeout !
-FAILURE in 109 iterations
-% SZS status Timeout for RNG019-6.p
-Order
- == is 100
- _ is 99
- add is 94
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- distributivity_of_difference1 is 71
- distributivity_of_difference2 is 70
- distributivity_of_difference3 is 69
- distributivity_of_difference4 is 68
- inverse_product1 is 73
- inverse_product2 is 72
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- product_of_inverses is 74
- prove_linearised_form1 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 96
- v is 95
- x is 98
- y is 97
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-Timeout !
-FAILURE in 149 iterations
-% SZS status Timeout for RNG019-7.p
-Order
- == is 100
- _ is 99
- add is 95
- additive_identity is 91
- additive_inverse is 85
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- commutativity_for_addition is 79
- commutator is 75
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 90
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 87
- multiply is 88
- prove_linearised_form2 is 92
- right_additive_identity is 89
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 86
- u is 97
- v is 96
- x is 98
- y is 94
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-Timeout !
-FAILURE in 109 iterations
-% SZS status Timeout for RNG020-6.p
-Order
- == is 100
- _ is 99
- a is 98
- add is 92
- additive_identity is 90
- additive_inverse is 91
- additive_inverse_additive_inverse is 82
- associativity_for_addition is 78
- associator is 93
- b is 97
- c is 95
- commutativity_for_addition is 79
- commutator is 75
- d is 94
- distribute1 is 81
- distribute2 is 80
- left_additive_identity is 88
- left_additive_inverse is 84
- left_alternative is 76
- left_multiplicative_zero is 86
- multiply is 96
- prove_teichmuller_identity is 89
- right_additive_identity is 87
- right_additive_inverse is 83
- right_alternative is 77
- right_multiplicative_zero is 85
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-Goal
- Id : 2, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-Timeout !
-FAILURE in 109 iterations
-% SZS status Timeout for RNG026-6.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- cx is 97
- cy is 96
- cz is 98
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 95
- product_of_inverses is 75
- prove_right_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-Timeout !
-FAILURE in 149 iterations
-% SZS status Timeout for RNG027-7.p
-Order
- == is 100
- _ is 99
- add is 91
- additive_identity is 92
- additive_inverse is 86
- additive_inverse_additive_inverse is 83
- associativity_for_addition is 79
- associator is 94
- commutativity_for_addition is 80
- commutator is 76
- distribute1 is 82
- distribute2 is 81
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 90
- left_additive_inverse is 85
- left_alternative is 77
- left_multiplicative_zero is 88
- multiply is 96
- product_of_inverses is 75
- prove_left_moufang is 93
- right_additive_identity is 89
- right_additive_inverse is 84
- right_alternative is 78
- right_multiplicative_zero is 87
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-Timeout !
-FAILURE in 149 iterations
-% SZS status Timeout for RNG028-9.p
-Order
- == is 100
- _ is 99
- add is 92
- additive_identity is 93
- additive_inverse is 87
- additive_inverse_additive_inverse is 84
- associativity_for_addition is 80
- associator is 77
- commutativity_for_addition is 81
- commutator is 76
- distribute1 is 83
- distribute2 is 82
- distributivity_of_difference1 is 72
- distributivity_of_difference2 is 71
- distributivity_of_difference3 is 70
- distributivity_of_difference4 is 69
- inverse_product1 is 74
- inverse_product2 is 73
- left_additive_identity is 91
- left_additive_inverse is 86
- left_alternative is 78
- left_multiplicative_zero is 89
- multiply is 96
- product_of_inverses is 75
- prove_middle_moufang is 94
- right_additive_identity is 90
- right_additive_inverse is 85
- right_alternative is 79
- right_multiplicative_zero is 88
- x is 98
- y is 97
- z is 95
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
- Id : 10, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
- Id : 12, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
- Id : 14, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
- Id : 16, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
- Id : 18, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
- Id : 20, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
- Id : 22, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
- Id : 24, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
- Id : 26, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
- Id : 28, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
- Id : 30, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
- Id : 32, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
- Id : 34, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
- Id : 36, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
- Id : 38, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
- Id : 40, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
- Id : 42, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
- Id : 44, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
- Id : 46, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-Goal
- Id : 2, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-Timeout !
-FAILURE in 150 iterations
-% SZS status Timeout for RNG029-7.p
-Order
- == is 100
- _ is 99
- a is 97
- a_times_b_is_c is 80
- add is 92
- additive_identity is 93
- additive_inverse is 89
- associativity_for_addition is 86
- associativity_for_multiplication is 84
- b is 98
- c is 95
- commutativity_for_addition is 85
- distribute1 is 83
- distribute2 is 82
- left_additive_identity is 91
- left_additive_inverse is 88
- multiply is 96
- prove_commutativity is 94
- right_additive_identity is 90
- right_additive_inverse is 87
- x_fourthed_is_x is 81
-Facts
- Id : 4, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
- Id : 6, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
- Id : 8, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
- Id : 10, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
- Id : 12, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
- Id : 14, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
- Id : 16, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
- Id : 18, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
- Id : 20, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
- Id : 22, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
- Id : 24, {_}: multiply a b =>= c [] by a_times_b_is_c
-Goal
- Id : 2, {_}: multiply b a =>= c [] by prove_commutativity
-Timeout !
-FAILURE in 743 iterations
-% SZS status Timeout for RNG035-7.p
-Order
- == is 100
- _ is 99
- a is 98
- absorbtion is 88
- add is 95
- associativity_of_add is 92
- b is 97
- c is 90
- commutativity_of_add is 93
- d is 89
- negate is 96
- prove_huntingtons_axiom is 94
- robbins_axiom is 91
-Facts
- Id : 4, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
- Id : 6, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
- Id : 8, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-Timeout !
-FAILURE in 61 iterations
-% SZS status Timeout for ROB006-1.p
-Order
- == is 100
- _ is 99
- absorbtion is 90
- add is 98
- associativity_of_add is 95
- c is 92
- commutativity_of_add is 96
- d is 91
- negate is 94
- prove_idempotence is 97
- robbins_axiom is 93
-Facts
- Id : 4, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
- Id : 6, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
- Id : 8, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
- Id : 10, {_}: add c d =>= d [] by absorbtion
-Goal
- Id : 2, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-Timeout !
-FAILURE in 30 iterations
-% SZS status Timeout for ROB006-2.p
+++ /dev/null
-CLASH, statistics insufficient
-4578: Facts:
-4578: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4578: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4578: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4578: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4578: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-4578: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-4578: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-4578: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-4578: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-4578: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-4578: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-4578: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-4578: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-4578: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-4578: Goal:
-4578: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4578: Order:
-4578: nrkbo
-4578: Leaf order:
-4578: additive_identity 4 0 0
-4578: multiplicative_identity 4 0 0
-4578: inverse 4 1 0
-4578: add 16 2 0 multiply
-4578: multiply 20 2 4 0,2add
-4578: c 2 0 2 2,2,2
-4578: b 2 0 2 1,2,2
-4578: a 2 0 2 1,2
-CLASH, statistics insufficient
-4579: Facts:
-4579: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4579: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4579: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4579: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4579: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-4579: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-4579: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-4579: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-4579: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-4579: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-4579: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-4579: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-4579: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-4579: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-4579: Goal:
-4579: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4579: Order:
-4579: kbo
-4579: Leaf order:
-4579: additive_identity 4 0 0
-4579: multiplicative_identity 4 0 0
-4579: inverse 4 1 0
-4579: add 16 2 0 multiply
-4579: multiply 20 2 4 0,2add
-4579: c 2 0 2 2,2,2
-4579: b 2 0 2 1,2,2
-4579: a 2 0 2 1,2
-CLASH, statistics insufficient
-4580: Facts:
-4580: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4580: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4580: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4580: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4580: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =>=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-4580: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =>=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-4580: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-4580: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-4580: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-4580: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-4580: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-4580: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-4580: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-4580: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-4580: Goal:
-4580: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4580: Order:
-4580: lpo
-4580: Leaf order:
-4580: additive_identity 4 0 0
-4580: multiplicative_identity 4 0 0
-4580: inverse 4 1 0
-4580: add 16 2 0 multiply
-4580: multiply 20 2 4 0,2add
-4580: c 2 0 2 2,2,2
-4580: b 2 0 2 1,2,2
-4580: a 2 0 2 1,2
-Statistics :
-Max weight : 22
-Found proof, 16.914436s
-% SZS status Unsatisfiable for BOO007-2.p
-% SZS output start CNFRefutation for BOO007-2.p
-Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
-Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
-Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
-Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
-Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
-Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
-Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
-Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
-Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
-Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2
-Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3
-Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
-Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3
-Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2
-Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2
-Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3
-Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2
-Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3
-Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
-Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3
-Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
-Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3
-Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3
-Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
-Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3
-Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2
-Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2
-Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2
-Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2
-Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3
-Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2
-Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3
-Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2
-Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3
-Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3
-Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2
-Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3
-Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3
-Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3
-Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2
-Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2
-Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
-Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3
-Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2
-Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2
-Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2
-Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3
-Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3
-Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2
-Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
-Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3
-Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2
-Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2
-Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2
-Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3
-Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3
-Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3
-Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3
-Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2
-Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2
-Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2
-Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3
-Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
-Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2
-Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3
-Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3
-Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3
-Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2
-Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3
-Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2
-Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2
-Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3
-Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2
-Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3
-Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3
-Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3
-Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2
-Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3
-Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2
-Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3
-Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2
-Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2
-Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3
-Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2
-Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3
-Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3
-Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3
-Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3
-Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3
-Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3
-Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3
-Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2
-Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3
-Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3
-Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3
-Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2
-Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3
-Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3
-Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3
-Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2
-Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3
-Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2
-Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3
-Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-2.p
-4579: solved BOO007-2.p in 8.372523 using kbo
-4579: status Unsatisfiable for BOO007-2.p
-CLASH, statistics insufficient
-4588: Facts:
-4588: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4588: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4588: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4588: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4588: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-4588: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-4588: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-4588: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-4588: Goal:
-4588: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4588: Order:
-4588: nrkbo
-4588: Leaf order:
-4588: inverse 2 1 0
-4588: multiplicative_identity 2 0 0
-4588: additive_identity 2 0 0
-4588: add 9 2 0 multiply
-4588: multiply 13 2 4 0,2add
-4588: c 2 0 2 2,2,2
-4588: b 2 0 2 1,2,2
-4588: a 2 0 2 1,2
-CLASH, statistics insufficient
-4589: Facts:
-4589: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4589: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4589: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4589: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4589: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-4589: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-4589: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-4589: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-4589: Goal:
-4589: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4589: Order:
-4589: kbo
-4589: Leaf order:
-4589: inverse 2 1 0
-4589: multiplicative_identity 2 0 0
-4589: additive_identity 2 0 0
-4589: add 9 2 0 multiply
-4589: multiply 13 2 4 0,2add
-4589: c 2 0 2 2,2,2
-4589: b 2 0 2 1,2,2
-4589: a 2 0 2 1,2
-CLASH, statistics insufficient
-4590: Facts:
-4590: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-4590: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-4590: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-4590: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =>=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-4590: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-4590: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-4590: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-4590: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-4590: Goal:
-4590: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-4590: Order:
-4590: lpo
-4590: Leaf order:
-4590: inverse 2 1 0
-4590: multiplicative_identity 2 0 0
-4590: additive_identity 2 0 0
-4590: add 9 2 0 multiply
-4590: multiply 13 2 4 0,2add
-4590: c 2 0 2 2,2,2
-4590: b 2 0 2 1,2,2
-4590: a 2 0 2 1,2
-Statistics :
-Max weight : 25
-Found proof, 23.495904s
-% SZS status Unsatisfiable for BOO007-4.p
-% SZS output start CNFRefutation for BOO007-4.p
-Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114
-Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
-Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
-Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
-Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64
-Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3
-Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3
-Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3
-Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3
-Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3
-Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3
-Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3
-Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3
-Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3
-Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3
-Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2
-Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2
-Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2
-Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3
-Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2
-Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3
-Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3
-Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2
-Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2
-Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3
-Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3
-Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2
-Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2
-Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3
-Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2
-Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2
-Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2
-Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2
-Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2
-Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3
-Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3
-Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2
-Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3
-Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3
-Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3
-Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3
-Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3
-Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3
-Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3
-Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3
-Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3
-Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3
-Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3
-Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3
-Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2
-Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2
-Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3
-Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3
-Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3
-Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3
-Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3
-Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3
-Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3
-Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3
-Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3
-Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2
-Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2
-Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3
-Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3
-Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2
-Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3
-Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3
-Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2
-Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3
-Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2
-Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3
-Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2
-Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3
-Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2
-Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3
-Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3
-Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2
-Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3
-Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2
-Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3
-Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3
-Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2
-Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2
-Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3
-Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2
-Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3
-Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2
-Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3
-Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-4.p
-4589: solved BOO007-4.p in 11.664728 using kbo
-4589: status Unsatisfiable for BOO007-4.p
-CLASH, statistics insufficient
-4606: Facts:
-4606: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-4606: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-4606: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-4606: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-4606: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-4606: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-4606: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-4606: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-4606: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-4606: Id : 11, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-4606: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-4606: Goal:
-4606: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-4606: Order:
-4606: nrkbo
-4606: Leaf order:
-4606: n0 1 0 0
-4606: n1 1 0 0
-4606: inverse 4 1 0
-4606: multiply 22 2 3 0,2add
-4606: add 21 2 2 0,2,2multiply
-4606: c 2 0 2 2,2,2
-4606: b 2 0 2 1,2,2
-4606: a 3 0 3 1,2
-CLASH, statistics insufficient
-4607: Facts:
-4607: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-4607: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-4607: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-4607: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-4607: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-4607: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-4607: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-4607: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-4607: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-4607: Id : 11, {_}:
- add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-CLASH, statistics insufficient
-4608: Facts:
-4608: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-4608: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-4608: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-4608: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-4608: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-4608: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-4608: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-4608: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-4608: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-4608: Id : 11, {_}:
- add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-4607: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-4607: Goal:
-4607: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-4607: Order:
-4607: kbo
-4607: Leaf order:
-4607: n0 1 0 0
-4607: n1 1 0 0
-4607: inverse 4 1 0
-4607: multiply 22 2 3 0,2add
-4607: add 21 2 2 0,2,2multiply
-4607: c 2 0 2 2,2,2
-4607: b 2 0 2 1,2,2
-4607: a 3 0 3 1,2
-4608: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-4608: Goal:
-4608: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-4608: Order:
-4608: lpo
-4608: Leaf order:
-4608: n0 1 0 0
-4608: n1 1 0 0
-4608: inverse 4 1 0
-4608: multiply 22 2 3 0,2add
-4608: add 21 2 2 0,2,2multiply
-4608: c 2 0 2 2,2,2
-4608: b 2 0 2 1,2,2
-4608: a 3 0 3 1,2
-Statistics :
-Max weight : 29
-Found proof, 44.648027s
-% SZS status Unsatisfiable for BOO031-1.p
-% SZS output start CNFRefutation for BOO031-1.p
-Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
-Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
-Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
-Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191
-Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
-Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
-Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60
-Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
-Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130
-Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
-Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
-Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2
-Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2
-Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2
-Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2
-Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2
-Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2
-Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2
-Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2
-Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2
-Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2
-Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3
-Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2
-Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2
-Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3
-Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2
-Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3
-Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2
-Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2
-Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2
-Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3
-Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2
-Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2
-Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2
-Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2
-Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2
-Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2
-Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2
-Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2
-Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3
-Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2
-Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3
-Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2
-Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3
-Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2
-Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2
-Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2
-Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3
-Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3
-Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3
-Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2
-Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2
-Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2
-Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2
-Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2
-Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2
-Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3
-Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2
-Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3
-Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3
-Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3
-Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2
-Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2
-Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2
-Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2
-Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3
-Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3
-Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3
-Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2
-Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2
-Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3
-Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2
-Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3
-Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2
-Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2
-Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2
-Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2
-Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2
-Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2
-Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2
-Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2
-Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2
-Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2
-Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3
-Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2
-Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2
-Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3
-Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2
-Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2
-Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3
-Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2
-Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3
-Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3
-Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2
-Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3
-Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2
-Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2
-Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2
-Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2
-Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2
-Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2
-Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2
-Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2
-Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2
-Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3
-Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2
-Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2
-Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3
-Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3
-Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3
-Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3
-Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3
-Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3
-Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2
-Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
-% SZS output end CNFRefutation for BOO031-1.p
-4607: solved BOO031-1.p in 22.309393 using kbo
-4607: status Unsatisfiable for BOO031-1.p
-NO CLASH, using fixed ground order
-4619: Facts:
-4619: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4619: Goal:
-4619: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
-4619: Order:
-4619: nrkbo
-4619: Leaf order:
-4619: inverse 7 1 0
-4619: add 8 2 2 0,2
-4619: a 2 0 2 2,2
-4619: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-4620: Facts:
-4620: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4620: Goal:
-4620: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
-4620: Order:
-4620: kbo
-4620: Leaf order:
-4620: inverse 7 1 0
-4620: add 8 2 2 0,2
-4620: a 2 0 2 2,2
-4620: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-4621: Facts:
-4621: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4621: Goal:
-4621: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
-4621: Order:
-4621: lpo
-4621: Leaf order:
-4621: inverse 7 1 0
-4621: add 8 2 2 0,2
-4621: a 2 0 2 2,2
-4621: b 2 0 2 1,2
-Statistics :
-Max weight : 70
-Found proof, 56.468020s
-% SZS status Unsatisfiable for BOO072-1.p
-% SZS output start CNFRefutation for BOO072-1.p
-Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
-Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
-Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
-Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
-Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
-Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
-Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
-Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
-Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
-Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
-Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
-Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
-Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
-Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
-Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
-Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
-Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
-Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
-Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
-Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
-Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
-Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
-Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
-Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
-Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
-Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
-Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
-Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
-Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
-Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
-Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
-Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
-Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
-Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
-Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
-Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
-Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
-Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
-Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
-Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
-Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
-Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
-Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
-Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
-Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
-Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
-Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
-Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3
-Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2
-Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3
-Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3
-Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2
-Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
-Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
-Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
-Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
-Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
-Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
-Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
-Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
-Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
-Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
-Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
-Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
-Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
-Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
-Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
-Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
-Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
-Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
-Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
-Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
-Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
-Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
-Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
-Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3
-Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2
-Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
-Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
-Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
-Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
-Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
-Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
-Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
-Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3
-Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3
-Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2
-Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2
-Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2
-Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3
-Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2
-Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3
-Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3
-Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3
-Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3
-Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2
-Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2
-Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3
-Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3
-Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3
-Id : 21981, {_}: add a b === add a b [] by Demod 1 with 21454 at 2
-Id : 1, {_}: add b a =>= add a b [] by huntinton_1
-% SZS output end CNFRefutation for BOO072-1.p
-4619: solved BOO072-1.p in 9.46059 using nrkbo
-4619: status Unsatisfiable for BOO072-1.p
-NO CLASH, using fixed ground order
-4637: Facts:
-4637: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4637: Goal:
-4637: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-4637: Order:
-4637: nrkbo
-4637: Leaf order:
-4637: inverse 7 1 0
-4637: c 2 0 2 2,2
-4637: add 10 2 4 0,2
-4637: b 2 0 2 2,1,2
-4637: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-4638: Facts:
-4638: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4638: Goal:
-4638: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-4638: Order:
-4638: kbo
-4638: Leaf order:
-4638: inverse 7 1 0
-4638: c 2 0 2 2,2
-4638: add 10 2 4 0,2
-4638: b 2 0 2 2,1,2
-4638: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-4639: Facts:
-4639: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4639: Goal:
-4639: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-4639: Order:
-4639: lpo
-4639: Leaf order:
-4639: inverse 7 1 0
-4639: c 2 0 2 2,2
-4639: add 10 2 4 0,2
-4639: b 2 0 2 2,1,2
-4639: a 2 0 2 1,1,2
-% SZS status Timeout for BOO073-1.p
-NO CLASH, using fixed ground order
-4666: Facts:
-4666: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4666: Goal:
-4666: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-4666: Order:
-4666: nrkbo
-4666: Leaf order:
-4666: add 9 2 3 0,2
-4666: b 2 0 2 2,1,1,2
-4666: inverse 12 1 5 0,1,2
-4666: a 3 0 3 1,1,1,1,2
-NO CLASH, using fixed ground order
-4667: Facts:
-4667: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4667: Goal:
-4667: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-4667: Order:
-4667: kbo
-4667: Leaf order:
-4667: add 9 2 3 0,2
-4667: b 2 0 2 2,1,1,2
-4667: inverse 12 1 5 0,1,2
-4667: a 3 0 3 1,1,1,1,2
-NO CLASH, using fixed ground order
-4668: Facts:
-4668: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-4668: Goal:
-4668: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-4668: Order:
-4668: lpo
-4668: Leaf order:
-4668: add 9 2 3 0,2
-4668: b 2 0 2 2,1,1,2
-4668: inverse 12 1 5 0,1,2
-4668: a 3 0 3 1,1,1,1,2
-Statistics :
-Max weight : 70
-Found proof, 17.395929s
-% SZS status Unsatisfiable for BOO074-1.p
-% SZS output start CNFRefutation for BOO074-1.p
-Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
-Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
-Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
-Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
-Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
-Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
-Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
-Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
-Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
-Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
-Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
-Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
-Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
-Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
-Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
-Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
-Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
-Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
-Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
-Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
-Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
-Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
-Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
-Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
-Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
-Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
-Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
-Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
-Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
-Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
-Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
-Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
-Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
-Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
-Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
-Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
-Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
-Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
-Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =?= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
-Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
-Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
-Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
-Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
-Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
-Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
-Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
-Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
-Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
-Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
-Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
-Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
-Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
-Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
-Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
-Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
-Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
-Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
-Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
-Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
-Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
-Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
-Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
-Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
-Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
-Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
-Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
-Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
-Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
-Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
-Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
-Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
-Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
-Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
-Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
-Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
-Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
-Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
-Id : 18644, {_}: a === a [] by Demod 18643 with 1733 at 2
-Id : 18643, {_}: inverse (inverse a) =>= a [] by Demod 18642 with 1761 at 2
-Id : 18642, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18641 with 18480 at 1,2,2
-Id : 18641, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2
-Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3
-% SZS output end CNFRefutation for BOO074-1.p
-4666: solved BOO074-1.p in 8.672542 using nrkbo
-4666: status Unsatisfiable for BOO074-1.p
-NO CLASH, using fixed ground order
-4673: Facts:
-4673: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4673: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4673: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-4673: Goal:
-4673: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4673: Order:
-4673: nrkbo
-4673: Leaf order:
-4673: w 4 0 0
-4673: b 6 0 0
-4673: apply 19 2 3 0,2
-4673: fixed_pt 3 0 3 2,2
-4673: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4674: Facts:
-4674: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4674: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4674: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-4674: Goal:
-4674: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4674: Order:
-4674: kbo
-4674: Leaf order:
-4674: w 4 0 0
-4674: b 6 0 0
-4674: apply 19 2 3 0,2
-4674: fixed_pt 3 0 3 2,2
-4674: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4675: Facts:
-4675: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4675: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4675: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-4675: Goal:
-4675: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4675: Order:
-4675: lpo
-4675: Leaf order:
-4675: w 4 0 0
-4675: b 6 0 0
-4675: apply 19 2 3 0,2
-4675: fixed_pt 3 0 3 2,2
-4675: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL003-12.p
-NO CLASH, using fixed ground order
-4697: Facts:
-4697: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4697: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4697: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-4697: Goal:
-4697: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4697: Order:
-4697: nrkbo
-4697: Leaf order:
-4697: w 4 0 0
-4697: b 7 0 0
-4697: apply 20 2 3 0,2
-4697: fixed_pt 3 0 3 2,2
-4697: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4698: Facts:
-4698: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4698: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4698: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-4698: Goal:
-4698: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4698: Order:
-4698: kbo
-4698: Leaf order:
-4698: w 4 0 0
-4698: b 7 0 0
-4698: apply 20 2 3 0,2
-4698: fixed_pt 3 0 3 2,2
-4698: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4699: Facts:
-4699: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4699: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4699: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-4699: Goal:
-4699: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4699: Order:
-4699: lpo
-4699: Leaf order:
-4699: w 4 0 0
-4699: b 7 0 0
-4699: apply 20 2 3 0,2
-4699: fixed_pt 3 0 3 2,2
-4699: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL003-17.p
-NO CLASH, using fixed ground order
-4971: Facts:
-4971: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4971: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4971: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-4971: Goal:
-4971: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4971: Order:
-4971: nrkbo
-4971: Leaf order:
-4971: w 4 0 0
-4971: b 7 0 0
-4971: apply 20 2 3 0,2
-4971: fixed_pt 3 0 3 2,2
-4971: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4972: Facts:
-4972: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4972: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4972: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-4972: Goal:
-4972: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4972: Order:
-4972: kbo
-4972: Leaf order:
-4972: w 4 0 0
-4972: b 7 0 0
-4972: apply 20 2 3 0,2
-4972: fixed_pt 3 0 3 2,2
-4972: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-4973: Facts:
-4973: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-4973: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-4973: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-4973: Goal:
-4973: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-4973: Order:
-4973: lpo
-4973: Leaf order:
-4973: w 4 0 0
-4973: b 7 0 0
-4973: apply 20 2 3 0,2
-4973: fixed_pt 3 0 3 2,2
-4973: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL003-18.p
-NO CLASH, using fixed ground order
-7458: Facts:
-7458: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-7458: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-7458: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-7458: Goal:
-7458: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-7458: Order:
-7458: nrkbo
-7458: Leaf order:
-7458: w 4 0 0
-7458: b 7 0 0
-7458: apply 20 2 3 0,2
-7458: fixed_pt 3 0 3 2,2
-7458: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-7459: Facts:
-7459: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-7459: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-7459: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-7459: Goal:
-7459: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-7459: Order:
-7459: kbo
-7459: Leaf order:
-7459: w 4 0 0
-7459: b 7 0 0
-7459: apply 20 2 3 0,2
-7459: fixed_pt 3 0 3 2,2
-7459: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-7460: Facts:
-7460: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-7460: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-7460: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-7460: Goal:
-7460: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-7460: Order:
-7460: lpo
-7460: Leaf order:
-7460: w 4 0 0
-7460: b 7 0 0
-7460: apply 20 2 3 0,2
-7460: fixed_pt 3 0 3 2,2
-7460: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL003-19.p
-CLASH, statistics insufficient
-9903: Facts:
-9903: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-9903: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-9903: Goal:
-9903: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-9903: Order:
-9903: nrkbo
-9903: Leaf order:
-9903: q1 1 0 0
-9903: o 1 0 0
-9903: apply 10 2 1 0,3
-9903: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-9904: Facts:
-9904: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-9904: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-9904: Goal:
-9904: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-9904: Order:
-9904: kbo
-9904: Leaf order:
-9904: q1 1 0 0
-9904: o 1 0 0
-9904: apply 10 2 1 0,3
-9904: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-9905: Facts:
-9905: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-9905: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-9905: Goal:
-9905: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-9905: Order:
-9905: lpo
-9905: Leaf order:
-9905: q1 1 0 0
-9905: o 1 0 0
-9905: apply 10 2 1 0,3
-9905: combinator 1 0 1 1,3
-% SZS status Timeout for COL011-1.p
-CLASH, statistics insufficient
-9926: Facts:
-9926: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9926: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9926: Id : 4, {_}:
- apply (apply t ?9) ?10 =>= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-9926: Goal:
-9926: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9926: Order:
-9926: nrkbo
-9926: Leaf order:
-9926: t 1 0 0
-9926: m 1 0 0
-9926: b 1 0 0
-9926: apply 13 2 3 0,2
-9926: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9927: Facts:
-9927: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9927: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9927: Id : 4, {_}:
- apply (apply t ?9) ?10 =>= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-9927: Goal:
-9927: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9927: Order:
-9927: kbo
-9927: Leaf order:
-9927: t 1 0 0
-9927: m 1 0 0
-9927: b 1 0 0
-9927: apply 13 2 3 0,2
-9927: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9928: Facts:
-9928: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9928: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9928: Id : 4, {_}:
- apply (apply t ?9) ?10 =?= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-9928: Goal:
-9928: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9928: Order:
-9928: lpo
-9928: Leaf order:
-9928: t 1 0 0
-9928: m 1 0 0
-9928: b 1 0 0
-9928: apply 13 2 3 0,2
-9928: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 62
-Found proof, 1.513358s
-% SZS status Unsatisfiable for COL034-1.p
-% SZS output start CNFRefutation for COL034-1.p
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2
-Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2
-Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2
-Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3
-Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2
-Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3
-Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL034-1.p
-9926: solved COL034-1.p in 0.528032 using nrkbo
-9926: status Unsatisfiable for COL034-1.p
-CLASH, statistics insufficient
-9933: Facts:
-9933: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-9933: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-9933: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-9933: Goal:
-9933: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9933: Order:
-9933: nrkbo
-9933: Leaf order:
-9933: c 1 0 0
-9933: b 1 0 0
-9933: s 1 0 0
-9933: apply 19 2 3 0,2
-9933: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9934: Facts:
-9934: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-9934: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-9934: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-9934: Goal:
-9934: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9934: Order:
-9934: kbo
-9934: Leaf order:
-9934: c 1 0 0
-9934: b 1 0 0
-9934: s 1 0 0
-9934: apply 19 2 3 0,2
-9934: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9935: Facts:
-9935: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-9935: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-9935: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-9935: Goal:
-9935: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9935: Order:
-9935: lpo
-9935: Leaf order:
-9935: c 1 0 0
-9935: b 1 0 0
-9935: s 1 0 0
-9935: apply 19 2 3 0,2
-9935: f 3 1 3 0,2,2
-% SZS status Timeout for COL037-1.p
-CLASH, statistics insufficient
-9973: Facts:
-9973: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9973: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9973: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-9973: Goal:
-9973: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9973: Order:
-9973: nrkbo
-9973: Leaf order:
-9973: c 1 0 0
-9973: m 1 0 0
-9973: b 1 0 0
-9973: apply 15 2 3 0,2
-9973: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9974: Facts:
-9974: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9974: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9974: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-9974: Goal:
-9974: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9974: Order:
-9974: kbo
-9974: Leaf order:
-9974: c 1 0 0
-9974: m 1 0 0
-9974: b 1 0 0
-9974: apply 15 2 3 0,2
-9974: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9975: Facts:
-9975: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9975: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-9975: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-9975: Goal:
-9975: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9975: Order:
-9975: lpo
-9975: Leaf order:
-9975: c 1 0 0
-9975: m 1 0 0
-9975: b 1 0 0
-9975: apply 15 2 3 0,2
-9975: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 54
-Found proof, 2.234152s
-% SZS status Unsatisfiable for COL041-1.p
-% SZS output start CNFRefutation for COL041-1.p
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
-Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2
-Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2
-Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3
-Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL041-1.p
-9973: solved COL041-1.p in 1.13607 using nrkbo
-9973: status Unsatisfiable for COL041-1.p
-CLASH, statistics insufficient
-9980: Facts:
-9980: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9980: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-9980: Goal:
-9980: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9980: Order:
-9980: nrkbo
-9980: Leaf order:
-9980: n 1 0 0
-9980: b 1 0 0
-9980: apply 14 2 3 0,2
-9980: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9981: Facts:
-9981: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9981: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-9981: Goal:
-9981: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9981: Order:
-9981: kbo
-9981: Leaf order:
-9981: n 1 0 0
-9981: b 1 0 0
-9981: apply 14 2 3 0,2
-9981: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9982: Facts:
-9982: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9982: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-9982: Goal:
-9982: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-9982: Order:
-9982: lpo
-9982: Leaf order:
-9982: n 1 0 0
-9982: b 1 0 0
-9982: apply 14 2 3 0,2
-9982: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 88
-Found proof, 76.191737s
-% SZS status Unsatisfiable for COL044-1.p
-% SZS output start CNFRefutation for COL044-1.p
-Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13
-Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2
-Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2
-Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2
-Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2
-Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3
-Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3
-Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL044-1.p
-9981: solved COL044-1.p in 12.724795 using kbo
-9981: status Unsatisfiable for COL044-1.p
-CLASH, statistics insufficient
-9998: Facts:
-9998: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9998: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-9998: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-9998: Goal:
-9998: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-9998: Order:
-9998: nrkbo
-9998: Leaf order:
-9998: m 1 0 0
-9998: w 1 0 0
-9998: b 1 0 0
-9998: apply 14 2 3 0,2
-9998: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-9999: Facts:
-9999: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-9999: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-9999: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-9999: Goal:
-9999: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-9999: Order:
-9999: kbo
-9999: Leaf order:
-9999: m 1 0 0
-9999: w 1 0 0
-9999: b 1 0 0
-9999: apply 14 2 3 0,2
-9999: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-10000: Facts:
-10000: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-10000: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-10000: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-10000: Goal:
-10000: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-10000: Order:
-10000: lpo
-10000: Leaf order:
-10000: m 1 0 0
-10000: w 1 0 0
-10000: b 1 0 0
-10000: apply 14 2 3 0,2
-10000: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 54
-Found proof, 12.856628s
-% SZS status Unsatisfiable for COL049-1.p
-% SZS output start CNFRefutation for COL049-1.p
-Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8
-Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2
-Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3
-Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3
-Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2
-Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2
-Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3
-Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
-% SZS output end CNFRefutation for COL049-1.p
-9998: solved COL049-1.p in 6.372397 using nrkbo
-9998: status Unsatisfiable for COL049-1.p
-CLASH, statistics insufficient
-10010: Facts:
-10010: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-10010: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-10010: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-10010: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-10010: Goal:
-10010: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-10010: Order:
-10010: nrkbo
-10010: Leaf order:
-10010: i 1 0 0
-10010: c 1 0 0
-10010: b 1 0 0
-10010: s 1 0 0
-10010: apply 20 2 3 0,2
-10010: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-10011: Facts:
-10011: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-10011: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-10011: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-10011: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-10011: Goal:
-10011: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-10011: Order:
-10011: kbo
-10011: Leaf order:
-10011: i 1 0 0
-10011: c 1 0 0
-10011: b 1 0 0
-10011: s 1 0 0
-10011: apply 20 2 3 0,2
-10011: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-10012: Facts:
-10012: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-10012: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-10012: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-10012: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-10012: Goal:
-10012: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-10012: Order:
-10012: lpo
-10012: Leaf order:
-10012: i 1 0 0
-10012: c 1 0 0
-10012: b 1 0 0
-10012: s 1 0 0
-10012: apply 20 2 3 0,2
-10012: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 84
-Found proof, 12.629405s
-% SZS status Unsatisfiable for COL057-1.p
-% SZS output start CNFRefutation for COL057-1.p
-Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
-Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
-Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3
-Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3
-Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2
-Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3
-Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
-% SZS output end CNFRefutation for COL057-1.p
-10010: solved COL057-1.p in 2.124132 using nrkbo
-10010: status Unsatisfiable for COL057-1.p
-NO CLASH, using fixed ground order
-10025: Facts:
-10025: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-10025: Goal:
-10025: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-10025: Order:
-10025: nrkbo
-10025: Leaf order:
-10025: inverse 5 1 0
-10025: multiply 10 2 4 0,2
-10025: c 2 0 2 2,2,2
-10025: b 2 0 2 1,2,2
-10025: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-10026: Facts:
-10026: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-10026: Goal:
-10026: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-10026: Order:
-10026: kbo
-10026: Leaf order:
-10026: inverse 5 1 0
-10026: multiply 10 2 4 0,2
-10026: c 2 0 2 2,2,2
-10026: b 2 0 2 1,2,2
-10026: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-10027: Facts:
-10027: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-10027: Goal:
-10027: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-10027: Order:
-10027: lpo
-10027: Leaf order:
-10027: inverse 5 1 0
-10027: multiply 10 2 4 0,2
-10027: c 2 0 2 2,2,2
-10027: b 2 0 2 1,2,2
-10027: a 2 0 2 1,2
-Statistics :
-Max weight : 62
-Found proof, 20.319552s
-% SZS status Unsatisfiable for GRP014-1.p
-% SZS output start CNFRefutation for GRP014-1.p
-Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
-Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
-Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
-Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
-Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
-Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
-Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
-Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
-Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
-Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
-Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
-Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
-Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
-Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
-Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
-Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
-Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
-Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
-Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
-Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
-Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
-Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
-Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
-Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
-Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
-Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
-Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
-Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
-Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
-Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
-Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
-Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
-Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
-Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
-Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
-Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
-Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
-Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
-Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
-Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
-Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
-Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
-Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
-Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
-Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
-Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
-Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
-Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
-Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
-Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
-Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
-Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
-Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
-Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
-Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
-Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
-Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
-Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
-Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
-Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
-Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
-Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
-Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
-Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
-Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
-Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
-Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
-Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
-Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
-Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
-Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
-Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
-Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
-Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
-Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
-Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
-Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
-Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
-Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
-Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
-Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
-Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
-Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
-Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
-Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
-Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
-Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
-Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
-Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
-Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
-Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
-Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
-Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
-Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
-Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
-Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
-Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
-Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
-Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
-Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
-Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
-Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
-Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
-Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
-Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
-Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
-Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
-Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
-Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
-Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
-Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
-Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
-Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
-Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
-Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
-Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
-Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
-Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
-Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
-Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
-Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for GRP014-1.p
-10025: solved GRP014-1.p in 10.216638 using nrkbo
-10025: status Unsatisfiable for GRP014-1.p
-CLASH, statistics insufficient
-10036: Facts:
-10036: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10036: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10036: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10036: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10036: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10036: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10036: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10036: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10036: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10036: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10036: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10036: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10036: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10036: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10036: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10036: Id : 17, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-10036: Id : 18, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-10036: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-10036: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-10036: Goal:
-10036: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10036: Order:
-10036: nrkbo
-10036: Leaf order:
-10036: least_upper_bound 19 2 0
-10036: greatest_lower_bound 19 2 0
-10036: inverse 1 1 0
-10036: identity 4 0 0
-10036: multiply 19 2 1 0,3
-10036: negative_part 2 1 1 0,2,3
-10036: positive_part 2 1 1 0,1,3
-10036: a 3 0 3 2
-CLASH, statistics insufficient
-10037: Facts:
-10037: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10037: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10037: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10037: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10037: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10037: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10037: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10037: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10037: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10037: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10037: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10037: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10037: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10037: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10037: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10037: Id : 17, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-10037: Id : 18, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-10037: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-10037: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-10037: Goal:
-10037: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10037: Order:
-10037: kbo
-10037: Leaf order:
-10037: least_upper_bound 19 2 0
-10037: greatest_lower_bound 19 2 0
-10037: inverse 1 1 0
-10037: identity 4 0 0
-10037: multiply 19 2 1 0,3
-10037: negative_part 2 1 1 0,2,3
-10037: positive_part 2 1 1 0,1,3
-10037: a 3 0 3 2
-CLASH, statistics insufficient
-10038: Facts:
-10038: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10038: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10038: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10038: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10038: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10038: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10038: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10038: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10038: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10038: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10038: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10038: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10038: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10038: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10038: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10038: Id : 17, {_}:
- positive_part ?50 =>= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-10038: Id : 18, {_}:
- negative_part ?52 =>= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-10038: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-10038: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =>=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-10038: Goal:
-10038: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10038: Order:
-10038: lpo
-10038: Leaf order:
-10038: least_upper_bound 19 2 0
-10038: greatest_lower_bound 19 2 0
-10038: inverse 1 1 0
-10038: identity 4 0 0
-10038: multiply 19 2 1 0,3
-10038: negative_part 2 1 1 0,2,3
-10038: positive_part 2 1 1 0,1,3
-10038: a 3 0 3 2
-Statistics :
-Max weight : 19
-Found proof, 19.804581s
-% SZS status Unsatisfiable for GRP167-1.p
-% SZS output start CNFRefutation for GRP167-1.p
-Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 134, {_}: multiply ?322 (least_upper_bound ?323 ?324) =<= least_upper_bound (multiply ?322 ?323) (multiply ?322 ?324) [324, 323, 322] by monotony_lub1 ?322 ?323 ?324
-Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 20, {_}: greatest_lower_bound ?58 (least_upper_bound ?59 ?60) =<= least_upper_bound (greatest_lower_bound ?58 ?59) (greatest_lower_bound ?58 ?60) [60, 59, 58] by lat4_4 ?58 ?59 ?60
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 237, {_}: multiply (greatest_lower_bound ?514 ?515) ?516 =<= greatest_lower_bound (multiply ?514 ?516) (multiply ?515 ?516) [516, 515, 514] by monotony_glb2 ?514 ?515 ?516
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =>= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71
-Id : 27, {_}: multiply identity ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Super 25 with 3 at 1,2
-Id : 31, {_}: ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Demod 27 with 2 at 2
-Id : 242, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= greatest_lower_bound identity (multiply ?533 ?532) [533, 532] by Super 237 with 3 at 1,3
-Id : 278, {_}: greatest_lower_bound identity ?584 =>= negative_part ?584 [584] by Super 5 with 18 at 3
-Id : 15662, {_}: multiply (greatest_lower_bound (inverse ?19569) ?19570) ?19569 =>= negative_part (multiply ?19570 ?19569) [19570, 19569] by Demod 242 with 278 at 3
-Id : 15688, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part (multiply identity ?19646) [19646] by Super 15662 with 18 at 1,2
-Id : 15740, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part ?19646 [19646] by Demod 15688 with 2 at 1,3
-Id : 15765, {_}: ?19710 =<= multiply (inverse (negative_part (inverse ?19710))) (negative_part ?19710) [19710] by Super 31 with 15740 at 2,3
-Id : 778, {_}: ?1461 =<= multiply (inverse ?1462) (multiply ?1462 ?1461) [1462, 1461] by Demod 27 with 2 at 2
-Id : 782, {_}: ?1472 =<= multiply (inverse (inverse ?1472)) identity [1472] by Super 778 with 3 at 2,3
-Id : 1371, {_}: multiply (inverse (inverse ?2316)) (least_upper_bound ?2317 identity) =?= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Super 13 with 782 at 2,3
-Id : 1392, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Demod 1371 with 17 at 2,2
-Id : 1393, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1392 with 6 at 3
-Id : 786, {_}: multiply ?1484 ?1485 =<= multiply (inverse (inverse ?1484)) ?1485 [1485, 1484] by Super 778 with 31 at 2,3
-Id : 2137, {_}: ?1472 =<= multiply ?1472 identity [1472] by Demod 782 with 786 at 3
-Id : 2138, {_}: inverse (inverse ?3405) =<= multiply ?3405 identity [3405] by Super 2137 with 786 at 3
-Id : 2189, {_}: inverse (inverse ?3405) =>= ?3405 [3405] by Demod 2138 with 2137 at 3
-Id : 49575, {_}: multiply ?2316 (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1393 with 2189 at 1,2
-Id : 49621, {_}: multiply ?54979 (positive_part ?54980) =<= least_upper_bound ?54979 (multiply ?54979 ?54980) [54980, 54979] by Demod 49575 with 2189 at 1,2,3
-Id : 15768, {_}: multiply (negative_part (inverse ?19715)) ?19715 =>= negative_part ?19715 [19715] by Demod 15688 with 2 at 1,3
-Id : 15773, {_}: multiply (negative_part ?19724) (inverse ?19724) =>= negative_part (inverse ?19724) [19724] by Super 15768 with 2189 at 1,1,2
-Id : 49652, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= least_upper_bound (negative_part ?55064) (negative_part (inverse ?55064)) [55064] by Super 49621 with 15773 at 2,3
-Id : 865, {_}: greatest_lower_bound identity (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Super 20 with 278 at 2,3
-Id : 880, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Demod 865 with 278 at 2
-Id : 881, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (negative_part ?1569) (negative_part ?1570) [1570, 1569] by Demod 880 with 278 at 1,3
-Id : 49776, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= negative_part (least_upper_bound ?55064 (inverse ?55064)) [55064] by Demod 49652 with 881 at 3
-Id : 15757, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19686)) ?19687) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Super 16 with 15740 at 1,3
-Id : 859, {_}: greatest_lower_bound identity (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Super 7 with 278 at 1,3
-Id : 890, {_}: negative_part (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 859 with 278 at 2
-Id : 281, {_}: greatest_lower_bound ?591 (greatest_lower_bound ?592 identity) =>= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Super 7 with 18 at 3
-Id : 289, {_}: greatest_lower_bound ?591 (negative_part ?592) =<= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Demod 281 with 18 at 2,2
-Id : 1628, {_}: greatest_lower_bound ?1558 (negative_part ?1559) =<= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 890 with 289 at 2
-Id : 15802, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Demod 15757 with 1628 at 1,2
-Id : 15803, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19687, 19686] by Demod 15802 with 1628 at 3
-Id : 15650, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= negative_part (multiply ?533 ?532) [533, 532] by Demod 242 with 278 at 3
-Id : 15804, {_}: negative_part (multiply (negative_part ?19687) ?19686) =<= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19686, 19687] by Demod 15803 with 15650 at 2
-Id : 49651, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part (inverse ?55062)) (negative_part ?55062) [55062] by Super 49621 with 15740 at 2,3
-Id : 49774, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part ?55062) (negative_part (inverse ?55062)) [55062] by Demod 49651 with 6 at 3
-Id : 49775, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= negative_part (least_upper_bound ?55062 (inverse ?55062)) [55062] by Demod 49774 with 881 at 3
-Id : 49840, {_}: negative_part (multiply (negative_part (negative_part (inverse ?55170))) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Super 15804 with 49775 at 1,2,3
-Id : 268, {_}: greatest_lower_bound ?569 (positive_part ?569) =>= ?569 [569] by Super 12 with 17 at 2,2
-Id : 139, {_}: multiply (inverse ?340) (least_upper_bound ?340 ?341) =>= least_upper_bound identity (multiply (inverse ?340) ?341) [341, 340] by Super 134 with 3 at 1,3
-Id : 264, {_}: least_upper_bound identity ?559 =>= positive_part ?559 [559] by Super 6 with 17 at 3
-Id : 4901, {_}: multiply (inverse ?7380) (least_upper_bound ?7380 ?7381) =>= positive_part (multiply (inverse ?7380) ?7381) [7381, 7380] by Demod 139 with 264 at 3
-Id : 4921, {_}: multiply (inverse ?7441) (positive_part ?7441) =?= positive_part (multiply (inverse ?7441) identity) [7441] by Super 4901 with 17 at 2,2
-Id : 4985, {_}: multiply (inverse ?7525) (positive_part ?7525) =>= positive_part (inverse ?7525) [7525] by Demod 4921 with 2137 at 1,3
-Id : 267, {_}: least_upper_bound ?566 (least_upper_bound ?567 identity) =>= positive_part (least_upper_bound ?566 ?567) [567, 566] by Super 8 with 17 at 3
-Id : 1187, {_}: least_upper_bound ?2080 (positive_part ?2081) =<= positive_part (least_upper_bound ?2080 ?2081) [2081, 2080] by Demod 267 with 17 at 2,2
-Id : 1199, {_}: least_upper_bound ?2117 (positive_part identity) =>= positive_part (positive_part ?2117) [2117] by Super 1187 with 17 at 1,3
-Id : 263, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2
-Id : 1218, {_}: least_upper_bound ?2117 identity =<= positive_part (positive_part ?2117) [2117] by Demod 1199 with 263 at 2,2
-Id : 1219, {_}: positive_part ?2117 =<= positive_part (positive_part ?2117) [2117] by Demod 1218 with 17 at 2
-Id : 4997, {_}: multiply (inverse (positive_part ?7553)) (positive_part ?7553) =>= positive_part (inverse (positive_part ?7553)) [7553] by Super 4985 with 1219 at 2,2
-Id : 5031, {_}: identity =<= positive_part (inverse (positive_part ?7553)) [7553] by Demod 4997 with 3 at 2
-Id : 5129, {_}: greatest_lower_bound (inverse (positive_part ?7677)) identity =>= inverse (positive_part ?7677) [7677] by Super 268 with 5031 at 2,2
-Id : 5176, {_}: greatest_lower_bound identity (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5129 with 5 at 2
-Id : 5177, {_}: negative_part (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5176 with 278 at 2
-Id : 5325, {_}: greatest_lower_bound (inverse (positive_part ?7851)) (negative_part ?7852) =>= greatest_lower_bound (inverse (positive_part ?7851)) ?7852 [7852, 7851] by Super 1628 with 5177 at 1,3
-Id : 15685, {_}: multiply (greatest_lower_bound (inverse (positive_part ?19637)) ?19638) (positive_part ?19637) =>= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19638, 19637] by Super 15662 with 5325 at 1,2
-Id : 15737, {_}: negative_part (multiply ?19638 (positive_part ?19637)) =<= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19637, 19638] by Demod 15685 with 15650 at 2
-Id : 49928, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Demod 49840 with 15737 at 2
-Id : 1648, {_}: greatest_lower_bound ?2900 (negative_part ?2901) =<= greatest_lower_bound (negative_part ?2900) ?2901 [2901, 2900] by Demod 890 with 289 at 2
-Id : 863, {_}: negative_part (least_upper_bound identity ?1566) =>= identity [1566] by Super 12 with 278 at 2
-Id : 886, {_}: negative_part (positive_part ?1566) =>= identity [1566] by Demod 863 with 264 at 1,2
-Id : 1653, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= greatest_lower_bound identity ?2915 [2915, 2914] by Super 1648 with 886 at 1,3
-Id : 1710, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= negative_part ?2915 [2915, 2914] by Demod 1653 with 278 at 3
-Id : 49929, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =>= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49928 with 1710 at 3
-Id : 49930, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =<= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49929 with 15737 at 2
-Id : 1014, {_}: greatest_lower_bound ?1717 (positive_part ?1717) =>= ?1717 [1717] by Super 12 with 17 at 2,2
-Id : 858, {_}: least_upper_bound identity (negative_part ?1556) =>= identity [1556] by Super 11 with 278 at 2,2
-Id : 891, {_}: positive_part (negative_part ?1556) =>= identity [1556] by Demod 858 with 264 at 2
-Id : 1019, {_}: greatest_lower_bound (negative_part ?1726) identity =>= negative_part ?1726 [1726] by Super 1014 with 891 at 2,2
-Id : 1039, {_}: greatest_lower_bound identity (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1019 with 5 at 2
-Id : 1040, {_}: negative_part (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1039 with 278 at 2
-Id : 49931, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =>= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49930 with 1040 at 3
-Id : 4960, {_}: multiply (inverse ?7441) (positive_part ?7441) =>= positive_part (inverse ?7441) [7441] by Demod 4921 with 2137 at 1,3
-Id : 49932, {_}: negative_part (positive_part (inverse ?55170)) =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49931 with 4960 at 1,2
-Id : 49933, {_}: identity =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49932 with 886 at 2
-Id : 53516, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= identity [55064] by Demod 49776 with 49933 at 3
-Id : 53529, {_}: positive_part (inverse ?58317) =<= multiply (inverse (negative_part ?58317)) identity [58317] by Super 31 with 53516 at 2,3
-Id : 53947, {_}: positive_part (inverse ?58761) =>= inverse (negative_part ?58761) [58761] by Demod 53529 with 2137 at 3
-Id : 53952, {_}: positive_part ?58770 =<= inverse (negative_part (inverse ?58770)) [58770] by Super 53947 with 2189 at 1,2
-Id : 54151, {_}: ?19710 =<= multiply (positive_part ?19710) (negative_part ?19710) [19710] by Demod 15765 with 53952 at 1,3
-Id : 54473, {_}: a =?= a [] by Demod 1 with 54151 at 3
-Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-1.p
-10037: solved GRP167-1.p in 9.872616 using kbo
-10037: status Unsatisfiable for GRP167-1.p
-CLASH, statistics insufficient
-10051: Facts:
-10051: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10051: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10051: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10051: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10051: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10051: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10051: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10051: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10051: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10051: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10051: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10051: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10051: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10051: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10051: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10051: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-10051: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-10051: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-10051: Id : 20, {_}:
- positive_part ?56 =<= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-10051: Id : 21, {_}:
- negative_part ?58 =<= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-10051: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-10051: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =<=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-10051: Goal:
-10051: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10051: Order:
-10051: nrkbo
-10051: Leaf order:
-10051: least_upper_bound 19 2 0
-10051: greatest_lower_bound 19 2 0
-10051: inverse 7 1 0
-10051: identity 6 0 0
-10051: multiply 21 2 1 0,3
-10051: negative_part 2 1 1 0,2,3
-10051: positive_part 2 1 1 0,1,3
-10051: a 3 0 3 2
-CLASH, statistics insufficient
-10052: Facts:
-10052: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10052: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10052: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10052: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10052: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10052: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10052: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10052: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10052: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10052: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10052: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10052: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10052: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10052: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10052: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10052: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-10052: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-10052: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-10052: Id : 20, {_}:
- positive_part ?56 =<= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-10052: Id : 21, {_}:
- negative_part ?58 =<= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-10052: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-10052: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =<=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-10052: Goal:
-10052: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10052: Order:
-10052: kbo
-10052: Leaf order:
-10052: least_upper_bound 19 2 0
-10052: greatest_lower_bound 19 2 0
-10052: inverse 7 1 0
-10052: identity 6 0 0
-10052: multiply 21 2 1 0,3
-10052: negative_part 2 1 1 0,2,3
-10052: positive_part 2 1 1 0,1,3
-10052: a 3 0 3 2
-CLASH, statistics insufficient
-10053: Facts:
-10053: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10053: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10053: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10053: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10053: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10053: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10053: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10053: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10053: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10053: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10053: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10053: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10053: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10053: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10053: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10053: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-10053: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-10053: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-10053: Id : 20, {_}:
- positive_part ?56 =>= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-10053: Id : 21, {_}:
- negative_part ?58 =>= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-10053: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-10053: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =>=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-10053: Goal:
-10053: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-10053: Order:
-10053: lpo
-10053: Leaf order:
-10053: least_upper_bound 19 2 0
-10053: greatest_lower_bound 19 2 0
-10053: inverse 7 1 0
-10053: identity 6 0 0
-10053: multiply 21 2 1 0,3
-10053: negative_part 2 1 1 0,2,3
-10053: positive_part 2 1 1 0,1,3
-10053: a 3 0 3 2
-Statistics :
-Max weight : 15
-Found proof, 6.844655s
-% SZS status Unsatisfiable for GRP167-2.p
-% SZS output start CNFRefutation for GRP167-2.p
-Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54
-Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
-Id : 210, {_}: multiply (least_upper_bound ?453 ?454) ?455 =<= least_upper_bound (multiply ?453 ?455) (multiply ?454 ?455) [455, 454, 453] by monotony_lub2 ?453 ?454 ?455
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
-Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 286, {_}: inverse (multiply ?614 ?615) =<= multiply (inverse ?615) (inverse ?614) [615, 614] by lat4_3 ?614 ?615
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =>= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-Id : 30, {_}: multiply identity ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Super 28 with 3 at 1,2
-Id : 34, {_}: ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Demod 30 with 2 at 2
-Id : 288, {_}: inverse (multiply (inverse ?619) ?620) =>= multiply (inverse ?620) ?619 [620, 619] by Super 286 with 18 at 2,3
-Id : 997, {_}: ?1719 =<= multiply (inverse ?1720) (multiply ?1720 ?1719) [1720, 1719] by Demod 30 with 2 at 2
-Id : 1001, {_}: ?1730 =<= multiply (inverse (inverse ?1730)) identity [1730] by Super 997 with 3 at 2,3
-Id : 1026, {_}: ?1730 =<= multiply ?1730 identity [1730] by Demod 1001 with 18 at 1,3
-Id : 1045, {_}: multiply ?1785 (least_upper_bound ?1786 identity) =?= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Super 13 with 1026 at 2,3
-Id : 1078, {_}: multiply ?1785 (positive_part ?1786) =<= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Demod 1045 with 20 at 2,2
-Id : 5086, {_}: multiply ?7297 (positive_part ?7298) =<= least_upper_bound ?7297 (multiply ?7297 ?7298) [7298, 7297] by Demod 1078 with 6 at 3
-Id : 5090, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound (inverse ?7308) identity [7308] by Super 5086 with 3 at 2,3
-Id : 5133, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound identity (inverse ?7308) [7308] by Demod 5090 with 6 at 3
-Id : 298, {_}: least_upper_bound identity ?640 =>= positive_part ?640 [640] by Super 6 with 20 at 3
-Id : 5134, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= positive_part (inverse ?7308) [7308] by Demod 5133 with 298 at 3
-Id : 5356, {_}: inverse (positive_part (inverse ?7872)) =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Super 288 with 5134 at 1,2
-Id : 1051, {_}: multiply ?1799 (greatest_lower_bound ?1800 identity) =?= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Super 14 with 1026 at 2,3
-Id : 1072, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Demod 1051 with 21 at 2,2
-Id : 4381, {_}: multiply ?6565 (negative_part ?6566) =<= greatest_lower_bound ?6565 (multiply ?6565 ?6566) [6566, 6565] by Demod 1072 with 5 at 3
-Id : 270, {_}: multiply ?567 (inverse ?567) =>= identity [567] by Super 3 with 18 at 1,2
-Id : 4388, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= greatest_lower_bound ?6585 identity [6585] by Super 4381 with 270 at 2,3
-Id : 4428, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 4388 with 21 at 3
-Id : 1073, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound ?1799 (multiply ?1799 ?1800) [1800, 1799] by Demod 1072 with 5 at 3
-Id : 215, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= least_upper_bound identity (multiply ?472 ?471) [472, 471] by Super 210 with 3 at 1,3
-Id : 11818, {_}: multiply (least_upper_bound (inverse ?15728) ?15729) ?15728 =>= positive_part (multiply ?15729 ?15728) [15729, 15728] by Demod 215 with 298 at 3
-Id : 11845, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part (multiply identity ?15810) [15810] by Super 11818 with 20 at 1,2
-Id : 12179, {_}: multiply (positive_part (inverse ?16312)) ?16312 =>= positive_part ?16312 [16312] by Demod 11845 with 2 at 1,3
-Id : 12183, {_}: multiply (positive_part ?16319) (inverse ?16319) =>= positive_part (inverse ?16319) [16319] by Super 12179 with 18 at 1,1,2
-Id : 12264, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= greatest_lower_bound (positive_part ?16391) (positive_part (inverse ?16391)) [16391] by Super 1073 with 12183 at 2,3
-Id : 849, {_}: least_upper_bound identity (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Super 22 with 298 at 2,3
-Id : 877, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Demod 849 with 298 at 2
-Id : 878, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (positive_part ?1555) (positive_part ?1556) [1556, 1555] by Demod 877 with 298 at 1,3
-Id : 12306, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= positive_part (greatest_lower_bound ?16391 (inverse ?16391)) [16391] by Demod 12264 with 878 at 3
-Id : 853, {_}: least_upper_bound identity (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Super 8 with 298 at 1,3
-Id : 874, {_}: positive_part (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 853 with 298 at 2
-Id : 297, {_}: least_upper_bound ?637 (least_upper_bound ?638 identity) =>= positive_part (least_upper_bound ?637 ?638) [638, 637] by Super 8 with 20 at 3
-Id : 307, {_}: least_upper_bound ?637 (positive_part ?638) =<= positive_part (least_upper_bound ?637 ?638) [638, 637] by Demod 297 with 20 at 2,2
-Id : 1518, {_}: least_upper_bound ?1564 (positive_part ?1565) =<= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 874 with 307 at 2
-Id : 309, {_}: least_upper_bound ?657 (negative_part ?657) =>= ?657 [657] by Super 11 with 21 at 2,2
-Id : 4385, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound (inverse ?6576) identity [6576] by Super 4381 with 3 at 2,3
-Id : 4422, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound identity (inverse ?6576) [6576] by Demod 4385 with 5 at 3
-Id : 312, {_}: greatest_lower_bound identity ?665 =>= negative_part ?665 [665] by Super 5 with 21 at 3
-Id : 4454, {_}: multiply (inverse ?6658) (negative_part ?6658) =>= negative_part (inverse ?6658) [6658] by Demod 4422 with 312 at 3
-Id : 1166, {_}: greatest_lower_bound ?1914 (positive_part ?1914) =>= ?1914 [1914] by Super 12 with 20 at 2,2
-Id : 898, {_}: least_upper_bound identity (negative_part ?1605) =>= identity [1605] by Super 11 with 312 at 2,2
-Id : 922, {_}: positive_part (negative_part ?1605) =>= identity [1605] by Demod 898 with 298 at 2
-Id : 1171, {_}: greatest_lower_bound (negative_part ?1923) identity =>= negative_part ?1923 [1923] by Super 1166 with 922 at 2,2
-Id : 1191, {_}: greatest_lower_bound identity (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1171 with 5 at 2
-Id : 1192, {_}: negative_part (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1191 with 312 at 2
-Id : 4460, {_}: multiply (inverse (negative_part ?6669)) (negative_part ?6669) =>= negative_part (inverse (negative_part ?6669)) [6669] by Super 4454 with 1192 at 2,2
-Id : 4502, {_}: identity =<= negative_part (inverse (negative_part ?6669)) [6669] by Demod 4460 with 3 at 2
-Id : 4607, {_}: least_upper_bound (inverse (negative_part ?6821)) identity =>= inverse (negative_part ?6821) [6821] by Super 309 with 4502 at 2,2
-Id : 4660, {_}: least_upper_bound identity (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4607 with 6 at 2
-Id : 4661, {_}: positive_part (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4660 with 298 at 2
-Id : 4799, {_}: least_upper_bound (inverse (negative_part ?6984)) (positive_part ?6985) =>= least_upper_bound (inverse (negative_part ?6984)) ?6985 [6985, 6984] by Super 1518 with 4661 at 1,3
-Id : 11842, {_}: multiply (least_upper_bound (inverse (negative_part ?15801)) ?15802) (negative_part ?15801) =>= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15802, 15801] by Super 11818 with 4799 at 1,2
-Id : 11803, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= positive_part (multiply ?472 ?471) [472, 471] by Demod 215 with 298 at 3
-Id : 11889, {_}: positive_part (multiply ?15802 (negative_part ?15801)) =<= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15801, 15802] by Demod 11842 with 11803 at 2
-Id : 11892, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part ?15810 [15810] by Demod 11845 with 2 at 1,3
-Id : 12165, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part (inverse ?16276)) (positive_part ?16276) [16276] by Super 1073 with 11892 at 2,3
-Id : 12217, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part ?16276) (positive_part (inverse ?16276)) [16276] by Demod 12165 with 5 at 3
-Id : 12218, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= positive_part (greatest_lower_bound ?16276 (inverse ?16276)) [16276] by Demod 12217 with 878 at 3
-Id : 12981, {_}: positive_part (multiply (inverse ?17147) (negative_part ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Super 11889 with 12218 at 1,3
-Id : 4423, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= negative_part (inverse ?6576) [6576] by Demod 4422 with 312 at 3
-Id : 13027, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Demod 12981 with 4423 at 1,2
-Id : 1230, {_}: least_upper_bound ?1974 (positive_part ?1975) =<= positive_part (least_upper_bound ?1974 ?1975) [1975, 1974] by Demod 297 with 20 at 2,2
-Id : 1242, {_}: least_upper_bound ?2011 (positive_part identity) =>= positive_part (positive_part ?2011) [2011] by Super 1230 with 20 at 1,3
-Id : 300, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
-Id : 1261, {_}: least_upper_bound ?2011 identity =<= positive_part (positive_part ?2011) [2011] by Demod 1242 with 300 at 2,2
-Id : 1262, {_}: positive_part ?2011 =<= positive_part (positive_part ?2011) [2011] by Demod 1261 with 20 at 2
-Id : 13028, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13027 with 1262 at 3
-Id : 13029, {_}: identity =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13028 with 922 at 2
-Id : 14199, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= identity [16391] by Demod 12306 with 13029 at 3
-Id : 14209, {_}: negative_part (inverse ?18032) =<= multiply (inverse (positive_part ?18032)) identity [18032] by Super 34 with 14199 at 2,3
-Id : 14275, {_}: negative_part (inverse ?18032) =>= inverse (positive_part ?18032) [18032] by Demod 14209 with 1026 at 3
-Id : 14351, {_}: multiply ?6585 (inverse (positive_part ?6585)) =>= negative_part ?6585 [6585] by Demod 4428 with 14275 at 2,2
-Id : 290, {_}: inverse (multiply ?624 (inverse ?625)) =>= multiply ?625 (inverse ?624) [625, 624] by Super 286 with 18 at 1,3
-Id : 12177, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part (inverse (inverse ?16308)))) [16308] by Super 290 with 11892 at 1,2
-Id : 12203, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part ?16308)) [16308] by Demod 12177 with 18 at 1,1,2,3
-Id : 14356, {_}: inverse (positive_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 14351 with 12203 at 2
-Id : 14357, {_}: negative_part ?7872 =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Demod 5356 with 14356 at 2
-Id : 13168, {_}: multiply (inverse (greatest_lower_bound ?17321 (inverse ?17321))) identity =>= positive_part (inverse (greatest_lower_bound ?17321 (inverse ?17321))) [17321] by Super 5134 with 13029 at 2,2
-Id : 15132, {_}: inverse (greatest_lower_bound ?18904 (inverse ?18904)) =<= positive_part (inverse (greatest_lower_bound ?18904 (inverse ?18904))) [18904] by Demod 13168 with 1026 at 2
-Id : 15140, {_}: inverse (greatest_lower_bound (positive_part (inverse ?18921)) (inverse (positive_part (inverse ?18921)))) =>= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Super 15132 with 14356 at 2,1,1,3
-Id : 899, {_}: greatest_lower_bound identity (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Super 7 with 312 at 1,3
-Id : 921, {_}: negative_part (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 899 with 312 at 2
-Id : 311, {_}: greatest_lower_bound ?662 (greatest_lower_bound ?663 identity) =>= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Super 7 with 21 at 3
-Id : 321, {_}: greatest_lower_bound ?662 (negative_part ?663) =<= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Demod 311 with 21 at 2,2
-Id : 1610, {_}: greatest_lower_bound ?2637 (negative_part ?2638) =<= greatest_lower_bound (negative_part ?2637) ?2638 [2638, 2637] by Demod 921 with 321 at 2
-Id : 903, {_}: negative_part (least_upper_bound identity ?1615) =>= identity [1615] by Super 12 with 312 at 2
-Id : 917, {_}: negative_part (positive_part ?1615) =>= identity [1615] by Demod 903 with 298 at 1,2
-Id : 1615, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= greatest_lower_bound identity ?2652 [2652, 2651] by Super 1610 with 917 at 1,3
-Id : 1662, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= negative_part ?2652 [2652, 2651] by Demod 1615 with 312 at 3
-Id : 4459, {_}: multiply (inverse (positive_part ?6667)) identity =>= negative_part (inverse (positive_part ?6667)) [6667] by Super 4454 with 917 at 2,2
-Id : 4501, {_}: inverse (positive_part ?6667) =<= negative_part (inverse (positive_part ?6667)) [6667] by Demod 4459 with 1026 at 2
-Id : 4523, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= negative_part (inverse (positive_part ?6722)) [6722, 6721] by Super 1662 with 4501 at 2,2
-Id : 4568, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= inverse (positive_part ?6722) [6722, 6721] by Demod 4523 with 4501 at 3
-Id : 15267, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Demod 15140 with 4568 at 1,2
-Id : 4810, {_}: positive_part (inverse (negative_part ?7011)) =>= inverse (negative_part ?7011) [7011] by Demod 4660 with 298 at 2
-Id : 4822, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (negative_part (greatest_lower_bound ?7038 ?7039)) [7039, 7038] by Super 4810 with 321 at 1,1,2
-Id : 4871, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (greatest_lower_bound ?7038 (negative_part ?7039)) [7039, 7038] by Demod 4822 with 321 at 1,3
-Id : 15268, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15267 with 4871 at 3
-Id : 15269, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15268 with 18 at 2
-Id : 15270, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (negative_part ?18921) (positive_part (inverse ?18921))) [18921] by Demod 15269 with 5 at 1,3
-Id : 1594, {_}: greatest_lower_bound ?1607 (negative_part ?1608) =<= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 921 with 321 at 2
-Id : 15271, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 (negative_part (positive_part (inverse ?18921)))) [18921] by Demod 15270 with 1594 at 1,3
-Id : 15272, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 identity) [18921] by Demod 15271 with 917 at 2,1,3
-Id : 15273, {_}: positive_part (inverse ?18921) =>= inverse (negative_part ?18921) [18921] by Demod 15272 with 21 at 1,3
-Id : 15393, {_}: negative_part (inverse ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Super 14357 with 15273 at 1,1,3
-Id : 15435, {_}: inverse (positive_part ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Demod 15393 with 14275 at 2
-Id : 15436, {_}: inverse (positive_part ?19045) =<= inverse (multiply ?19045 (inverse (negative_part ?19045))) [19045] by Demod 15435 with 19 at 3
-Id : 15437, {_}: inverse (positive_part ?19045) =<= multiply (negative_part ?19045) (inverse ?19045) [19045] by Demod 15436 with 290 at 3
-Id : 15800, {_}: inverse ?19405 =<= multiply (inverse (negative_part ?19405)) (inverse (positive_part ?19405)) [19405] by Super 34 with 15437 at 2,3
-Id : 15843, {_}: inverse ?19405 =<= inverse (multiply (positive_part ?19405) (negative_part ?19405)) [19405] by Demod 15800 with 19 at 3
-Id : 20580, {_}: inverse (inverse ?23723) =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Super 18 with 15843 at 1,2
-Id : 20668, {_}: ?23723 =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Demod 20580 with 18 at 2
-Id : 20964, {_}: a =?= a [] by Demod 1 with 20668 at 3
-Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-2.p
-10052: solved GRP167-2.p in 3.352209 using kbo
-10052: status Unsatisfiable for GRP167-2.p
-NO CLASH, using fixed ground order
-10058: Facts:
-10058: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10058: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10058: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10058: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10058: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10058: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10058: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10058: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10058: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10058: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10058: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10058: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10058: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10058: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10058: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10058: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-10058: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-10058: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-10058: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-10058: Goal:
-10058: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-10058: Order:
-10058: nrkbo
-10058: Leaf order:
-10058: least_upper_bound 16 2 0
-10058: inverse 1 1 0
-10058: identity 6 0 0
-10058: greatest_lower_bound 16 2 2 0,2
-10058: multiply 19 2 1 0,2,2
-10058: c 4 0 2 2,2,2
-10058: b 4 0 1 1,2,2
-10058: a 5 0 2 1,2
-NO CLASH, using fixed ground order
-10059: Facts:
-10059: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10059: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10059: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10059: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10059: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10059: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10059: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-NO CLASH, using fixed ground order
-10060: Facts:
-10060: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10060: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10060: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10060: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10060: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10060: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10059: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10059: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10059: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10059: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10059: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10059: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10059: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10059: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10059: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-10059: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-10059: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-10059: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-10059: Goal:
-10059: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-10059: Order:
-10059: kbo
-10059: Leaf order:
-10059: least_upper_bound 16 2 0
-10059: inverse 1 1 0
-10059: identity 6 0 0
-10059: greatest_lower_bound 16 2 2 0,2
-10059: multiply 19 2 1 0,2,2
-10059: c 4 0 2 2,2,2
-10059: b 4 0 1 1,2,2
-10059: a 5 0 2 1,2
-10060: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10060: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10060: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10060: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10060: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10060: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10060: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10060: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10060: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10060: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-10060: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-10060: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-10060: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-10060: Goal:
-10060: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-10060: Order:
-10060: lpo
-10060: Leaf order:
-10060: least_upper_bound 16 2 0
-10060: inverse 1 1 0
-10060: identity 6 0 0
-10060: greatest_lower_bound 16 2 2 0,2
-10060: multiply 19 2 1 0,2,2
-10060: c 4 0 2 2,2,2
-10060: b 4 0 1 1,2,2
-10060: a 5 0 2 1,2
-% SZS status Timeout for GRP178-1.p
-NO CLASH, using fixed ground order
-10102: Facts:
-10102: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10102: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10102: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10102: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10102: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10102: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10102: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10102: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10102: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10102: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10102: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10102: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10102: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10102: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10102: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10102: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-10102: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-10102: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-10102: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-10102: Goal:
-10102: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-10102: Order:
-10102: nrkbo
-10102: Leaf order:
-10102: least_upper_bound 13 2 0
-10102: inverse 1 1 0
-10102: identity 9 0 0
-10102: greatest_lower_bound 19 2 2 0,2
-10102: multiply 19 2 1 0,2,2
-10102: c 3 0 2 2,2,2
-10102: b 3 0 1 1,2,2
-10102: a 4 0 2 1,2
-NO CLASH, using fixed ground order
-10103: Facts:
-10103: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10103: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10103: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10103: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10103: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10103: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10103: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10103: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10103: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10103: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10103: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10103: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10103: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10103: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10103: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10103: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-10103: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-10103: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-10103: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-10103: Goal:
-10103: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-10103: Order:
-10103: kbo
-10103: Leaf order:
-10103: least_upper_bound 13 2 0
-10103: inverse 1 1 0
-10103: identity 9 0 0
-10103: greatest_lower_bound 19 2 2 0,2
-10103: multiply 19 2 1 0,2,2
-10103: c 3 0 2 2,2,2
-10103: b 3 0 1 1,2,2
-10103: a 4 0 2 1,2
-NO CLASH, using fixed ground order
-10104: Facts:
-10104: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10104: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10104: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10104: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10104: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10104: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10104: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10104: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10104: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10104: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10104: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10104: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10104: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10104: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10104: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10104: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-10104: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-10104: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-10104: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-10104: Goal:
-10104: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-10104: Order:
-10104: lpo
-10104: Leaf order:
-10104: least_upper_bound 13 2 0
-10104: inverse 1 1 0
-10104: identity 9 0 0
-10104: greatest_lower_bound 19 2 2 0,2
-10104: multiply 19 2 1 0,2,2
-10104: c 3 0 2 2,2,2
-10104: b 3 0 1 1,2,2
-10104: a 4 0 2 1,2
-% SZS status Timeout for GRP178-2.p
-CLASH, statistics insufficient
-10125: Facts:
-10125: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10125: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10125: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10125: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10125: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10125: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10125: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10125: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10125: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10125: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10125: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10125: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10125: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10125: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10125: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10125: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-10125: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-10125: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =<=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-10125: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =<=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-10125: Goal:
-10125: Id : 1, {_}: a =>= b [] by prove_p12x
-10125: Order:
-10125: nrkbo
-10125: Leaf order:
-10125: c 4 0 0
-10125: least_upper_bound 17 2 0
-10125: greatest_lower_bound 17 2 0
-10125: inverse 7 1 0
-10125: multiply 18 2 0
-10125: identity 2 0 0
-10125: b 3 0 1 3
-10125: a 3 0 1 2
-CLASH, statistics insufficient
-10126: Facts:
-10126: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10126: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10126: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10126: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10126: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10126: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10126: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10126: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10126: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10126: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10126: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10126: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10126: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10126: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10126: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10126: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-10126: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-10126: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =<=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-10126: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =<=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-10126: Goal:
-10126: Id : 1, {_}: a =>= b [] by prove_p12x
-10126: Order:
-10126: kbo
-10126: Leaf order:
-10126: c 4 0 0
-10126: least_upper_bound 17 2 0
-10126: greatest_lower_bound 17 2 0
-10126: inverse 7 1 0
-10126: multiply 18 2 0
-10126: identity 2 0 0
-10126: b 3 0 1 3
-10126: a 3 0 1 2
-CLASH, statistics insufficient
-10127: Facts:
-10127: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10127: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10127: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10127: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10127: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10127: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10127: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10127: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10127: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10127: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10127: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10127: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10127: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10127: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10127: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10127: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-10127: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-10127: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =>=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-10127: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =>=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-10127: Goal:
-10127: Id : 1, {_}: a =>= b [] by prove_p12x
-10127: Order:
-10127: lpo
-10127: Leaf order:
-10127: c 4 0 0
-10127: least_upper_bound 17 2 0
-10127: greatest_lower_bound 17 2 0
-10127: inverse 7 1 0
-10127: multiply 18 2 0
-10127: identity 2 0 0
-10127: b 3 0 1 3
-10127: a 3 0 1 2
-% SZS status Timeout for GRP181-3.p
-NO CLASH, using fixed ground order
-10150: Facts:
-10150: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10150: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10150: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10150: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10150: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10150: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10150: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10150: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10150: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10150: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10150: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10150: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10150: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10150: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10150: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10150: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-10150: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-10150: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-10150: Goal:
-10150: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-10150: Order:
-10150: nrkbo
-10150: Leaf order:
-10150: multiply 22 2 2 0,2
-10150: inverse 9 1 2 0,2,2
-10150: greatest_lower_bound 15 2 2 0,1,2,2
-10150: least_upper_bound 15 2 2 0,1,2
-10150: identity 8 0 4 2,1,2
-10150: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-10151: Facts:
-10151: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10151: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10151: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10151: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10151: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10151: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10151: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10151: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10151: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10151: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10151: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10151: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10151: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10151: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10151: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10151: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-10151: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-10151: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-10151: Goal:
-10151: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-10151: Order:
-10151: kbo
-10151: Leaf order:
-10151: multiply 22 2 2 0,2
-10151: inverse 9 1 2 0,2,2
-10151: greatest_lower_bound 15 2 2 0,1,2,2
-10151: least_upper_bound 15 2 2 0,1,2
-10151: identity 8 0 4 2,1,2
-10151: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-10152: Facts:
-10152: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10152: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10152: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10152: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10152: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10152: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10152: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10152: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10152: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10152: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10152: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10152: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10152: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10152: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10152: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10152: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-10152: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-10152: Id : 19, {_}:
- inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-10152: Goal:
-10152: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-10152: Order:
-10152: lpo
-10152: Leaf order:
-10152: multiply 22 2 2 0,2
-10152: inverse 9 1 2 0,2,2
-10152: greatest_lower_bound 15 2 2 0,1,2,2
-10152: least_upper_bound 15 2 2 0,1,2
-10152: identity 8 0 4 2,1,2
-10152: a 4 0 4 1,1,2
-% SZS status Timeout for GRP184-2.p
-NO CLASH, using fixed ground order
-10174: Facts:
-10174: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10174: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10174: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10174: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10174: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10174: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10174: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10174: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10174: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10174: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10174: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10174: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10174: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10174: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10174: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10174: Goal:
-10174: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10174: Order:
-10174: nrkbo
-10174: Leaf order:
-10174: greatest_lower_bound 13 2 0
-10174: inverse 1 1 0
-10174: least_upper_bound 19 2 6 0,2
-10174: identity 7 0 5 2,1,2
-10174: multiply 21 2 3 0,1,1,2
-10174: b 3 0 3 2,1,1,2
-10174: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-10175: Facts:
-10175: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10175: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10175: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10175: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10175: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10175: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10175: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10175: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10175: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10175: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10175: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10175: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10175: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10175: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10175: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10175: Goal:
-10175: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10175: Order:
-10175: kbo
-10175: Leaf order:
-10175: greatest_lower_bound 13 2 0
-10175: inverse 1 1 0
-10175: least_upper_bound 19 2 6 0,2
-10175: identity 7 0 5 2,1,2
-10175: multiply 21 2 3 0,1,1,2
-10175: b 3 0 3 2,1,1,2
-10175: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-10176: Facts:
-10176: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10176: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10176: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10176: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10176: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10176: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10176: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10176: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10176: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10176: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10176: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10176: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10176: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10176: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10176: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10176: Goal:
-10176: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10176: Order:
-10176: lpo
-10176: Leaf order:
-10176: greatest_lower_bound 13 2 0
-10176: inverse 1 1 0
-10176: least_upper_bound 19 2 6 0,2
-10176: identity 7 0 5 2,1,2
-10176: multiply 21 2 3 0,1,1,2
-10176: b 3 0 3 2,1,1,2
-10176: a 3 0 3 1,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 4.014671s
-% SZS status Unsatisfiable for GRP185-1.p
-% SZS output start CNFRefutation for GRP185-1.p
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 67, {_}: least_upper_bound ?151 (least_upper_bound ?152 ?153) =<= least_upper_bound (least_upper_bound ?151 ?152) ?153 [153, 152, 151] by associativity_of_lub ?151 ?152 ?153
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 68, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =<= least_upper_bound (least_upper_bound ?156 ?155) ?157 [157, 156, 155] by Super 67 with 6 at 1,3
-Id : 74, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =?= least_upper_bound ?156 (least_upper_bound ?155 ?157) [157, 156, 155] by Demod 68 with 8 at 3
-Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
-Id : 562, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
-Id : 564, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 562 with 3 at 2,3
-Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
-Id : 570, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 562 with 27 at 2,3
-Id : 855, {_}: ?599 =<= multiply ?599 identity [599] by Demod 564 with 570 at 3
-Id : 65, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
-Id : 85, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
-Id : 5149, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) === least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5148 with 74 at 2,2
-Id : 5148, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5147 with 9 at 2,2,2,2
-Id : 5147, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5146 with 2 at 1,2,2,2
-Id : 5146, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5145 with 85 at 2
-Id : 5145, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5144 with 74 at 3
-Id : 5144, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5143 with 65 at 2,2,2,2
-Id : 5143, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5142 with 855 at 1,2,2,2
-Id : 5142, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5141 with 2 at 1,2,2
-Id : 5141, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5140 with 855 at 1,2,2,3
-Id : 5140, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5139 with 2 at 1,2,3
-Id : 5139, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5138 with 8 at 2,2
-Id : 5138, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5137 with 8 at 2,3
-Id : 5137, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5136 with 2 at 1,3
-Id : 5136, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5135 with 74 at 2,2
-Id : 5135, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5134 with 74 at 3
-Id : 5134, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5133 with 15 at 2,2,2,2
-Id : 5133, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5132 with 15 at 1,2,2,2
-Id : 5132, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5131 with 15 at 2,3
-Id : 5131, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 5130 with 15 at 1,3
-Id : 5130, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 237 with 74 at 2
-Id : 237, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 236 with 6 at 1,2,2,2,2
-Id : 236, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 235 with 6 at 1,1,2,2,2
-Id : 235, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 234 with 6 at 1,2,3
-Id : 234, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b) [] by Demod 233 with 6 at 1,1,3
-Id : 233, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 232 with 6 at 2,2,2
-Id : 232, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 231 with 6 at 3
-Id : 231, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 230 with 13 at 2,2,2
-Id : 230, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 229 with 13 at 3
-Id : 229, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2
-Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
-% SZS output end CNFRefutation for GRP185-1.p
-10176: solved GRP185-1.p in 1.916119 using lpo
-10176: status Unsatisfiable for GRP185-1.p
-NO CLASH, using fixed ground order
-10187: Facts:
-10187: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10187: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10187: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10187: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10187: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10187: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10187: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10187: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10187: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10187: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10187: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10187: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10187: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10187: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10187: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10187: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-10187: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-10187: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-10187: Goal:
-10187: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10187: Order:
-10187: nrkbo
-10187: Leaf order:
-10187: greatest_lower_bound 13 2 0
-10187: inverse 7 1 0
-10187: least_upper_bound 19 2 6 0,2
-10187: identity 9 0 5 2,1,2
-10187: multiply 23 2 3 0,1,1,2
-10187: b 3 0 3 2,1,1,2
-10187: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-10188: Facts:
-10188: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10188: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10188: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10188: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10188: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10188: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10188: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10188: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10188: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10188: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10188: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10188: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10188: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10188: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10188: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10188: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-10188: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-10188: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-10188: Goal:
-10188: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10188: Order:
-10188: kbo
-10188: Leaf order:
-10188: greatest_lower_bound 13 2 0
-10188: inverse 7 1 0
-10188: least_upper_bound 19 2 6 0,2
-10188: identity 9 0 5 2,1,2
-10188: multiply 23 2 3 0,1,1,2
-10188: b 3 0 3 2,1,1,2
-10188: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-10189: Facts:
-10189: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10189: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-10189: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-10189: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-10189: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-10189: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-10189: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-10189: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-10189: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-10189: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-10189: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-10189: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-10189: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-10189: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-10189: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-10189: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-10189: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-10189: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-10189: Goal:
-10189: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-10189: Order:
-10189: lpo
-10189: Leaf order:
-10189: greatest_lower_bound 13 2 0
-10189: inverse 7 1 0
-10189: least_upper_bound 19 2 6 0,2
-10189: identity 9 0 5 2,1,2
-10189: multiply 23 2 3 0,1,1,2
-10189: b 3 0 3 2,1,1,2
-10189: a 3 0 3 1,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 5.587205s
-% SZS status Unsatisfiable for GRP185-2.p
-% SZS output start CNFRefutation for GRP185-2.p
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-Id : 506, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 782, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3
-Id : 1203, {_}: least_upper_bound ?943 (least_upper_bound ?944 ?943) =>= least_upper_bound ?943 ?944 [944, 943] by Super 782 with 6 at 2,2
-Id : 1211, {_}: least_upper_bound ?966 (least_upper_bound ?967 (least_upper_bound ?968 ?966)) =>= least_upper_bound ?966 (least_upper_bound ?967 ?968) [968, 967, 966] by Super 1203 with 8 at 2,2
-Id : 507, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 506 with 17 at 2,3
-Id : 571, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 507 with 2 at 1,2
-Id : 573, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 571 with 18 at 1,3
-Id : 581, {_}: ?572 =<= multiply ?572 identity [572] by Demod 573 with 18 at 2
-Id : 88, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3
-Id : 3310, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) === least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3309 with 88 at 2
-Id : 3309, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3308 with 2 at 1,2,2,2,2
-Id : 3308, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3307 with 581 at 1,2,2,2
-Id : 3307, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3306 with 2 at 1,2,2
-Id : 3306, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3305 with 8 at 2,2
-Id : 3305, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3304 with 8 at 2,2
-Id : 3304, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b)) (multiply a b)) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3303 with 6 at 2,2
-Id : 3303, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3302 with 2 at 1,2,2,3
-Id : 3302, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3301 with 581 at 1,2,3
-Id : 3301, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3300 with 2 at 1,3
-Id : 3300, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3299 with 1211 at 2,2
-Id : 3299, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3298 with 8 at 3
-Id : 3298, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3297 with 15 at 2,2,2,2
-Id : 3297, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3296 with 15 at 1,2,2,2
-Id : 3296, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3295 with 15 at 2,3
-Id : 3295, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 3294 with 15 at 1,3
-Id : 3294, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3293 with 13 at 2,2,2
-Id : 3293, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3292 with 13 at 3
-Id : 3292, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 67 with 8 at 2
-Id : 67, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 66 with 6 at 2,3
-Id : 66, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound identity a) (least_upper_bound b identity) [] by Demod 65 with 6 at 1,3
-Id : 65, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 64 with 6 at 2,2,2
-Id : 64, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound b identity)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 63 with 6 at 1,2,2
-Id : 63, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
-% SZS output end CNFRefutation for GRP185-2.p
-10189: solved GRP185-2.p in 0.988061 using lpo
-10189: status Unsatisfiable for GRP185-2.p
-CLASH, statistics insufficient
-10194: Facts:
-10194: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10194: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10194: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10194: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10194: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10194: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10194: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10194: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10194: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-10194: Goal:
-10194: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-10194: Order:
-10194: nrkbo
-10194: Leaf order:
-10194: left_inverse 1 1 0
-10194: right_inverse 1 1 0
-10194: right_division 2 2 0
-10194: left_division 2 2 0
-10194: identity 4 0 0
-10194: c 2 0 2 2,1,2
-10194: multiply 20 2 6 0,2
-10194: b 4 0 4 2,1,1,2
-10194: a 2 0 2 1,1,1,2
-CLASH, statistics insufficient
-10195: Facts:
-10195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10195: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10195: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10195: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10195: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10195: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10195: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10195: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10195: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =>=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-10195: Goal:
-10195: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-10195: Order:
-10195: kbo
-10195: Leaf order:
-10195: left_inverse 1 1 0
-10195: right_inverse 1 1 0
-10195: right_division 2 2 0
-10195: left_division 2 2 0
-10195: identity 4 0 0
-10195: c 2 0 2 2,1,2
-10195: multiply 20 2 6 0,2
-10195: b 4 0 4 2,1,1,2
-10195: a 2 0 2 1,1,1,2
-CLASH, statistics insufficient
-10196: Facts:
-10196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10196: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10196: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10196: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10196: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10196: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10196: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10196: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10196: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =>=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-10196: Goal:
-10196: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-10196: Order:
-10196: lpo
-10196: Leaf order:
-10196: left_inverse 1 1 0
-10196: right_inverse 1 1 0
-10196: right_division 2 2 0
-10196: left_division 2 2 0
-10196: identity 4 0 0
-10196: c 2 0 2 2,1,2
-10196: multiply 20 2 6 0,2
-10196: b 4 0 4 2,1,1,2
-10196: a 2 0 2 1,1,1,2
-% SZS status Timeout for GRP200-1.p
-CLASH, statistics insufficient
-10959: Facts:
-10959: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10959: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10959: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10959: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10959: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10959: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10959: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10959: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10959: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =?=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-10959: Goal:
-10959: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-10959: Order:
-10959: nrkbo
-10959: Leaf order:
-10959: left_inverse 1 1 0
-10959: right_inverse 1 1 0
-10959: right_division 2 2 0
-10959: left_division 2 2 0
-10959: identity 4 0 0
-10959: c 2 0 2 2,2
-10959: multiply 20 2 6 0,2
-10959: b 2 0 2 2,1,1,2
-10959: a 4 0 4 1,1,1,2
-CLASH, statistics insufficient
-10960: Facts:
-10960: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10960: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10960: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10960: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10960: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10960: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10960: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10960: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10960: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =>=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-10960: Goal:
-10960: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-10960: Order:
-10960: kbo
-10960: Leaf order:
-10960: left_inverse 1 1 0
-10960: right_inverse 1 1 0
-10960: right_division 2 2 0
-10960: left_division 2 2 0
-10960: identity 4 0 0
-10960: c 2 0 2 2,2
-10960: multiply 20 2 6 0,2
-10960: b 2 0 2 2,1,1,2
-10960: a 4 0 4 1,1,1,2
-CLASH, statistics insufficient
-10961: Facts:
-10961: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10961: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10961: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10961: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10961: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10961: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10961: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10961: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10961: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =>=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-10961: Goal:
-10961: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-10961: Order:
-10961: lpo
-10961: Leaf order:
-10961: left_inverse 1 1 0
-10961: right_inverse 1 1 0
-10961: right_division 2 2 0
-10961: left_division 2 2 0
-10961: identity 4 0 0
-10961: c 2 0 2 2,2
-10961: multiply 20 2 6 0,2
-10961: b 2 0 2 2,1,1,2
-10961: a 4 0 4 1,1,1,2
-Statistics :
-Max weight : 15
-Found proof, 24.390962s
-% SZS status Unsatisfiable for GRP201-1.p
-% SZS output start CNFRefutation for GRP201-1.p
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121
-Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2
-Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3
-Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2
-Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2
-Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2
-Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2
-Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2
-Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2
-Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2
-Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3
-Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2
-Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3
-Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2
-Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3
-Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2
-Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2
-Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2
-Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2
-Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3
-Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2
-Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2
-Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2
-Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2
-Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2
-Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2
-Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2
-Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3
-Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2
-Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2
-Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2
-Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3
-Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3
-Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3
-Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2
-Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2
-Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3
-Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2
-Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2
-Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2
-Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2
-Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3
-Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3
-Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2
-Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2
-Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2
-Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3
-Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2
-Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3
-Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3
-Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3
-Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2
-Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3
-Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2
-Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2
-Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3
-% SZS output end CNFRefutation for GRP201-1.p
-10960: solved GRP201-1.p in 12.208762 using kbo
-10960: status Unsatisfiable for GRP201-1.p
-CLASH, statistics insufficient
-10977: Facts:
-10977: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10977: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10977: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10977: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10977: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10977: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10977: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10977: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10977: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-10977: Goal:
-10977: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-10977: Order:
-10977: nrkbo
-10977: Leaf order:
-10977: left_inverse 1 1 0
-10977: right_inverse 1 1 0
-10977: right_division 2 2 0
-10977: left_division 2 2 0
-10977: identity 4 0 0
-10977: multiply 20 2 6 0,2
-10977: c 2 0 2 2,2,1,2
-10977: b 2 0 2 1,2,1,2
-10977: a 4 0 4 1,1,2
-CLASH, statistics insufficient
-10978: Facts:
-10978: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10978: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10978: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10978: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10978: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10978: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10978: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10978: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10978: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-10978: Goal:
-10978: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-10978: Order:
-10978: kbo
-10978: Leaf order:
-10978: left_inverse 1 1 0
-10978: right_inverse 1 1 0
-10978: right_division 2 2 0
-10978: left_division 2 2 0
-10978: identity 4 0 0
-10978: multiply 20 2 6 0,2
-10978: c 2 0 2 2,2,1,2
-10978: b 2 0 2 1,2,1,2
-10978: a 4 0 4 1,1,2
-CLASH, statistics insufficient
-10979: Facts:
-10979: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-10979: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-10979: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-10979: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-10979: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-10979: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-10979: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-10979: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-10979: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-10979: Goal:
-10979: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-10979: Order:
-10979: lpo
-10979: Leaf order:
-10979: left_inverse 1 1 0
-10979: right_inverse 1 1 0
-10979: right_division 2 2 0
-10979: left_division 2 2 0
-10979: identity 4 0 0
-10979: multiply 20 2 6 0,2
-10979: c 2 0 2 2,2,1,2
-10979: b 2 0 2 1,2,1,2
-10979: a 4 0 4 1,1,2
-Statistics :
-Max weight : 20
-Found proof, 29.848585s
-% SZS status Unsatisfiable for GRP202-1.p
-% SZS output start CNFRefutation for GRP202-1.p
-Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
-Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
-Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
-Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2
-Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
-Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
-Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
-Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
-Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
-Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2
-Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2
-Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2
-Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2
-Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2
-Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3
-Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
-Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
-Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2
-Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2
-Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2
-Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2
-Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2
-Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3
-Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2
-Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3
-Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2
-Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
-Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2
-Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
-Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3
-Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3
-Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2
-Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2
-Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3
-Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2
-Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2
-Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3
-Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3
-Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3
-Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3
-Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3
-Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2
-Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2
-Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2
-Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3
-Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3
-Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2
-Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2
-Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3
-Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2
-Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3
-Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2
-Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2
-Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3
-Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2
-Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3
-Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2
-Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3
-Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2
-Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3
-Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3
-Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2
-Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2
-Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3
-Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2
-Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3
-Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2
-Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3
-Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3
-Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3
-Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2
-Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3
-Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3
-Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2
-Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3
-Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2
-Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2
-Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3
-Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3
-Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
-Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
-Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3
-Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2
-Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2
-Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2
-Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2
-Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2
-Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3
-Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2
-Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3
-Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2
-Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3
-Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2
-Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3
-Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3
-Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2
-Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2
-Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3
-Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2
-Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
-Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2
-Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3
-Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2
-Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3
-Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2
-Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3
-Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2
-Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2
-Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3
-Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2
-Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3
-Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2
-Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3
-Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2
-Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2
-Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3
-Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3
-Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2
-Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2
-Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2
-Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3
-Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2
-Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2
-Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3
-Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2
-Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3
-Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3
-Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2
-Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2
-Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2
-Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3
-Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2
-Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3
-Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3
-Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3
-Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3
-Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2
-Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
-% SZS output end CNFRefutation for GRP202-1.p
-10978: solved GRP202-1.p in 14.864928 using kbo
-10978: status Unsatisfiable for GRP202-1.p
-NO CLASH, using fixed ground order
-10984: Facts:
-10984: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-10984: Goal:
-10984: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-10984: Order:
-10984: nrkbo
-10984: Leaf order:
-10984: a2 2 0 2 2,2
-10984: multiply 8 2 2 0,2
-10984: inverse 6 1 1 0,1,1,2
-10984: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-10985: Facts:
-10985: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-10985: Goal:
-10985: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-10985: Order:
-10985: kbo
-10985: Leaf order:
-10985: a2 2 0 2 2,2
-10985: multiply 8 2 2 0,2
-10985: inverse 6 1 1 0,1,1,2
-10985: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-10986: Facts:
-10986: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-10986: Goal:
-10986: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-10986: Order:
-10986: lpo
-10986: Leaf order:
-10986: a2 2 0 2 2,2
-10986: multiply 8 2 2 0,2
-10986: inverse 6 1 1 0,1,1,2
-10986: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP404-1.p
-NO CLASH, using fixed ground order
-11033: Facts:
-11033: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11033: Goal:
-11033: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11033: Order:
-11033: nrkbo
-11033: Leaf order:
-11033: inverse 5 1 0
-11033: c3 2 0 2 2,2
-11033: multiply 10 2 4 0,2
-11033: b3 2 0 2 2,1,2
-11033: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11034: Facts:
-11034: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11034: Goal:
-11034: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11034: Order:
-11034: kbo
-11034: Leaf order:
-11034: inverse 5 1 0
-11034: c3 2 0 2 2,2
-11034: multiply 10 2 4 0,2
-11034: b3 2 0 2 2,1,2
-11034: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11035: Facts:
-11035: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11035: Goal:
-11035: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11035: Order:
-11035: lpo
-11035: Leaf order:
-11035: inverse 5 1 0
-11035: c3 2 0 2 2,2
-11035: multiply 10 2 4 0,2
-11035: b3 2 0 2 2,1,2
-11035: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP405-1.p
-NO CLASH, using fixed ground order
-11052: Facts:
-11052: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11052: Goal:
-11052: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11052: Order:
-11052: nrkbo
-11052: Leaf order:
-11052: a2 2 0 2 2,2
-11052: multiply 8 2 2 0,2
-11052: inverse 6 1 1 0,1,1,2
-11052: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11053: Facts:
-11053: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11053: Goal:
-11053: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11053: Order:
-11053: kbo
-11053: Leaf order:
-11053: a2 2 0 2 2,2
-11053: multiply 8 2 2 0,2
-11053: inverse 6 1 1 0,1,1,2
-11053: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11054: Facts:
-11054: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11054: Goal:
-11054: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11054: Order:
-11054: lpo
-11054: Leaf order:
-11054: a2 2 0 2 2,2
-11054: multiply 8 2 2 0,2
-11054: inverse 6 1 1 0,1,1,2
-11054: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP410-1.p
-NO CLASH, using fixed ground order
-11087: Facts:
-11087: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11087: Goal:
-11087: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11087: Order:
-11087: nrkbo
-11087: Leaf order:
-11087: inverse 5 1 0
-11087: c3 2 0 2 2,2
-11087: multiply 10 2 4 0,2
-11087: b3 2 0 2 2,1,2
-11087: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11088: Facts:
-11088: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11088: Goal:
-11088: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11088: Order:
-11088: kbo
-11088: Leaf order:
-11088: inverse 5 1 0
-11088: c3 2 0 2 2,2
-11088: multiply 10 2 4 0,2
-11088: b3 2 0 2 2,1,2
-11088: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11089: Facts:
-11089: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11089: Goal:
-11089: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11089: Order:
-11089: lpo
-11089: Leaf order:
-11089: inverse 5 1 0
-11089: c3 2 0 2 2,2
-11089: multiply 10 2 4 0,2
-11089: b3 2 0 2 2,1,2
-11089: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP411-1.p
-NO CLASH, using fixed ground order
-11106: Facts:
-11106: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11106: Goal:
-11106: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11106: Order:
-11106: nrkbo
-11106: Leaf order:
-11106: a2 2 0 2 2,2
-11106: multiply 8 2 2 0,2
-11106: inverse 8 1 1 0,1,1,2
-11106: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11107: Facts:
-11107: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11107: Goal:
-11107: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11107: Order:
-11107: kbo
-11107: Leaf order:
-11107: a2 2 0 2 2,2
-11107: multiply 8 2 2 0,2
-11107: inverse 8 1 1 0,1,1,2
-11107: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11108: Facts:
-11108: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11108: Goal:
-11108: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11108: Order:
-11108: lpo
-11108: Leaf order:
-11108: a2 2 0 2 2,2
-11108: multiply 8 2 2 0,2
-11108: inverse 8 1 1 0,1,1,2
-11108: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP419-1.p
-NO CLASH, using fixed ground order
-11140: Facts:
-11140: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11140: Goal:
-11140: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11140: Order:
-11140: nrkbo
-11140: Leaf order:
-11140: a2 2 0 2 2,2
-11140: multiply 8 2 2 0,2
-11140: inverse 8 1 1 0,1,1,2
-11140: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11141: Facts:
-11141: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11141: Goal:
-11141: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11141: Order:
-11141: kbo
-11141: Leaf order:
-11141: a2 2 0 2 2,2
-11141: multiply 8 2 2 0,2
-11141: inverse 8 1 1 0,1,1,2
-11141: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11142: Facts:
-11142: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11142: Goal:
-11142: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11142: Order:
-11142: lpo
-11142: Leaf order:
-11142: a2 2 0 2 2,2
-11142: multiply 8 2 2 0,2
-11142: inverse 8 1 1 0,1,1,2
-11142: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP422-1.p
-NO CLASH, using fixed ground order
-11162: Facts:
-NO CLASH, using fixed ground order
-11164: Facts:
-11164: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11164: Goal:
-11164: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11164: Order:
-11164: lpo
-11164: Leaf order:
-11164: inverse 7 1 0
-11164: c3 2 0 2 2,2
-11164: multiply 10 2 4 0,2
-11164: b3 2 0 2 2,1,2
-11164: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11163: Facts:
-11163: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11163: Goal:
-11163: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11163: Order:
-11163: kbo
-11163: Leaf order:
-11163: inverse 7 1 0
-11163: c3 2 0 2 2,2
-11163: multiply 10 2 4 0,2
-11163: b3 2 0 2 2,1,2
-11163: a3 2 0 2 1,1,2
-11162: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11162: Goal:
-11162: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11162: Order:
-11162: nrkbo
-11162: Leaf order:
-11162: inverse 7 1 0
-11162: c3 2 0 2 2,2
-11162: multiply 10 2 4 0,2
-11162: b3 2 0 2 2,1,2
-11162: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP423-1.p
-NO CLASH, using fixed ground order
-11197: Facts:
-11197: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11197: Goal:
-11197: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11197: Order:
-11197: kbo
-11197: Leaf order:
-11197: inverse 5 1 0
-11197: c3 2 0 2 2,2
-11197: multiply 10 2 4 0,2
-11197: b3 2 0 2 2,1,2
-11197: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11198: Facts:
-11198: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11198: Goal:
-11198: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11198: Order:
-11198: lpo
-11198: Leaf order:
-11198: inverse 5 1 0
-11198: c3 2 0 2 2,2
-11198: multiply 10 2 4 0,2
-11198: b3 2 0 2 2,1,2
-11198: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11196: Facts:
-11196: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11196: Goal:
-11196: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11196: Order:
-11196: nrkbo
-11196: Leaf order:
-11196: inverse 5 1 0
-11196: c3 2 0 2 2,2
-11196: multiply 10 2 4 0,2
-11196: b3 2 0 2 2,1,2
-11196: a3 2 0 2 1,1,2
-Statistics :
-Max weight : 62
-Found proof, 60.632898s
-% SZS status Unsatisfiable for GRP429-1.p
-% SZS output start CNFRefutation for GRP429-1.p
-Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
-Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
-Id : 1086, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5854) (multiply (inverse (inverse ?5855)) (multiply (inverse ?5855) ?5856)))) ?5857) (inverse (multiply ?5854 ?5857))) =>= ?5856 [5857, 5856, 5855, 5854] by Super 2 with 5 at 2
-Id : 473, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1916) (multiply (inverse (inverse ?1917)) (multiply (inverse ?1917) ?1918)))) ?1919) (inverse (multiply ?1916 ?1919))) =>= ?1918 [1919, 1918, 1917, 1916] by Super 2 with 5 at 2
-Id : 1106, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?5983) (multiply (inverse (inverse ?5984)) (multiply (inverse ?5984) ?5985)))) ?5986) (inverse (multiply ?5983 ?5986))))) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5986, 5985, 5984, 5983, 5982] by Super 1086 with 473 at 1,2,2,1,1,1,1,2
-Id : 2050, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?13160) (multiply (inverse ?13161) (multiply ?13161 ?13162)))) ?13163) (inverse (multiply ?13160 ?13163))) =>= ?13162 [13163, 13162, 13161, 13160] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
-Id : 472, {_}: multiply (inverse ?1911) (multiply ?1911 (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912, 1911] by Super 2 with 5 at 2,2
-Id : 1697, {_}: multiply (inverse ?11063) (multiply ?11063 ?11064) =?= multiply (inverse (inverse ?11065)) (multiply (inverse ?11065) ?11064) [11065, 11064, 11063] by Super 472 with 473 at 2,2,2
-Id : 1084, {_}: multiply (inverse ?5842) (multiply ?5842 ?5843) =?= multiply (inverse (inverse ?5844)) (multiply (inverse ?5844) ?5843) [5844, 5843, 5842] by Super 472 with 473 at 2,2,2
-Id : 1735, {_}: multiply (inverse ?11276) (multiply ?11276 ?11277) =?= multiply (inverse ?11278) (multiply ?11278 ?11277) [11278, 11277, 11276] by Super 1697 with 1084 at 3
-Id : 2837, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18056) (multiply ?18056 (multiply ?18057 ?18058)))) ?18059) (inverse (multiply (inverse ?18057) ?18059))) =>= ?18058 [18059, 18058, 18057, 18056] by Super 2050 with 1735 at 1,1,1,1,2
-Id : 2876, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18341) (multiply ?18341 (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342, 18341] by Super 2837 with 1735 at 2,2,1,1,1,1,2
-Id : 930, {_}: multiply (inverse ?5077) (multiply ?5077 (inverse (multiply (multiply (inverse (multiply (inverse ?5078) ?5079)) ?5080) (inverse (multiply ?5078 ?5080))))) =>= ?5079 [5080, 5079, 5078, 5077] by Super 2 with 5 at 2,2
-Id : 983, {_}: multiply (inverse ?5420) (multiply ?5420 (multiply ?5421 (inverse (multiply (multiply (inverse (multiply (inverse ?5422) ?5423)) ?5424) (inverse (multiply ?5422 ?5424)))))) =>= multiply (inverse (inverse ?5421)) ?5423 [5424, 5423, 5422, 5421, 5420] by Super 930 with 5 at 2,2,2
-Id : 1838, {_}: multiply (inverse ?11737) (multiply ?11737 (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738, 11737] by Super 472 with 1735 at 1,1,1,1,2,2,2
-Id : 2618, {_}: multiply ?16805 (inverse (multiply (multiply (inverse (multiply (inverse ?16806) (multiply ?16806 ?16807))) ?16808) (inverse (multiply (inverse ?16805) ?16808)))) =>= ?16807 [16808, 16807, 16806, 16805] by Super 2 with 1735 at 1,1,1,1,2,2
-Id : 7049, {_}: multiply ?47447 (inverse (multiply (multiply (inverse (multiply (inverse ?47448) (multiply ?47448 ?47449))) (multiply ?47447 ?47450)) (inverse (multiply (inverse ?47451) (multiply ?47451 ?47450))))) =>= ?47449 [47451, 47450, 47449, 47448, 47447] by Super 2618 with 1735 at 1,2,1,2,2
-Id : 7182, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse (multiply (inverse ?48548) (multiply ?48548 (inverse (multiply (multiply (inverse (multiply (inverse ?48549) ?48547)) ?48550) (inverse (multiply ?48549 ?48550))))))))) =>= ?48546 [48550, 48549, 48548, 48547, 48546, 48545] by Super 7049 with 472 at 1,1,2,2
-Id : 7272, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse ?48547))) =>= ?48546 [48547, 48546, 48545] by Demod 7182 with 472 at 1,2,1,2,2
-Id : 7322, {_}: multiply (inverse (multiply (inverse ?48938) (multiply ?48938 ?48939))) ?48939 =?= multiply (inverse (multiply (inverse ?48940) (multiply ?48940 ?48941))) ?48941 [48941, 48940, 48939, 48938] by Super 1838 with 7272 at 2,2
-Id : 9244, {_}: multiply (inverse (inverse (multiply (inverse ?63609) (multiply ?63609 (inverse (multiply (multiply (inverse (multiply (inverse ?63610) ?63611)) ?63612) (inverse (multiply ?63610 ?63612)))))))) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63612, 63611, 63610, 63609] by Super 472 with 7322 at 2,2
-Id : 9553, {_}: multiply (inverse (inverse ?63611)) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63611] by Demod 9244 with 472 at 1,1,1,2
-Id : 9607, {_}: multiply (inverse ?66347) (multiply ?66347 (multiply ?66348 (inverse (multiply (multiply (inverse ?66349) ?66350) (inverse (multiply (inverse ?66349) ?66350)))))) =?= multiply (inverse (inverse ?66348)) (multiply (inverse (multiply (inverse ?66351) (multiply ?66351 ?66352))) ?66352) [66352, 66351, 66350, 66349, 66348, 66347] by Super 983 with 9553 at 1,1,1,1,2,2,2,2
-Id : 13028, {_}: multiply (inverse ?88877) (multiply ?88877 (multiply ?88878 (inverse (multiply (multiply (inverse ?88879) ?88880) (inverse (multiply (inverse ?88879) ?88880)))))) =>= ?88878 [88880, 88879, 88878, 88877] by Demod 9607 with 9553 at 3
-Id : 2125, {_}: inverse (multiply (multiply (inverse ?13666) (multiply ?13666 ?13667)) (inverse (multiply ?13668 (multiply (multiply (inverse ?13668) (multiply (inverse ?13669) (multiply ?13669 ?13670))) ?13667)))) =>= ?13670 [13670, 13669, 13668, 13667, 13666] by Super 2050 with 1735 at 1,1,2
-Id : 7292, {_}: inverse (multiply (multiply (inverse ?48720) (multiply ?48720 (inverse (multiply ?48721 (inverse ?48721))))) (inverse (multiply (inverse ?48722) (multiply ?48722 ?48723)))) =>= ?48723 [48723, 48722, 48721, 48720] by Super 2125 with 7272 at 2,1,2,1,2
-Id : 13145, {_}: multiply (inverse ?89741) (multiply ?89741 (multiply ?89742 (inverse (multiply ?89743 (inverse ?89743))))) =>= ?89742 [89743, 89742, 89741] by Super 13028 with 7292 at 2,2,2,2
-Id : 1878, {_}: multiply ?12021 (inverse (multiply (multiply (inverse ?12022) (multiply ?12022 ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12022, 12021] by Super 2 with 1735 at 1,1,2,2
-Id : 13510, {_}: multiply (inverse (inverse ?91449)) (multiply (inverse ?91450) (multiply ?91450 (inverse (multiply ?91451 (inverse ?91451))))) =>= ?91449 [91451, 91450, 91449] by Super 9553 with 13145 at 1,1,2,2
-Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
-Id : 98, {_}: multiply ?266 (inverse (multiply (multiply (inverse (multiply (inverse ?267) ?268)) ?269) (inverse (multiply ?267 ?269)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?270) (multiply (inverse (inverse ?266)) ?268))) (inverse (multiply (multiply (inverse (multiply (inverse ?271) (multiply (inverse ?270) ?272))) ?273) (inverse (multiply ?271 ?273))))) (inverse ?272)) [273, 272, 271, 270, 269, 268, 267, 266] by Super 2 with 4 at 2,1,1,1,1,2,2
-Id : 13781, {_}: multiply ?92573 (inverse (multiply (multiply (inverse (multiply (inverse ?92574) (multiply (inverse ?92573) (inverse (multiply ?92575 (inverse ?92575)))))) ?92576) (inverse (multiply ?92574 ?92576)))) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92576, 92575, 92574, 92573] by Super 98 with 13510 at 1,1,1,1,3
-Id : 13970, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92575] by Demod 13781 with 2 at 2
-Id : 13971, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply ?92579 (inverse ?92579)) [92579, 92575] by Demod 13970 with 2 at 1,1,3
-Id : 14410, {_}: multiply (inverse (inverse (multiply ?96419 (inverse ?96419)))) (multiply (inverse ?96420) (multiply ?96420 (inverse (multiply ?96421 (inverse ?96421))))) =?= multiply ?96422 (inverse ?96422) [96422, 96421, 96420, 96419] by Super 13510 with 13971 at 1,1,2
-Id : 14473, {_}: multiply ?96419 (inverse ?96419) =?= multiply ?96422 (inverse ?96422) [96422, 96419] by Demod 14410 with 13510 at 2
-Id : 14531, {_}: multiply (multiply (inverse ?96810) (multiply ?96811 (inverse ?96811))) (inverse (multiply ?96812 (inverse ?96812))) =>= inverse ?96810 [96812, 96811, 96810] by Super 7272 with 14473 at 2,1,2
-Id : 15237, {_}: multiply ?101459 (inverse (multiply (multiply (inverse ?101460) (multiply ?101460 (inverse (multiply ?101461 (inverse ?101461))))) (inverse (multiply ?101462 (inverse ?101462))))) =>= inverse (inverse ?101459) [101462, 101461, 101460, 101459] by Super 1878 with 14531 at 2,1,2,1,2,2
-Id : 15353, {_}: multiply ?101459 (inverse (inverse (multiply ?101461 (inverse ?101461)))) =>= inverse (inverse ?101459) [101461, 101459] by Demod 15237 with 7272 at 1,2,2
-Id : 16356, {_}: multiply (inverse (inverse ?111717)) (multiply (inverse (multiply (inverse ?111718) (inverse (inverse ?111718)))) (inverse (inverse (multiply ?111719 (inverse ?111719))))) =>= ?111717 [111719, 111718, 111717] by Super 9553 with 15353 at 2,1,1,2,2
-Id : 18221, {_}: multiply (inverse (inverse ?121427)) (inverse (inverse (inverse (multiply (inverse ?121428) (inverse (inverse ?121428)))))) =>= ?121427 [121428, 121427] by Demod 16356 with 15353 at 2,2
-Id : 16345, {_}: multiply ?111675 (inverse ?111675) =?= inverse (inverse (inverse (multiply ?111676 (inverse ?111676)))) [111676, 111675] by Super 14473 with 15353 at 3
-Id : 18293, {_}: multiply (inverse (inverse ?121732)) (multiply ?121733 (inverse ?121733)) =>= ?121732 [121733, 121732] by Super 18221 with 16345 at 2,2
-Id : 18567, {_}: multiply ?122956 (inverse (multiply ?122957 (inverse ?122957))) =>= inverse (inverse ?122956) [122957, 122956] by Super 7272 with 18293 at 1,2
-Id : 18716, {_}: multiply (inverse ?89741) (multiply ?89741 (inverse (inverse ?89742))) =>= ?89742 [89742, 89741] by Demod 13145 with 18567 at 2,2,2
-Id : 18916, {_}: multiply (inverse (inverse ?124642)) (inverse (inverse (multiply ?124643 (inverse ?124643)))) =>= ?124642 [124643, 124642] by Super 18293 with 18567 at 2,2
-Id : 18985, {_}: inverse (inverse (inverse (inverse ?124642))) =>= ?124642 [124642] by Demod 18916 with 15353 at 2
-Id : 19175, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= inverse (inverse ?124948) [124948, 124947] by Super 18716 with 18985 at 2,2,2
-Id : 19474, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342] by Demod 2876 with 19175 at 1,1,1,1,2
-Id : 19475, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19474 with 19175 at 1,1,1,1,1,1,2
-Id : 19512, {_}: inverse (multiply (multiply (inverse ?18343) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19475 with 18985 at 1,1,1,2
-Id : 19345, {_}: multiply ?126114 (multiply ?126115 (inverse ?126115)) =>= inverse (inverse ?126114) [126115, 126114] by Super 18293 with 18985 at 1,2
-Id : 19935, {_}: inverse (multiply (multiply (inverse ?128594) (multiply ?128595 (inverse ?128595))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128595, 128594] by Super 19512 with 19345 at 1,2,1,2
-Id : 19990, {_}: inverse (multiply (inverse (inverse (inverse ?128594))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128594] by Demod 19935 with 19345 at 1,1,2
-Id : 20507, {_}: inverse (multiply (inverse (inverse (inverse ?130153))) (inverse ?130154)) =>= multiply ?130154 ?130153 [130154, 130153] by Demod 19990 with 18985 at 2,1,2
-Id : 20571, {_}: inverse (multiply ?130433 (inverse ?130434)) =>= multiply ?130434 (inverse ?130433) [130434, 130433] by Super 20507 with 18985 at 1,1,2
-Id : 21794, {_}: multiply (multiply (inverse (inverse ?18345)) ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 19512 with 20571 at 2
-Id : 21760, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 21, 22, 20, 19] by Demod 5 with 20571 at 2,2
-Id : 21761, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 22, 20, 19] by Demod 21760 with 20571 at 3
-Id : 19480, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912] by Demod 472 with 19175 at 2
-Id : 21790, {_}: inverse (inverse (multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)))) =>= ?1913 [1913, 1914, 1912] by Demod 19480 with 20571 at 1,1,2
-Id : 21791, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))) =>= ?1913 [1914, 1913, 1912] by Demod 21790 with 20571 at 1,2
-Id : 21792, {_}: multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)) =>= ?1913 [1913, 1914, 1912] by Demod 21791 with 20571 at 2
-Id : 21810, {_}: multiply ?19 ?21 =<= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 19] by Demod 21761 with 21792 at 2,2
-Id : 21811, {_}: multiply ?19 ?21 =<= multiply (inverse (inverse ?19)) ?21 [21, 19] by Demod 21810 with 21792 at 3
-Id : 21822, {_}: multiply (multiply ?18345 ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 21794 with 21811 at 1,2
-Id : 21949, {_}: multiply (multiply ?139581 (inverse ?139582)) (multiply ?139582 (inverse (inverse ?139583))) =>= multiply ?139581 ?139583 [139583, 139582, 139581] by Super 21822 with 20571 at 2,2
-Id : 19491, {_}: multiply ?12021 (inverse (multiply (inverse (inverse ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12021] by Demod 1878 with 19175 at 1,1,2,2
-Id : 21735, {_}: multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse (inverse (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 19491 with 20571 at 2,2
-Id : 3075, {_}: multiply (inverse ?19377) (multiply ?19377 (multiply ?19378 (inverse (multiply (multiply (inverse (multiply (inverse ?19379) ?19380)) ?19381) (inverse (multiply ?19379 ?19381)))))) =>= multiply (inverse (inverse ?19378)) ?19380 [19381, 19380, 19379, 19378, 19377] by Super 930 with 5 at 2,2,2
-Id : 1191, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse ?5985) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5985, 5982] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
-Id : 3153, {_}: multiply (inverse ?20008) (multiply ?20008 (multiply ?20009 ?20010)) =?= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009, 20008] by Super 3075 with 1191 at 2,2,2,2
-Id : 19484, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009] by Demod 3153 with 19175 at 2
-Id : 19485, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (inverse (inverse ?20010)) [20010, 20009] by Demod 19484 with 19175 at 2,3
-Id : 21818, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply ?20009 (inverse (inverse ?20010)) [20010, 20009] by Demod 19485 with 21811 at 3
-Id : 21880, {_}: multiply ?12021 (inverse (inverse (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21735 with 21818 at 2,2
-Id : 21881, {_}: inverse (inverse (multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21880 with 21818 at 2
-Id : 1840, {_}: multiply (inverse ?11749) (multiply ?11749 (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750, 11749] by Super 472 with 1735 at 1,1,2,2,2
-Id : 19489, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750] by Demod 1840 with 19175 at 2
-Id : 19490, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751] by Demod 19489 with 19175 at 1,1,1,1,2
-Id : 21784, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))))) =>= ?11753 [11751, 11753, 11752] by Demod 19490 with 20571 at 1,1,2
-Id : 21785, {_}: inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21784 with 20571 at 1,2
-Id : 21786, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21785 with 20571 at 2
-Id : 21834, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21786 with 21818 at 2
-Id : 21842, {_}: inverse (multiply ?11751 (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21834 with 20571 at 1,2
-Id : 21843, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751) =>= ?11753 [11751, 11753, 11752] by Demod 21842 with 20571 at 2
-Id : 21882, {_}: inverse (inverse (multiply ?12021 (multiply (inverse ?12021) ?12025))) =>= ?12025 [12025, 12021] by Demod 21881 with 21843 at 2,1,1,2
-Id : 1876, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (multiply (inverse ?12012) (multiply ?12012 ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12012, 12011] by Super 2 with 1735 at 1,1,1,1,2,2
-Id : 19478, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (inverse (inverse ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12011] by Demod 1876 with 19175 at 1,1,1,1,2,2
-Id : 21793, {_}: multiply ?12011 (multiply (multiply (inverse ?12011) ?12014) (inverse (multiply (inverse (inverse (inverse ?12013))) ?12014))) =>= ?12013 [12013, 12014, 12011] by Demod 19478 with 20571 at 2,2
-Id : 19486, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738] by Demod 1838 with 19175 at 2
-Id : 19487, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 19486 with 19175 at 1,1,1,1,1,1,2
-Id : 21787, {_}: inverse (inverse (multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)))) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 19487 with 20571 at 1,1,2
-Id : 21788, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 21787 with 20571 at 1,2
-Id : 21789, {_}: multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 21788 with 20571 at 2
-Id : 21802, {_}: multiply ?12011 (multiply (inverse ?12011) ?12013) =>= ?12013 [12013, 12011] by Demod 21793 with 21789 at 2,2
-Id : 21883, {_}: inverse (inverse ?12025) =>= ?12025 [12025] by Demod 21882 with 21802 at 1,1,2
-Id : 22088, {_}: multiply (multiply ?140028 (inverse ?140029)) (multiply ?140029 ?140030) =>= multiply ?140028 ?140030 [140030, 140029, 140028] by Demod 21949 with 21883 at 2,2,2
-Id : 21892, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= ?124948 [124948, 124947] by Demod 19175 with 21883 at 3
-Id : 22102, {_}: multiply (multiply ?140094 (inverse (inverse ?140095))) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Super 22088 with 21892 at 2,2
-Id : 22180, {_}: multiply (multiply ?140094 ?140095) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Demod 22102 with 21883 at 2,1,2
-Id : 22441, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 22180 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP429-1.p
-11197: solved GRP429-1.p in 30.365897 using kbo
-11197: status Unsatisfiable for GRP429-1.p
-NO CLASH, using fixed ground order
-11215: Facts:
-11215: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11215: Goal:
-11215: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11215: Order:
-11215: nrkbo
-11215: Leaf order:
-11215: inverse 3 1 0
-11215: c3 2 0 2 2,2
-11215: multiply 10 2 4 0,2
-11215: b3 2 0 2 2,1,2
-11215: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11216: Facts:
-11216: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11216: Goal:
-11216: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11216: Order:
-11216: kbo
-11216: Leaf order:
-11216: inverse 3 1 0
-11216: c3 2 0 2 2,2
-11216: multiply 10 2 4 0,2
-11216: b3 2 0 2 2,1,2
-11216: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11217: Facts:
-11217: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11217: Goal:
-11217: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11217: Order:
-11217: lpo
-11217: Leaf order:
-11217: inverse 3 1 0
-11217: c3 2 0 2 2,2
-11217: multiply 10 2 4 0,2
-11217: b3 2 0 2 2,1,2
-11217: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP444-1.p
-NO CLASH, using fixed ground order
-11235: Facts:
-NO CLASH, using fixed ground order
-11236: Facts:
-11236: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11236: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-11236: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-11236: Goal:
-11236: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11236: Order:
-11236: kbo
-11236: Leaf order:
-11236: divide 13 2 0
-11236: a2 2 0 2 2,2
-11236: multiply 3 2 2 0,2
-11236: inverse 2 1 1 0,1,1,2
-11236: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11237: Facts:
-11237: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11237: Id : 3, {_}:
- multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-11237: Id : 4, {_}:
- inverse ?10 =?= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-11237: Goal:
-11237: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11237: Order:
-11237: lpo
-11237: Leaf order:
-11237: divide 13 2 0
-11237: a2 2 0 2 2,2
-11237: multiply 3 2 2 0,2
-11237: inverse 2 1 1 0,1,1,2
-11237: b2 2 0 2 1,1,1,2
-11235: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-11235: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-11235: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-11235: Goal:
-11235: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11235: Order:
-11235: nrkbo
-11235: Leaf order:
-11235: divide 13 2 0
-11235: a2 2 0 2 2,2
-11235: multiply 3 2 2 0,2
-11235: inverse 2 1 1 0,1,1,2
-11235: b2 2 0 2 1,1,1,2
-Statistics :
-Max weight : 38
-Found proof, 1.775197s
-% SZS status Unsatisfiable for GRP452-1.p
-% SZS output start CNFRefutation for GRP452-1.p
-Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
-Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
-Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
-Id : 122, {_}: multiply (divide ?250 ?250) ?251 =>= inverse (inverse ?251) [251, 250] by Super 29 with 4 at 3
-Id : 128, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= inverse (inverse ?269) [269, 268] by Super 122 with 29 at 1,2
-Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
-Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
-Id : 481, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
-Id : 482, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 481 with 4 at 1,2,1,1,1,2
-Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
-Id : 483, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 482 with 36 at 2,1,1,1,2
-Id : 484, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 483 with 29 at 1,1,1,2
-Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
-Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
-Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
-Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
-Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
-Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
-Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
-Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
-Id : 896, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
-Id : 911, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 896 with 36 at 2,1,1,3
-Id : 944, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 911 with 4 at 1,1,2
-Id : 978, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 911 with 4 at 1,1,2
-Id : 989, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =?= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 978 with 32 at 1,1,3
-Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
-Id : 1018, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 989 with 223 at 2
-Id : 1036, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1018 at 2,3
-Id : 1074, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1036 with 29 at 3
-Id : 1107, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 944 with 1074 at 1,1,3
-Id : 1180, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1107 with 29 at 2
-Id : 1223, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 944 with 1180 at 1,1,3
-Id : 1540, {_}: multiply (inverse (inverse (inverse (inverse ?3274)))) ?3275 =<= inverse (inverse (inverse (inverse (multiply ?3274 ?3275)))) [3275, 3274] by Demod 1223 with 29 at 2
-Id : 10, {_}: divide (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) (divide (divide ?37 ?37) ?36) =>= ?35 [37, 36, 35, 34] by Super 2 with 3 at 2,2,2,1,2
-Id : 24, {_}: multiply (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 10 with 3 at 2
-Id : 793, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 24 with 4 at 1,2
-Id : 794, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (inverse ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 793 with 4 at 1,2,2,1,1,2
-Id : 1550, {_}: multiply (inverse (inverse (inverse (inverse (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))))))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Super 1540 with 794 at 1,1,1,1,3
-Id : 1600, {_}: multiply (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Demod 1550 with 1018 at 1,2
-Id : 1601, {_}: ?3308 =<= inverse (inverse (inverse (inverse ?3308))) [3308] by Demod 1600 with 794 at 2
-Id : 1634, {_}: multiply ?3404 (inverse (inverse (inverse ?3405))) =>= divide ?3404 ?3405 [3405, 3404] by Super 29 with 1601 at 2,3
-Id : 1707, {_}: divide (inverse (inverse ?3544)) (inverse (inverse ?3545)) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Super 944 with 1634 at 1,1,3
-Id : 1741, {_}: multiply (inverse (inverse ?3544)) (inverse ?3545) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Demod 1707 with 29 at 2
-Id : 1807, {_}: divide (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) (inverse ?3667) =>= inverse (inverse ?3666) [3667, 3666] by Super 484 with 1741 at 1,1,1,2
-Id : 1849, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1807 with 29 at 2
-Id : 1850, {_}: multiply (divide ?3666 ?3667) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1849 with 1601 at 1,2
-Id : 1880, {_}: inverse (inverse ?3792) =<= divide (divide ?3792 (inverse (inverse (inverse ?3793)))) ?3793 [3793, 3792] by Super 1634 with 1850 at 2
-Id : 2688, {_}: inverse (inverse ?5905) =<= divide (multiply ?5905 (inverse (inverse ?5906))) ?5906 [5906, 5905] by Demod 1880 with 29 at 1,3
-Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
-Id : 2714, {_}: inverse (inverse (inverse (inverse (divide ?5996 ?5996)))) =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Super 2688 with 224 at 1,3
-Id : 2767, {_}: divide ?5996 ?5996 =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Demod 2714 with 1601 at 2
-Id : 2768, {_}: divide ?5996 ?5996 =?= divide ?5997 ?5997 [5997, 5996] by Demod 2767 with 1601 at 1,3
-Id : 2830, {_}: divide (inverse (divide ?6176 (divide (inverse ?6177) (divide (inverse ?6176) ?6178)))) ?6178 =?= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6178, 6177, 6176] by Super 145 with 2768 at 2,1,3
-Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
-Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
-Id : 2905, {_}: inverse ?6177 =<= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6177] by Demod 2830 with 31 at 2
-Id : 2962, {_}: divide ?6532 (divide ?6533 ?6533) =?= inverse (inverse (inverse (inverse ?6532))) [6533, 6532] by Super 1601 with 2905 at 1,1,1,3
-Id : 3014, {_}: divide ?6532 (divide ?6533 ?6533) =>= ?6532 [6533, 6532] by Demod 2962 with 1601 at 3
-Id : 3088, {_}: divide (inverse (divide ?6789 ?6790)) (divide ?6791 ?6791) =>= inverse (inverse (multiply ?6790 (inverse ?6789))) [6791, 6790, 6789] by Super 250 with 3014 at 2,1,1,3
-Id : 3148, {_}: inverse (divide ?6789 ?6790) =<= inverse (inverse (multiply ?6790 (inverse ?6789))) [6790, 6789] by Demod 3088 with 3014 at 2
-Id : 3149, {_}: inverse (divide ?6789 ?6790) =<= divide (inverse (inverse ?6790)) ?6789 [6790, 6789] by Demod 3148 with 944 at 3
-Id : 3377, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 484 with 3149 at 2
-Id : 3423, {_}: inverse (divide ?7500 ?7501) =<= divide (inverse (inverse ?7501)) ?7500 [7501, 7500] by Demod 3148 with 944 at 3
-Id : 3441, {_}: inverse (divide ?7566 (inverse (inverse ?7567))) =>= divide ?7567 ?7566 [7567, 7566] by Super 3423 with 1601 at 1,3
-Id : 3536, {_}: inverse (multiply ?7566 (inverse ?7567)) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3441 with 29 at 1,2
-Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
-Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
-Id : 3378, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3149 at 3
-Id : 3383, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3378 with 29 at 1,3
-Id : 3089, {_}: multiply ?6793 (divide ?6794 ?6794) =>= inverse (inverse ?6793) [6794, 6793] by Super 1850 with 3014 at 1,2
-Id : 3760, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3383 with 3089 at 1,3
-Id : 3763, {_}: multiply ?3404 (inverse ?3405) =>= divide ?3404 ?3405 [3405, 3404] by Demod 1634 with 3760 at 2,2
-Id : 3764, {_}: inverse (divide ?7566 ?7567) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3536 with 3763 at 1,2
-Id : 3776, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3377 with 3764 at 2
-Id : 1886, {_}: multiply (divide ?3813 ?3814) ?3814 =>= inverse (inverse ?3813) [3814, 3813] by Demod 1849 with 1601 at 1,2
-Id : 1895, {_}: multiply (multiply ?3842 ?3843) (inverse ?3843) =>= inverse (inverse ?3842) [3843, 3842] by Super 1886 with 29 at 1,2
-Id : 3766, {_}: divide (multiply ?3842 ?3843) ?3843 =>= inverse (inverse ?3842) [3843, 3842] by Demod 1895 with 3763 at 2
-Id : 3800, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3776 with 3766 at 2
-Id : 3806, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= ?269 [269, 268] by Demod 128 with 3800 at 3
-Id : 3889, {_}: a2 =?= a2 [] by Demod 1 with 3806 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP452-1.p
-11236: solved GRP452-1.p in 0.984061 using kbo
-11236: status Unsatisfiable for GRP452-1.p
-NO CLASH, using fixed ground order
-11242: Facts:
-11242: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11242: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11242: Goal:
-11242: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11242: Order:
-11242: nrkbo
-11242: Leaf order:
-11242: divide 7 2 0
-11242: b1 2 0 2 1,1,3
-11242: multiply 3 2 2 0,2
-11242: inverse 4 1 2 0,1,2
-11242: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11243: Facts:
-11243: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11243: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11243: Goal:
-11243: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11243: Order:
-11243: kbo
-11243: Leaf order:
-11243: divide 7 2 0
-11243: b1 2 0 2 1,1,3
-11243: multiply 3 2 2 0,2
-11243: inverse 4 1 2 0,1,2
-11243: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11244: Facts:
-11244: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11244: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11244: Goal:
-11244: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11244: Order:
-11244: lpo
-11244: Leaf order:
-11244: divide 7 2 0
-11244: b1 2 0 2 1,1,3
-11244: multiply 3 2 2 0,2
-11244: inverse 4 1 2 0,1,2
-11244: a1 2 0 2 1,1,2
-% SZS status Timeout for GRP469-1.p
-NO CLASH, using fixed ground order
-11271: Facts:
-11271: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11271: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11271: Goal:
-11271: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11271: Order:
-11271: nrkbo
-11271: Leaf order:
-11271: divide 7 2 0
-11271: a2 2 0 2 2,2
-11271: multiply 3 2 2 0,2
-11271: inverse 3 1 1 0,1,1,2
-11271: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11272: Facts:
-11272: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11272: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11272: Goal:
-11272: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11272: Order:
-11272: kbo
-11272: Leaf order:
-11272: divide 7 2 0
-11272: a2 2 0 2 2,2
-11272: multiply 3 2 2 0,2
-11272: inverse 3 1 1 0,1,1,2
-11272: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11273: Facts:
-11273: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11273: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11273: Goal:
-11273: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11273: Order:
-11273: lpo
-11273: Leaf order:
-11273: divide 7 2 0
-11273: a2 2 0 2 2,2
-11273: multiply 3 2 2 0,2
-11273: inverse 3 1 1 0,1,1,2
-11273: b2 2 0 2 1,1,1,2
-Statistics :
-Max weight : 55
-Found proof, 64.719986s
-% SZS status Unsatisfiable for GRP470-1.p
-% SZS output start CNFRefutation for GRP470-1.p
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
-Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
-Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
-Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
-Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
-Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
-Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
-Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
-Id : 7613, {_}: ?38021 =<= multiply (multiply (divide (inverse ?38022) ?38023) (divide (multiply ?38023 ?38022) (divide ?38024 ?38021))) ?38024 [38024, 38023, 38022, 38021] by Super 7101 with 3 at 1,2,1,3
-Id : 7678, {_}: ?38552 =<= multiply (multiply (multiply (inverse ?38553) ?38554) (divide (multiply (inverse ?38554) ?38553) (divide ?38555 ?38552))) ?38555 [38555, 38554, 38553, 38552] by Super 7613 with 3 at 1,1,3
-Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
-Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
-Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
-Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
-Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
-Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
-Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
-Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
-Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
-Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
-Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
-Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
-Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
-Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
-Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
-Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
-Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
-Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
-Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
-Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
-Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
-Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
-Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
-Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
-Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
-Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
-Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
-Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
-Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
-Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
-Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
-Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
-Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
-Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
-Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
-Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
-Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
-Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
-Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
-Id : 12991, {_}: inverse (inverse (divide (divide ?67798 ?67799) (multiply ?67800 (multiply (inverse ?67801) ?67802)))) =>= multiply ?67798 (multiply (inverse ?67799) (inverse (multiply (divide ?67800 ?67801) ?67802))) [67802, 67801, 67800, 67799, 67798] by Super 12770 with 12807 at 1,1,2
-Id : 15565, {_}: inverse (inverse (divide (divide ?82879 ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883)))) =>= multiply ?82879 (divide (inverse ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883))) [82883, 82882, 82881, 82880, 82879] by Demod 12991 with 12807 at 2,3
-Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
-Id : 15584, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =<= multiply ?83055 (divide (inverse ?83056) (multiply (multiply (divide ?83058 ?83059) (divide (divide ?83059 ?83058) (divide (multiply (inverse ?83060) ?83061) ?83057))) (multiply (inverse ?83060) ?83061))) [83061, 83060, 83059, 83058, 83057, 83056, 83055] by Super 15565 with 6973 at 2,1,1,2
-Id : 15659, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =>= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15584 with 6973 at 2,2,3
-Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
-Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =>= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
-Id : 13083, {_}: inverse (inverse (divide (multiply ?68472 ?68473) (multiply ?68474 (multiply (inverse ?68475) ?68476)))) =>= multiply ?68472 (multiply (inverse (inverse ?68473)) (inverse (multiply (divide ?68474 ?68475) ?68476))) [68476, 68475, 68474, 68473, 68472] by Super 12858 with 12807 at 1,1,2
-Id : 14137, {_}: inverse (inverse (divide (multiply ?73757 ?73758) (multiply ?73759 (multiply (inverse ?73760) ?73761)))) =>= multiply ?73757 (divide (inverse (inverse ?73758)) (multiply ?73759 (multiply (inverse ?73760) ?73761))) [73761, 73760, 73759, 73758, 73757] by Demod 13083 with 12807 at 2,3
-Id : 14155, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =<= multiply ?73925 (divide (inverse (inverse ?73926)) (multiply (multiply (divide ?73928 ?73929) (divide (divide ?73929 ?73928) (divide (multiply (inverse ?73930) ?73931) ?73927))) (multiply (inverse ?73930) ?73931))) [73931, 73930, 73929, 73928, 73927, 73926, 73925] by Super 14137 with 6973 at 2,1,1,2
-Id : 14212, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =>= multiply ?73925 (divide (inverse (inverse ?73926)) ?73927) [73927, 73926, 73925] by Demod 14155 with 6973 at 2,2,3
-Id : 15715, {_}: multiply ?83687 (inverse (divide (divide ?83688 ?83689) ?83690)) =>= divide ?83687 (multiply ?83688 (divide (inverse ?83689) ?83690)) [83690, 83689, 83688, 83687] by Super 3 with 15659 at 2,3
-Id : 15912, {_}: divide (divide ?84886 (divide (inverse ?84887) ?84888)) (divide ?84889 ?84890) =<= divide (multiply ?84886 ?84888) (multiply ?84889 (divide (inverse ?84890) ?84887)) [84890, 84889, 84888, 84887, 84886] by Super 9552 with 15715 at 3
-Id : 16736, {_}: inverse (inverse (divide (divide ?88411 (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415))) =>= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Super 14212 with 15912 at 1,1,2
-Id : 16823, {_}: multiply ?88411 (divide (inverse (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415)) =<= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Demod 16736 with 15659 at 2
-Id : 19503, {_}: inverse (divide (inverse (inverse ?101466)) (multiply ?101467 (divide (inverse ?101468) ?101469))) =<= multiply (multiply (divide (inverse ?101470) ?101471) (divide (multiply ?101471 ?101470) (multiply ?101472 (divide (inverse (divide (inverse ?101469) ?101466)) (divide ?101467 ?101468))))) ?101472 [101472, 101471, 101470, 101469, 101468, 101467, 101466] by Super 7337 with 16823 at 2,2,1,3
-Id : 20509, {_}: inverse (divide (inverse (inverse ?107024)) (multiply ?107025 (divide (inverse ?107026) ?107027))) =>= inverse (divide (inverse (divide (inverse ?107027) ?107024)) (divide ?107025 ?107026)) [107027, 107026, 107025, 107024] by Demod 19503 with 7337 at 3
-Id : 15122, {_}: multiply ?80264 (inverse (divide (multiply ?80265 ?80266) ?80267)) =<= divide ?80264 (multiply ?80265 (divide (inverse (inverse ?80266)) ?80267)) [80267, 80266, 80265, 80264] by Super 3 with 14212 at 2,3
-Id : 20594, {_}: inverse (multiply (inverse (inverse ?107698)) (inverse (divide (multiply ?107699 ?107700) ?107701))) =>= inverse (divide (inverse (divide (inverse ?107701) ?107698)) (divide ?107699 (inverse ?107700))) [107701, 107700, 107699, 107698] by Super 20509 with 15122 at 1,2
-Id : 20893, {_}: inverse (multiply (inverse (inverse ?108369)) (inverse (divide (multiply ?108370 ?108371) ?108372))) =>= inverse (divide (inverse (divide (inverse ?108372) ?108369)) (multiply ?108370 ?108371)) [108372, 108371, 108370, 108369] by Demod 20594 with 3 at 2,1,3
-Id : 20903, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =<= inverse (divide (inverse (divide (inverse ?108449) ?108447)) (multiply (multiply (divide ?108450 ?108451) (divide (divide ?108451 ?108450) (divide ?108452 ?108448))) ?108452)) [108452, 108451, 108450, 108449, 108448, 108447] by Super 20893 with 6973 at 1,1,2,1,2
-Id : 21279, {_}: inverse (multiply (inverse (inverse ?109423)) (inverse (divide ?109424 ?109425))) =>= inverse (divide (inverse (divide (inverse ?109425) ?109423)) ?109424) [109425, 109424, 109423] by Demod 20903 with 6973 at 2,1,3
-Id : 21354, {_}: inverse (multiply (multiply ?109942 (divide (inverse ?109943) ?109944)) (inverse (divide ?109945 ?109946))) =>= inverse (divide (inverse (divide (inverse ?109946) (divide (divide ?109942 ?109943) ?109944))) ?109945) [109946, 109945, 109944, 109943, 109942] by Super 21279 with 15659 at 1,1,2
-Id : 25671, {_}: inverse (divide (divide ?128948 (divide (inverse ?128949) (divide (inverse ?128950) ?128951))) ?128952) =<= inverse (divide (inverse (divide (inverse ?128949) (divide (divide ?128948 ?128950) ?128951))) ?128952) [128952, 128951, 128950, 128949, 128948] by Demod 21354 with 9552 at 1,2
-Id : 25729, {_}: inverse (divide (divide ?129446 (divide (inverse (divide ?129447 (divide (divide ?129448 (divide (divide ?129449 ?129450) ?129447)) (divide ?129450 ?129449)))) (divide (inverse ?129451) ?129452))) ?129453) =>= inverse (divide (inverse (divide ?129448 (divide (divide ?129446 ?129451) ?129452))) ?129453) [129453, 129452, 129451, 129450, 129449, 129448, 129447, 129446] by Super 25671 with 53 at 1,1,1,1,3
-Id : 26075, {_}: inverse (divide (divide ?131096 (divide ?131097 (divide (inverse ?131098) ?131099))) ?131100) =<= inverse (divide (inverse (divide ?131097 (divide (divide ?131096 ?131098) ?131099))) ?131100) [131100, 131099, 131098, 131097, 131096] by Demod 25729 with 53 at 1,2,1,1,2
-Id : 26111, {_}: inverse (divide (divide ?131425 (divide ?131426 (divide (inverse (inverse ?131427)) ?131428))) ?131429) =>= inverse (divide (inverse (divide ?131426 (divide (multiply ?131425 ?131427) ?131428))) ?131429) [131429, 131428, 131427, 131426, 131425] by Super 26075 with 3 at 1,2,1,1,1,3
-Id : 30666, {_}: inverse (inverse (divide (inverse (divide ?153822 (divide (multiply ?153823 ?153824) ?153825))) ?153826)) =>= multiply ?153823 (divide (inverse (divide ?153822 (divide (inverse (inverse ?153824)) ?153825))) ?153826) [153826, 153825, 153824, 153823, 153822] by Super 15659 with 26111 at 1,2
-Id : 30731, {_}: inverse (inverse (multiply ?154370 ?154371)) =<= multiply ?154370 (divide (inverse (divide ?154372 (divide (inverse (inverse ?154371)) (divide ?154373 ?154374)))) (divide (divide ?154374 ?154373) ?154372)) [154374, 154373, 154372, 154371, 154370] by Super 30666 with 2 at 1,1,2
-Id : 31025, {_}: inverse (inverse (multiply ?155310 ?155311)) =>= multiply ?155310 (inverse (inverse ?155311)) [155311, 155310] by Demod 30731 with 2 at 2,3
-Id : 7367, {_}: inverse ?36880 =<= multiply (multiply (multiply ?36881 ?36882) (divide (divide (inverse ?36882) ?36881) (multiply ?36883 ?36880))) ?36883 [36883, 36882, 36881, 36880] by Super 7303 with 3 at 1,1,3
-Id : 15740, {_}: inverse (inverse (divide (divide ?83867 ?83868) ?83869)) =>= multiply ?83867 (divide (inverse ?83868) ?83869) [83869, 83868, 83867] by Demod 15584 with 6973 at 2,2,3
-Id : 15787, {_}: inverse (inverse (multiply (multiply ?84179 ?84180) (inverse (multiply ?84181 ?84182)))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Super 15740 with 9554 at 1,1,2
-Id : 15809, {_}: multiply ?84179 (multiply (inverse (inverse ?84180)) (inverse (multiply ?84181 ?84182))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Demod 15787 with 12858 at 2
-Id : 16238, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =<= multiply (multiply (multiply ?86043 ?86044) (divide (divide (inverse ?86044) ?86043) (multiply ?86045 (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041)))) ?86045 [86045, 86044, 86043, 86042, 86041, 86040] by Super 7367 with 15809 at 2,2,1,3
-Id : 16326, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =>= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86042, 86041, 86040] by Demod 16238 with 7367 at 3
-Id : 31064, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?155519)) ?155520)) ?155521)) =>= multiply (inverse (inverse ?155520)) (inverse (inverse (inverse (multiply ?155521 ?155519)))) [155521, 155520, 155519] by Super 31025 with 16326 at 1,2
-Id : 30884, {_}: inverse (inverse (multiply ?154370 ?154371)) =>= multiply ?154370 (inverse (inverse ?154371)) [154371, 154370] by Demod 30731 with 2 at 2,3
-Id : 32647, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?161221)) ?161222)) ?161223)) =>= multiply (inverse (inverse ?161222)) (inverse (multiply ?161223 (inverse (inverse ?161221)))) [161223, 161222, 161221] by Demod 31064 with 30884 at 1,2,3
-Id : 32648, {_}: inverse (inverse (divide (inverse (divide (inverse ?161225) ?161226)) ?161227)) =<= multiply (inverse (inverse ?161226)) (inverse (multiply ?161227 (inverse (inverse (divide ?161228 (divide (divide ?161225 (divide (divide ?161229 ?161230) ?161228)) (divide ?161230 ?161229))))))) [161230, 161229, 161228, 161227, 161226, 161225] by Super 32647 with 53 at 1,1,1,1,1,1,2
-Id : 33188, {_}: inverse (inverse (divide (inverse (divide (inverse ?162681) ?162682)) ?162683)) =>= multiply (inverse (inverse ?162682)) (inverse (multiply ?162683 (inverse ?162681))) [162683, 162682, 162681] by Demod 32648 with 53 at 1,2,1,2,3
-Id : 33189, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =<= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 (inverse (divide ?162688 (divide (divide ?162685 (divide (divide ?162689 ?162690) ?162688)) (divide ?162690 ?162689)))))) [162690, 162689, 162688, 162687, 162686, 162685] by Super 33188 with 53 at 1,1,1,1,1,2
-Id : 33732, {_}: inverse (inverse (divide (inverse (divide ?164373 ?164374)) ?164375)) =>= multiply (inverse (inverse ?164374)) (inverse (multiply ?164375 ?164373)) [164375, 164374, 164373] by Demod 33189 with 53 at 2,1,2,3
-Id : 33815, {_}: inverse (inverse (multiply (inverse (divide ?164946 ?164947)) ?164948)) =<= multiply (inverse (inverse ?164947)) (inverse (multiply (inverse ?164948) ?164946)) [164948, 164947, 164946] by Super 33732 with 3 at 1,1,2
-Id : 34748, {_}: multiply (inverse (divide ?166758 ?166759)) (inverse (inverse ?166760)) =<= multiply (inverse (inverse ?166759)) (inverse (multiply (inverse ?166760) ?166758)) [166760, 166759, 166758] by Demod 33815 with 30884 at 2
-Id : 34749, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse (inverse (divide ?166764 (divide (divide ?166765 (divide (divide ?166766 ?166767) ?166764)) (divide ?166767 ?166766))))) =>= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166767, 166766, 166765, 166764, 166763, 166762] by Super 34748 with 53 at 1,1,2,3
-Id : 35052, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse ?166765) =<= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166765, 166763, 166762] by Demod 34749 with 53 at 1,2,2
-Id : 35278, {_}: multiply (inverse (divide ?167869 ?167870)) (inverse (divide ?167871 ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Super 12807 with 35052 at 2
-Id : 33419, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 ?162685)) [162687, 162686, 162685] by Demod 33189 with 53 at 2,1,2,3
-Id : 35198, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (divide ?162685 ?162686)) (inverse ?162687) [162687, 162686, 162685] by Demod 33419 with 35052 at 3
-Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
-Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
-Id : 38131, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =<= multiply (inverse (divide (inverse (divide ?178376 (divide ?178374 (multiply (divide ?178377 ?178378) (divide ?178378 (divide ?178379 (multiply (divide (divide ?178380 ?178381) ?178382) (divide ?178382 (divide ?178377 (divide ?178381 ?178380)))))))))) (divide ?178379 ?178376))) (inverse ?178375) [178382, 178381, 178380, 178379, 178378, 178377, 178376, 178375, 178374] by Super 35198 with 38 at 1,1,1,1,2
-Id : 38834, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =>= multiply (inverse ?178374) (inverse ?178375) [178375, 178374] by Demod 38131 with 38 at 1,1,3
-Id : 39627, {_}: multiply ?187316 (inverse (divide (inverse ?187317) ?187318)) =>= divide ?187316 (multiply (inverse ?187317) (inverse ?187318)) [187318, 187317, 187316] by Super 3 with 38834 at 2,3
-Id : 39628, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =<= divide ?187320 (multiply (inverse (divide ?187323 (divide (divide ?187321 (divide (divide ?187324 ?187325) ?187323)) (divide ?187325 ?187324)))) (inverse ?187322)) [187325, 187324, 187323, 187322, 187321, 187320] by Super 39627 with 53 at 1,1,2,2
-Id : 39950, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =>= divide ?187320 (multiply ?187321 (inverse ?187322)) [187322, 187321, 187320] by Demod 39628 with 53 at 1,2,3
-Id : 45468, {_}: divide (inverse (divide ?167869 ?167870)) (multiply ?167871 (inverse ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Demod 35278 with 39950 at 2
-Id : 45552, {_}: divide (inverse ?204144) (multiply (divide ?204145 ?204146) (divide (divide ?204146 ?204145) (divide ?204144 (divide (inverse (divide ?204147 ?204148)) (multiply ?204149 (inverse ?204150)))))) =>= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204150, 204149, 204148, 204147, 204146, 204145, 204144] by Super 362 with 45468 at 2,2,2,2,2
-Id : 45856, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204148, 204147, 204150, 204149] by Demod 45552 with 362 at 2
-Id : 45857, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= multiply (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse ?204148) [204148, 204147, 204150, 204149] by Demod 45856 with 3 at 3
-Id : 46240, {_}: multiply (multiply ?206273 (inverse ?206274)) (divide ?206275 ?206276) =<= multiply (multiply ?206273 (multiply (inverse ?206274) ?206275)) (inverse ?206276) [206276, 206275, 206274, 206273] by Demod 45857 with 3 at 2
-Id : 30915, {_}: multiply (multiply ?67174 ?67175) (inverse (inverse ?67176)) =?= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 30884 at 2
-Id : 46333, {_}: multiply (multiply ?207013 (inverse (inverse ?207014))) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Super 46240 with 30915 at 1,3
-Id : 1890, {_}: divide (inverse (divide (divide ?8674 ?8675) ?8676)) ?8677 =<= inverse (divide (inverse (divide ?8678 ?8677)) (divide ?8676 (divide ?8678 (divide ?8675 ?8674)))) [8678, 8677, 8676, 8675, 8674] by Super 7 with 1266 at 2,2
-Id : 1908, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide ?8836 ?8835)) (divide ?8834 (divide ?8836 (multiply ?8833 ?8832)))) [8836, 8835, 8834, 8833, 8832] by Super 1890 with 3 at 2,2,2,1,3
-Id : 61, {_}: divide (inverse (divide ?349 ?350)) (divide (divide ?351 (divide ?352 ?353)) ?349) =>= inverse (divide ?351 (divide ?350 (divide ?353 ?352))) [353, 352, 351, 350, 349] by Super 4 with 2 at 2,1,1,2
-Id : 65, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide ?384 (divide ?383 (divide (inverse ?386) ?385))) [386, 385, 384, 383, 382] by Super 61 with 3 at 2,1,2,2
-Id : 16676, {_}: divide (inverse ?87869) (multiply (divide ?87870 ?87871) (divide (divide ?87871 ?87870) (divide ?87869 (divide (divide ?87872 (divide (inverse ?87873) ?87874)) (divide ?87875 ?87876))))) =>= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87876, 87875, 87874, 87873, 87872, 87871, 87870, 87869] by Super 362 with 15912 at 2,2,2,2,2
-Id : 16850, {_}: divide (divide ?87875 ?87876) (divide ?87872 (divide (inverse ?87873) ?87874)) =<= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87874, 87873, 87872, 87876, 87875] by Demod 16676 with 362 at 2
-Id : 17219, {_}: inverse (inverse (divide (divide ?91192 ?91193) (divide ?91194 (divide (inverse ?91195) ?91196)))) =>= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Super 14212 with 16850 at 1,1,2
-Id : 17309, {_}: multiply ?91192 (divide (inverse ?91193) (divide ?91194 (divide (inverse ?91195) ?91196))) =<= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Demod 17219 with 15659 at 2
-Id : 22082, {_}: inverse (divide (inverse (inverse (divide (inverse ?112093) ?112094))) (multiply ?112095 ?112096)) =<= multiply (multiply (divide (inverse ?112097) ?112098) (divide (multiply ?112098 ?112097) (multiply ?112099 (divide (inverse ?112093) (divide ?112095 (divide (inverse ?112094) ?112096)))))) ?112099 [112099, 112098, 112097, 112096, 112095, 112094, 112093] by Super 7337 with 17309 at 2,2,1,3
-Id : 22476, {_}: inverse (divide (inverse (inverse (divide (inverse ?113967) ?113968))) (multiply ?113969 ?113970)) =>= inverse (divide (inverse ?113967) (divide ?113969 (divide (inverse ?113968) ?113970))) [113970, 113969, 113968, 113967] by Demod 22082 with 7337 at 3
-Id : 22508, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =<= inverse (divide (inverse (divide ?114208 (divide (divide ?114204 (divide (divide ?114209 ?114210) ?114208)) (divide ?114210 ?114209)))) (divide ?114206 (divide (inverse ?114205) ?114207))) [114210, 114209, 114208, 114207, 114206, 114205, 114204] by Super 22476 with 53 at 1,1,1,1,1,2
-Id : 22780, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =>= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22508 with 53 at 1,1,3
-Id : 40158, {_}: inverse (inverse (divide ?188657 ?188658)) =<= multiply (multiply (multiply ?188659 ?188660) (divide (divide (inverse ?188660) ?188659) (divide ?188661 (multiply ?188657 (inverse ?188658))))) ?188661 [188661, 188660, 188659, 188658, 188657] by Super 7367 with 39950 at 2,2,1,3
-Id : 7191, {_}: ?36095 =<= multiply (multiply (multiply ?36096 ?36097) (divide (divide (inverse ?36097) ?36096) (divide ?36098 ?36095))) ?36098 [36098, 36097, 36096, 36095] by Super 7101 with 3 at 1,1,3
-Id : 40350, {_}: inverse (inverse (divide ?188657 ?188658)) =>= multiply ?188657 (inverse ?188658) [188658, 188657] by Demod 40158 with 7191 at 3
-Id : 40577, {_}: inverse (divide (multiply ?114204 (inverse ?114205)) (multiply ?114206 ?114207)) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22780 with 40350 at 1,1,2
-Id : 40645, {_}: divide (divide ?189801 (divide (multiply ?189802 (inverse ?189803)) ?189804)) ?189805 =<= multiply (multiply ?189801 ?189804) (inverse (multiply ?189805 (divide ?189802 ?189803))) [189805, 189804, 189803, 189802, 189801] by Super 9554 with 40350 at 1,2,1,2
-Id : 30968, {_}: multiply ?154958 (inverse (multiply ?154959 ?154960)) =<= divide ?154958 (multiply ?154959 (inverse (inverse ?154960))) [154960, 154959, 154958] by Super 3 with 30884 at 2,3
-Id : 40629, {_}: multiply ?189704 (inverse (multiply ?189705 (divide ?189706 ?189707))) =>= divide ?189704 (multiply ?189705 (multiply ?189706 (inverse ?189707))) [189707, 189706, 189705, 189704] by Super 30968 with 40350 at 2,2,3
-Id : 62131, {_}: divide (divide ?257834 (divide (multiply ?257835 (inverse ?257836)) ?257837)) ?257838 =<= divide (multiply ?257834 ?257837) (multiply ?257838 (multiply ?257835 (inverse ?257836))) [257838, 257837, 257836, 257835, 257834] by Demod 40645 with 40629 at 3
-Id : 62178, {_}: divide (divide ?258249 (divide (multiply (multiply (divide ?258250 ?258251) (divide (divide ?258251 ?258250) (divide (inverse ?258252) ?258253))) (inverse ?258252)) ?258254)) ?258255 =>= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258252, 258251, 258250, 258249] by Super 62131 with 6973 at 2,2,3
-Id : 62493, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =<= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258249] by Demod 62178 with 6973 at 1,2,1,2
-Id : 62632, {_}: inverse (divide (divide ?114204 (divide ?114207 (inverse ?114205))) ?114206) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 40577 with 62493 at 1,2
-Id : 62637, {_}: inverse (divide (divide ?114204 (multiply ?114207 ?114205)) ?114206) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 62632 with 3 at 2,1,1,2
-Id : 62641, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide (divide ?384 (multiply ?385 ?386)) ?383) [386, 385, 384, 383, 382] by Demod 65 with 62637 at 3
-Id : 19, {_}: divide (inverse ?90) (divide (divide ?91 ?92) (inverse (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93)))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Super 2 with 15 at 1,1,2
-Id : 40, {_}: divide (inverse ?90) (multiply (divide ?91 ?92) (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Demod 19 with 3 at 2,2
-Id : 89822, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =?= inverse (divide (divide (inverse ?333800) (multiply (divide ?333801 ?333802) (divide (divide ?333802 ?333801) (divide ?333800 (multiply (divide (divide ?333803 ?333804) ?333805) (divide ?333805 (divide ?333799 (divide ?333804 ?333803)))))))) ?333798) [333805, 333804, 333803, 333802, 333801, 333800, 333799, 333798, 333797] by Super 62641 with 40 at 1,2,2
-Id : 90396, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =>= inverse (divide ?333799 ?333798) [333799, 333798, 333797] by Demod 89822 with 40 at 1,1,3
-Id : 101099, {_}: inverse (divide (divide ?31 (divide ?32 ?33)) ?30) =?= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [30, 33, 32, 31] by Demod 7 with 90396 at 2
-Id : 101112, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (divide (inverse (divide ?8836 ?8835)) (divide (multiply ?8833 ?8832) ?8836)) ?8834) [8836, 8835, 8834, 8833, 8832] by Demod 1908 with 101099 at 3
-Id : 101118, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8835, 8834, 8833, 8832] by Demod 101112 with 90396 at 1,1,3
-Id : 101316, {_}: divide (inverse (divide (divide (inverse ?356253) ?356254) (divide ?356255 (multiply ?356254 ?356253)))) ?356256 =>= inverse (inverse (divide ?356255 ?356256)) [356256, 356255, 356254, 356253] by Super 101118 with 90396 at 1,3
-Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
-Id : 101095, {_}: inverse (divide (divide (inverse ?56) ?55) (divide ?54 (multiply ?55 ?56))) =>= ?54 [54, 55, 56] by Demod 12 with 90396 at 2
-Id : 101519, {_}: divide ?356255 ?356256 =<= inverse (inverse (divide ?356255 ?356256)) [356256, 356255] by Demod 101316 with 101095 at 1,2
-Id : 101520, {_}: divide ?356255 ?356256 =<= multiply ?356255 (inverse ?356256) [356256, 356255] by Demod 101519 with 40350 at 3
-Id : 102152, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Demod 46333 with 101520 at 1,2
-Id : 102153, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= divide (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) ?207016 [207016, 207015, 207014, 207013] by Demod 102152 with 101520 at 3
-Id : 102154, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =>= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102153 with 101520 at 1,3
-Id : 102308, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =<= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102154 with 3 at 1,2
-Id : 102309, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =>= divide (multiply (multiply ?207013 ?207014) ?207015) ?207016 [207016, 207015, 207014, 207013] by Demod 102308 with 3 at 1,3
-Id : 102310, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38554) (multiply (inverse ?38554) ?38553)) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 7678 with 102309 at 1,3
-Id : 52549, {_}: multiply (multiply ?225200 (inverse (inverse ?225201))) (divide ?225202 ?225203) =<= multiply (multiply (multiply ?225200 ?225201) (inverse (inverse ?225202))) (inverse ?225203) [225203, 225202, 225201, 225200] by Super 46240 with 30915 at 1,3
-Id : 52684, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (divide ?226213 (inverse ?226214)) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Super 52549 with 30915 at 3
-Id : 53235, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 52684 with 3 at 2,2
-Id : 102165, {_}: multiply (divide ?226211 (inverse ?226212)) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 53235 with 101520 at 1,2
-Id : 102295, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 102165 with 3 at 1,2
-Id : 30916, {_}: multiply (divide ?66357 ?66358) (inverse (inverse ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12770 with 30884 at 2
-Id : 9965, {_}: divide (divide ?51846 (divide (inverse (inverse ?51847)) ?51848)) ?51849 =>= multiply (multiply ?51846 ?51848) (inverse (multiply ?51849 ?51847)) [51849, 51848, 51847, 51846] by Super 9472 with 7237 at 1,1,3
-Id : 9976, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (multiply ?51938 (inverse ?51940)) (inverse (multiply ?51941 ?51939)) [51941, 51940, 51939, 51938] by Super 9965 with 3 at 2,1,2
-Id : 40724, {_}: inverse (inverse (divide ?190294 ?190295)) =>= multiply ?190294 (inverse ?190295) [190295, 190294] by Demod 40158 with 7191 at 3
-Id : 40043, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= divide (multiply ?49359 ?49361) (multiply ?49362 (inverse ?49360)) [49362, 49361, 49360, 49359] by Demod 9552 with 39950 at 3
-Id : 40771, {_}: inverse (inverse (divide (divide ?190577 (divide (inverse ?190578) ?190579)) ?190580)) =>= multiply (multiply ?190577 ?190579) (inverse (multiply ?190580 (inverse ?190578))) [190580, 190579, 190578, 190577] by Super 40724 with 40043 at 1,1,2
-Id : 42949, {_}: multiply (divide ?196696 (divide (inverse ?196697) ?196698)) (inverse ?196699) =<= multiply (multiply ?196696 ?196698) (inverse (multiply ?196699 (inverse ?196697))) [196699, 196698, 196697, 196696] by Demod 40771 with 40350 at 2
-Id : 42950, {_}: multiply (divide ?196701 (divide (inverse (divide ?196702 (divide (divide ?196703 (divide (divide ?196704 ?196705) ?196702)) (divide ?196705 ?196704)))) ?196706)) (inverse ?196707) =>= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196705, 196704, 196703, 196702, 196701] by Super 42949 with 53 at 2,1,2,3
-Id : 43226, {_}: multiply (divide ?196701 (divide ?196703 ?196706)) (inverse ?196707) =<= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196703, 196701] by Demod 42950 with 53 at 1,2,1,2
-Id : 43404, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (divide ?51938 (divide ?51939 (inverse ?51940))) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 9976 with 43226 at 3
-Id : 43406, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= multiply (divide ?51938 (multiply ?51939 ?51940)) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 43404 with 3 at 2,1,3
-Id : 62671, {_}: divide (divide (divide ?259262 (divide ?259263 ?259264)) (inverse (inverse ?259265))) ?259266 =>= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Super 43406 with 62493 at 1,2
-Id : 63074, {_}: divide (multiply (divide ?259262 (divide ?259263 ?259264)) (inverse ?259265)) ?259266 =<= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Demod 62671 with 3 at 1,2
-Id : 84448, {_}: divide (multiply (divide ?320603 (divide ?320604 ?320605)) (inverse ?320606)) ?320607 =<= multiply (divide (divide ?320603 (divide ?320604 ?320605)) ?320606) (inverse ?320607) [320607, 320606, 320605, 320604, 320603] by Demod 63074 with 62493 at 1,3
-Id : 84555, {_}: divide (multiply (divide (inverse (divide ?321565 (divide ?321566 (multiply (divide (divide ?321567 ?321568) ?321569) (divide ?321569 (divide ?321570 (divide ?321568 ?321567))))))) (divide ?321570 ?321565)) (inverse ?321571)) ?321572 =>= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321570, 321569, 321568, 321567, 321566, 321565] by Super 84448 with 15 at 1,1,3
-Id : 85061, {_}: divide (multiply ?321566 (inverse ?321571)) ?321572 =<= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321566] by Demod 84555 with 15 at 1,1,2
-Id : 85186, {_}: divide (multiply ?66357 (inverse ?66358)) (inverse ?66359) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 30916 with 85061 at 2
-Id : 85229, {_}: multiply (multiply ?66357 (inverse ?66358)) ?66359 =?= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85186 with 3 at 2
-Id : 102180, {_}: multiply (divide ?66357 ?66358) ?66359 =<= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85229 with 101520 at 1,2
-Id : 102296, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse (inverse (inverse ?226213)))) ?226214 [226214, 226213, 226212, 226211] by Demod 102295 with 102180 at 3
-Id : 102297, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply (multiply ?226211 ?226212) (inverse (inverse ?226213))) ?226214 [226214, 226213, 226212, 226211] by Demod 102296 with 3 at 1,3
-Id : 102298, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse ?226213)) ?226214 [226214, 226213, 226212, 226211] by Demod 102297 with 101520 at 1,3
-Id : 102299, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =?= multiply (multiply (multiply ?226211 ?226212) ?226213) ?226214 [226214, 226213, 226212, 226211] by Demod 102298 with 3 at 1,3
-Id : 102317, {_}: ?38552 =<= multiply (divide (multiply (multiply (multiply (inverse ?38553) ?38554) (inverse ?38554)) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102310 with 102299 at 1,1,3
-Id : 102318, {_}: ?38552 =<= multiply (divide (multiply (divide (multiply (inverse ?38553) ?38554) ?38554) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102317 with 101520 at 1,1,1,3
-Id : 2791, {_}: divide (divide (inverse (multiply ?13892 ?13893)) (divide (divide (inverse ?13894) ?13895) ?13892)) (multiply ?13895 ?13894) =>= inverse ?13893 [13895, 13894, 13893, 13892] by Super 2771 with 3 at 2,2
-Id : 89847, {_}: divide (inverse ?334058) (multiply (divide ?334059 ?334060) (divide (divide ?334060 ?334059) (divide ?334058 (multiply (divide (divide ?334061 ?334062) ?334063) (divide ?334063 (divide ?334064 (divide ?334062 ?334061))))))) =>= ?334064 [334064, 334063, 334062, 334061, 334060, 334059, 334058] by Demod 19 with 3 at 2,2
-Id : 43403, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (divide ?49369 (divide ?49370 ?49371)) (inverse ?49372) [49372, 49371, 49370, 49369] by Demod 9554 with 43226 at 3
-Id : 85181, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (multiply ?49369 (inverse (divide ?49370 ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 43403 with 85061 at 3
-Id : 85235, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (divide ?49369 (multiply ?49370 (inverse ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 85181 with 39950 at 1,3
-Id : 89956, {_}: divide (inverse ?335244) (multiply (divide ?335245 ?335246) (divide (divide ?335246 ?335245) (divide ?335244 (multiply (divide (divide ?335247 ?335248) ?335249) (divide ?335249 (divide (divide ?335250 (multiply ?335251 (inverse ?335252))) (divide ?335248 ?335247))))))) =>= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250, 335249, 335248, 335247, 335246, 335245, 335244] by Super 89847 with 85235 at 2,2,2,2,2,2,2
-Id : 90764, {_}: divide ?335250 (multiply ?335251 (inverse ?335252)) =<= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250] by Demod 89956 with 40 at 2
-Id : 92959, {_}: divide (inverse (inverse ?344076)) ?344077 =<= multiply (multiply (multiply (inverse ?344078) ?344079) (divide (multiply (inverse ?344079) ?344078) (divide ?344080 (multiply ?344076 (inverse ?344077))))) ?344080 [344080, 344079, 344078, 344077, 344076] by Super 7678 with 90764 at 2,2,1,3
-Id : 93432, {_}: divide (inverse (inverse ?344076)) ?344077 =>= multiply ?344076 (inverse ?344077) [344077, 344076] by Demod 92959 with 7678 at 3
-Id : 94198, {_}: multiply (inverse (inverse ?346092)) (inverse (multiply ?346093 ?346094)) =?= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346094, 346093, 346092] by Super 30968 with 93432 at 3
-Id : 95063, {_}: multiply (inverse (divide ?346094 ?346092)) (inverse ?346093) =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 94198 with 35052 at 2
-Id : 102213, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 95063 with 101520 at 2
-Id : 102214, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= divide ?346092 (multiply ?346093 (inverse (inverse ?346094))) [346093, 346092, 346094] by Demod 102213 with 101520 at 3
-Id : 102215, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =?= divide ?346092 (divide ?346093 (inverse ?346094)) [346093, 346092, 346094] by Demod 102214 with 101520 at 2,3
-Id : 102222, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =>= divide ?346092 (multiply ?346093 ?346094) [346093, 346092, 346094] by Demod 102215 with 3 at 2,3
-Id : 102235, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8833, 8832, 8835, 8834] by Demod 101118 with 102222 at 2
-Id : 102236, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102235 with 102222 at 1,3
-Id : 35199, {_}: inverse (multiply (inverse (divide ?86042 ?86040)) (inverse ?86041)) =<= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86041, 86040, 86042] by Demod 16326 with 35052 at 1,2
-Id : 40695, {_}: inverse (multiply (inverse (divide (divide ?190115 ?190116) ?190117)) (inverse ?190118)) =>= inverse (divide (inverse (divide (multiply ?190115 (inverse ?190116)) ?190117)) ?190118) [190118, 190117, 190116, 190115] by Super 35199 with 40350 at 1,1,1,1,3
-Id : 46674, {_}: inverse (inverse (divide (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) ?207383)) =>= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Super 30884 with 40695 at 1,2
-Id : 47015, {_}: multiply (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) (inverse ?207383) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Demod 46674 with 40350 at 2
-Id : 31439, {_}: multiply ?157170 (inverse (multiply ?157171 ?157172)) =<= divide ?157170 (multiply ?157171 (inverse (inverse ?157172))) [157172, 157171, 157170] by Super 3 with 30884 at 2,3
-Id : 31475, {_}: multiply ?157430 (inverse (multiply ?157431 (multiply ?157432 ?157433))) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Super 31439 with 30884 at 2,2,3
-Id : 45490, {_}: multiply (inverse (inverse ?203652)) (inverse (multiply ?203653 (multiply (inverse ?203654) ?203655))) =>= divide (inverse (divide (inverse (inverse ?203655)) ?203652)) (multiply ?203653 (inverse ?203654)) [203655, 203654, 203653, 203652] by Super 31475 with 45468 at 3
-Id : 71413, {_}: multiply (inverse (divide (multiply (inverse ?287029) ?287030) ?287031)) (inverse ?287032) =<= divide (inverse (divide (inverse (inverse ?287030)) ?287031)) (multiply ?287032 (inverse ?287029)) [287032, 287031, 287030, 287029] by Demod 45490 with 35052 at 2
-Id : 71414, {_}: multiply (inverse (divide (multiply (inverse (divide ?287034 (divide (divide ?287035 (divide (divide ?287036 ?287037) ?287034)) (divide ?287037 ?287036)))) ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287037, 287036, 287035, 287034] by Super 71413 with 53 at 2,2,3
-Id : 72001, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =<= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 71414 with 53 at 1,1,1,1,2
-Id : 94096, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (multiply ?287038 (inverse ?287039))) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 72001 with 93432 at 1,1,3
-Id : 94118, {_}: divide (inverse (multiply (inverse ?207381) (inverse ?207382))) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 47015 with 94096 at 2
-Id : 102205, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 94118 with 101520 at 1,1,2
-Id : 102206, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207380, 207383, 207382, 207381] by Demod 102205 with 101520 at 3
-Id : 102244, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207381, 207380, 207383, 207382] by Demod 102206 with 102222 at 2
-Id : 102245, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102244 with 102222 at 3
-Id : 102246, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102245 with 101520 at 2,2
-Id : 85182, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= divide (multiply ?51938 (inverse (multiply ?51939 ?51940))) ?51941 [51941, 51940, 51939, 51938] by Demod 43406 with 85061 at 3
-Id : 89950, {_}: divide (inverse ?335180) (multiply (divide ?335181 ?335182) (divide (divide ?335182 ?335181) (divide ?335180 (multiply (divide (divide ?335183 ?335184) ?335185) (divide ?335185 (divide (multiply ?335186 (inverse (multiply ?335187 ?335188))) (divide ?335184 ?335183))))))) =>= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186, 335185, 335184, 335183, 335182, 335181, 335180] by Super 89847 with 85182 at 2,2,2,2,2,2,2
-Id : 90760, {_}: multiply ?335186 (inverse (multiply ?335187 ?335188)) =<= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186] by Demod 89950 with 40 at 2
-Id : 94126, {_}: multiply (inverse (inverse ?345644)) (inverse (multiply ?345645 ?345646)) =?= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345646, 345645, 345644] by Super 90760 with 93432 at 3
-Id : 95228, {_}: multiply (inverse (divide ?345646 ?345644)) (inverse ?345645) =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 94126 with 35052 at 2
-Id : 102219, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 95228 with 101520 at 2
-Id : 102220, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345645, 345644, 345646] by Demod 102219 with 101520 at 3
-Id : 102238, {_}: divide ?345644 (multiply ?345645 ?345646) =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345646, 345645, 345644] by Demod 102220 with 102222 at 2
-Id : 102247, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply ?207383 (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102246 with 102238 at 3
-Id : 102262, {_}: divide ?8834 (divide (multiply ?8835 (inverse ?8832)) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102236 with 102247 at 2
-Id : 102264, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102262 with 101520 at 1,2,2
-Id : 101098, {_}: inverse (divide (divide ?5 ?4) (divide ?3 (divide ?4 ?5))) =>= ?3 [3, 4, 5] by Demod 2 with 90396 at 2
-Id : 102493, {_}: divide (divide (inverse (divide (inverse ?357684) ?357685)) (multiply (divide ?357686 ?357687) ?357684)) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357687, 357686, 357685, 357684] by Super 2814 with 101520 at 1,1,1,2
-Id : 102761, {_}: divide (divide ?357685 (multiply (multiply (divide ?357686 ?357687) ?357684) (inverse ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102493 with 102222 at 1,2
-Id : 102131, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Demod 31475 with 101520 at 2
-Id : 102132, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (divide ?157432 (inverse ?157433))) [157433, 157432, 157431, 157430] by Demod 102131 with 101520 at 2,2,3
-Id : 102348, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (divide (multiply ?157431 ?157432) (inverse ?157433)) [157433, 157432, 157431, 157430] by Demod 102132 with 102247 at 3
-Id : 102349, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =?= divide ?157430 (multiply (multiply ?157431 ?157432) ?157433) [157433, 157432, 157431, 157430] by Demod 102348 with 3 at 2,3
-Id : 102762, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (multiply ?357684 (inverse ?357684)))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102761 with 102349 at 1,2
-Id : 102763, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (divide ?357684 ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102762 with 101520 at 2,2,1,2
-Id : 41245, {_}: multiply ?191831 (inverse (multiply ?191832 (divide ?191833 ?191834))) =>= divide ?191831 (multiply ?191832 (multiply ?191833 (inverse ?191834))) [191834, 191833, 191832, 191831] by Super 30968 with 40350 at 2,2,3
-Id : 40574, {_}: multiply (divide ?83055 ?83056) (inverse ?83057) =?= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15659 with 40350 at 2
-Id : 41328, {_}: multiply ?192465 (divide (inverse ?192466) (multiply ?192467 (divide ?192468 ?192469))) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Super 41245 with 40574 at 2
-Id : 85188, {_}: divide (multiply ?83055 (inverse ?83056)) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 40574 with 85061 at 2
-Id : 85202, {_}: divide (multiply ?192465 (inverse ?192466)) (multiply ?192467 (divide ?192468 ?192469)) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Demod 41328 with 85188 at 2
-Id : 85220, {_}: divide (divide ?192465 (divide (divide ?192468 ?192469) (inverse ?192466))) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85202 with 62493 at 2
-Id : 85221, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =<= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85220 with 3 at 2,1,2
-Id : 102178, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (divide ?192468 ?192469)) [192467, 192466, 192469, 192468, 192465] by Demod 85221 with 101520 at 2,2,3
-Id : 102288, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (divide (multiply ?192467 ?192468) ?192469) [192467, 192466, 192469, 192468, 192465] by Demod 102178 with 102247 at 3
-Id : 102764, {_}: divide (divide ?357685 (divide ?357684 ?357684)) (divide (multiply (divide ?357687 ?357686) ?357686) ?357687) =>= inverse (inverse ?357685) [357686, 357687, 357684, 357685] by Demod 102763 with 102288 at 2
-Id : 101094, {_}: divide (inverse (divide (divide ?5777 ?5778) ?5776)) (divide ?5778 ?5777) =>= ?5776 [5776, 5778, 5777] by Demod 1266 with 90396 at 1,2
-Id : 102237, {_}: divide ?5776 (multiply (divide ?5778 ?5777) (divide ?5777 ?5778)) =>= ?5776 [5777, 5778, 5776] by Demod 101094 with 102222 at 2
-Id : 102251, {_}: divide ?5776 (divide (multiply (divide ?5778 ?5777) ?5777) ?5778) =>= ?5776 [5777, 5778, 5776] by Demod 102237 with 102247 at 2
-Id : 102765, {_}: divide ?357685 (divide ?357684 ?357684) =>= inverse (inverse ?357685) [357684, 357685] by Demod 102764 with 102251 at 2
-Id : 102313, {_}: inverse ?36880 =<= multiply (divide (multiply (multiply ?36881 ?36882) (divide (inverse ?36882) ?36881)) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 7367 with 102309 at 1,3
-Id : 102314, {_}: inverse ?36880 =<= multiply (divide (divide (multiply (multiply ?36881 ?36882) (inverse ?36882)) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102313 with 102309 at 1,1,3
-Id : 102315, {_}: inverse ?36880 =<= multiply (divide (divide (divide (multiply ?36881 ?36882) ?36882) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102314 with 101520 at 1,1,1,3
-Id : 102533, {_}: inverse (inverse ?357905) =<= multiply (divide (divide (divide (multiply ?357906 ?357907) ?357907) ?357906) (divide ?357908 ?357905)) ?357908 [357908, 357907, 357906, 357905] by Super 102315 with 101520 at 2,1,3
-Id : 102311, {_}: ?36095 =<= multiply (divide (multiply (multiply ?36096 ?36097) (divide (inverse ?36097) ?36096)) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 7191 with 102309 at 1,3
-Id : 102312, {_}: ?36095 =<= multiply (divide (divide (multiply (multiply ?36096 ?36097) (inverse ?36097)) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102311 with 102309 at 1,1,3
-Id : 102316, {_}: ?36095 =<= multiply (divide (divide (divide (multiply ?36096 ?36097) ?36097) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102312 with 101520 at 1,1,1,3
-Id : 102664, {_}: inverse (inverse ?357905) =>= ?357905 [357905] by Demod 102533 with 102316 at 3
-Id : 103069, {_}: divide ?357685 (divide ?357684 ?357684) =>= ?357685 [357684, 357685] by Demod 102765 with 102664 at 3
-Id : 103199, {_}: inverse (divide ?359423 ?359424) =>= divide ?359424 ?359423 [359424, 359423] by Super 101098 with 103069 at 1,2
-Id : 103718, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =?= divide (multiply ?8834 (multiply ?8833 ?8832)) ?8835 [8833, 8832, 8835, 8834] by Demod 102264 with 103199 at 3
-Id : 103734, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (inverse ?13894)) (multiply ?13895 ?13894) =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 2791 with 103718 at 1,2
-Id : 40697, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (multiply ?190126 (inverse ?190127)) (inverse (multiply ?190128 ?190125)) [190128, 190127, 190126, 190125] by Super 35052 with 40350 at 1,3
-Id : 40823, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (divide ?190126 (multiply (inverse (inverse ?190125)) ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 40697 with 9976 at 3
-Id : 43409, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (divide ?190126 (multiply ?190125 ?190127)) (inverse ?190128) [190128, 190127, 190126, 190125] by Demod 40823 with 43406 at 3
-Id : 85192, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 43409 with 85061 at 3
-Id : 102170, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 85192 with 101520 at 2
-Id : 102171, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 102170 with 101520 at 1,3
-Id : 102293, {_}: divide (divide ?190126 ?190127) (multiply ?190128 ?190125) =?= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190125, 190128, 190127, 190126] by Demod 102171 with 102222 at 2
-Id : 103736, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (multiply ?13894 (inverse ?13894))) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103734 with 102293 at 2
-Id : 103737, {_}: divide (divide (divide (inverse (multiply ?13892 ?13893)) (divide (inverse ?13894) (multiply ?13892 ?13895))) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103736 with 62493 at 1,2
-Id : 40061, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (multiply ?188029 (inverse ?188030))) [188032, 188031, 188030, 188029, 188028] by Super 40043 with 39950 at 2,3
-Id : 102158, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =>= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188031, 188030, 188029, 188028] by Demod 40061 with 101520 at 2,2,3
-Id : 102302, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188029, 188031, 188030, 188028] by Demod 102158 with 102222 at 2,1,2
-Id : 103711, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =<= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30] by Demod 101099 with 103199 at 2
-Id : 103712, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =?= divide (divide ?30 (divide ?33 ?32)) ?31 [33, 32, 31, 30] by Demod 103711 with 103199 at 3
-Id : 103741, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =?= divide (divide (multiply ?188028 ?188031) (divide ?188030 ?188029)) ?188032 [188032, 188029, 188031, 188030, 188028] by Demod 102302 with 103712 at 3
-Id : 103744, {_}: divide (divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide (inverse ?13894) ?13895)) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103737 with 103741 at 1,2
-Id : 103708, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114205, 114207, 114204, 114206] by Demod 62637 with 103199 at 2
-Id : 103709, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= divide (divide ?114206 (divide (inverse ?114205) ?114207)) ?114204 [114205, 114207, 114204, 114206] by Demod 103708 with 103199 at 3
-Id : 103749, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide ?13894 (multiply ?13895 ?13894))) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103744 with 103709 at 1,2
-Id : 103750, {_}: divide (divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) (divide ?13894 ?13894)) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103749 with 103741 at 2
-Id : 103751, {_}: divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) ?13895 =>= inverse ?13893 [13895, 13893, 13892] by Demod 103750 with 103069 at 1,2
-Id : 2811, {_}: divide (divide (inverse (multiply ?14050 ?14051)) (divide (multiply ?14052 ?14053) ?14050)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Super 2771 with 3 at 1,2,1,2
-Id : 103699, {_}: divide (divide ?346092 ?346094) ?346093 =?= divide ?346092 (multiply ?346093 ?346094) [346093, 346094, 346092] by Demod 102222 with 103199 at 1,2
-Id : 103754, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =?= divide (divide (multiply ?258249 ?258254) ?258253) ?258255 [258255, 258254, 258253, 258249] by Demod 62493 with 103699 at 3
-Id : 103756, {_}: divide (divide (multiply (inverse (multiply ?14050 ?14051)) ?14050) (multiply ?14052 ?14053)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Demod 2811 with 103754 at 2
-Id : 103714, {_}: divide (divide ?54 (multiply ?55 ?56)) (divide (inverse ?56) ?55) =>= ?54 [56, 55, 54] by Demod 101095 with 103199 at 2
-Id : 103765, {_}: multiply (inverse (multiply ?14050 ?14051)) ?14050 =>= inverse ?14051 [14051, 14050] by Demod 103756 with 103714 at 2
-Id : 103766, {_}: divide (multiply (inverse ?13893) ?13895) ?13895 =>= inverse ?13893 [13895, 13893] by Demod 103751 with 103765 at 1,1,2
-Id : 103767, {_}: ?38552 =<= multiply (divide (multiply (inverse ?38553) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38553, 38552] by Demod 102318 with 103766 at 1,1,1,3
-Id : 103801, {_}: multiply ?360754 (divide ?360755 ?360756) =>= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Super 3 with 103199 at 2,3
-Id : 102172, {_}: divide (divide ?83055 ?83056) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 85188 with 101520 at 1,2
-Id : 102958, {_}: divide (divide ?358448 (inverse ?358449)) ?358450 =>= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Super 102172 with 102664 at 1,2,3
-Id : 103012, {_}: divide (multiply ?358448 ?358449) ?358450 =<= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Demod 102958 with 3 at 1,2
-Id : 104738, {_}: divide (multiply ?360754 ?360755) ?360756 =?= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Demod 103801 with 103012 at 2
-Id : 104742, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38553) ?38552) ?38555) ?38555 [38555, 38553, 38552] by Demod 103767 with 104738 at 1,3
-Id : 102256, {_}: divide (inverse ?35) (divide (multiply (divide ?36 ?37) (divide ?37 ?36)) (divide ?35 (divide ?38 ?39))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 362 with 102247 at 2
-Id : 102304, {_}: divide (inverse ?35) (divide (divide (divide ?36 ?37) (divide ?39 (multiply (divide ?37 ?36) ?38))) ?35) =>= divide ?39 ?38 [38, 39, 37, 36, 35] by Demod 102256 with 102302 at 2,2
-Id : 103730, {_}: divide (multiply (inverse ?35) (multiply ?35 (divide ?39 (multiply (divide ?37 ?36) ?38)))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 102304 with 103718 at 2
-Id : 104003, {_}: divide (multiply (inverse ?35) (divide (multiply ?35 ?39) (multiply (divide ?37 ?36) ?38))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 103730 with 103012 at 2,1,2
-Id : 104004, {_}: divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) (multiply (divide ?37 ?36) ?38)) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 104003 with 103012 at 1,2
-Id : 104036, {_}: divide (divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38) (divide ?37 ?36)) (divide ?36 ?37) =>= divide ?39 ?38 [36, 37, 38, 39, 35] by Demod 104004 with 103699 at 1,2
-Id : 103700, {_}: divide (divide ?3 (divide ?4 ?5)) (divide ?5 ?4) =>= ?3 [5, 4, 3] by Demod 101098 with 103199 at 2
-Id : 104037, {_}: divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104036 with 103700 at 2
-Id : 21134, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 20903 with 6973 at 2,1,3
-Id : 40046, {_}: inverse (divide (inverse (inverse ?108447)) (multiply ?108448 (inverse ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 21134 with 39950 at 1,2
-Id : 40707, {_}: inverse (divide (multiply ?190184 (inverse ?190185)) (multiply ?190186 (inverse ?190187))) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190187, 190186, 190185, 190184] by Super 40046 with 40350 at 1,1,2
-Id : 40813, {_}: inverse (divide (divide ?190184 (divide (inverse ?190187) (inverse ?190185))) ?190186) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190186, 190185, 190187, 190184] by Demod 40707 with 40043 at 1,2
-Id : 47405, {_}: inverse (divide (divide ?210380 (multiply (inverse ?210381) ?210382)) ?210383) =<= inverse (divide (inverse (divide (inverse ?210381) (divide ?210380 ?210382))) ?210383) [210383, 210382, 210381, 210380] by Demod 40813 with 3 at 2,1,1,2
-Id : 47459, {_}: inverse (divide (divide ?210809 (multiply (inverse (divide ?210810 (divide (divide ?210811 (divide (divide ?210812 ?210813) ?210810)) (divide ?210813 ?210812)))) ?210814)) ?210815) =>= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210813, 210812, 210811, 210810, 210809] by Super 47405 with 53 at 1,1,1,1,3
-Id : 48148, {_}: inverse (divide (divide ?212886 (multiply ?212887 ?212888)) ?212889) =<= inverse (divide (inverse (divide ?212887 (divide ?212886 ?212888))) ?212889) [212889, 212888, 212887, 212886] by Demod 47459 with 53 at 1,2,1,1,2
-Id : 48271, {_}: inverse (divide (divide ?213823 (multiply ?213824 ?213825)) (inverse ?213826)) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Super 48148 with 3 at 1,3
-Id : 48613, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Demod 48271 with 3 at 1,2
-Id : 103705, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =?= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213826, 213825, 213824, 213823] by Demod 48613 with 103199 at 1,1,3
-Id : 106200, {_}: divide (multiply ?367270 ?367271) ?367271 =>= ?367270 [367271, 367270] by Super 103069 with 104738 at 2
-Id : 106204, {_}: divide (inverse ?367290) ?367291 =<= inverse (multiply ?367291 ?367290) [367291, 367290] by Super 106200 with 103765 at 1,2
-Id : 106549, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =<= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213825, 213824, 213823, 213826] by Demod 103705 with 106204 at 2
-Id : 106550, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =?= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213824, 213823, 213826] by Demod 106549 with 106204 at 3
-Id : 47859, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =<= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210811, 210809] by Demod 47459 with 53 at 1,2,1,1,2
-Id : 102230, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =?= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210815, 210814, 210811, 210809] by Demod 47859 with 102222 at 1,3
-Id : 103696, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =<= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210814, 210811, 210809, 210815] by Demod 102230 with 103199 at 2
-Id : 103697, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =?= divide (multiply ?210815 ?210811) (divide ?210809 ?210814) [210814, 210811, 210809, 210815] by Demod 103696 with 103199 at 3
-Id : 106566, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =<= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213823, 213824, 213826] by Demod 106550 with 103697 at 2
-Id : 106567, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =?= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213825, 213823, 213824, 213826] by Demod 106566 with 103718 at 3
-Id : 106568, {_}: divide (multiply (multiply (inverse ?213826) ?213824) ?213825) ?213823 =<= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213823, 213825, 213824, 213826] by Demod 106567 with 104738 at 2
-Id : 106569, {_}: divide (multiply (multiply (inverse ?35) ?35) ?39) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104037 with 106568 at 2
-Id : 106570, {_}: ?38552 =<= multiply (divide ?38552 ?38555) ?38555 [38555, 38552] by Demod 104742 with 106569 at 1,3
-Id : 104876, {_}: divide (multiply ?363468 ?363469) ?363469 =>= ?363468 [363469, 363468] by Super 103069 with 104738 at 2
-Id : 106173, {_}: inverse ?367130 =<= divide ?367131 (multiply ?367130 ?367131) [367131, 367130] by Super 103199 with 104876 at 1,2
-Id : 106805, {_}: ?367778 =<= multiply (inverse ?367779) (multiply ?367779 ?367778) [367779, 367778] by Super 106570 with 106173 at 1,3
-Id : 106633, {_}: multiply ?367594 (multiply ?367595 ?367596) =<= divide ?367594 (divide (inverse ?367596) ?367595) [367596, 367595, 367594] by Super 3 with 106204 at 2,3
-Id : 104940, {_}: multiply (multiply ?363900 ?363901) ?363902 =<= divide ?363900 (divide (inverse ?363902) ?363901) [363902, 363901, 363900] by Super 3 with 104738 at 3
-Id : 108764, {_}: multiply ?367594 (multiply ?367595 ?367596) =?= multiply (multiply ?367594 ?367595) ?367596 [367596, 367595, 367594] by Demod 106633 with 104940 at 3
-Id : 109130, {_}: ?367778 =<= multiply (multiply (inverse ?367779) ?367779) ?367778 [367779, 367778] by Demod 106805 with 108764 at 3
-Id : 109444, {_}: a2 === a2 [] by Demod 1 with 109130 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP470-1.p
-11271: solved GRP470-1.p in 32.33802 using nrkbo
-11271: status Unsatisfiable for GRP470-1.p
-NO CLASH, using fixed ground order
-11326: Facts:
-11326: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11326: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11326: Goal:
-11326: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11326: Order:
-11326: nrkbo
-11326: Leaf order:
-11326: inverse 2 1 0
-11326: divide 7 2 0
-11326: c3 2 0 2 2,2
-11326: multiply 5 2 4 0,2
-11326: b3 2 0 2 2,1,2
-11326: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11327: Facts:
-11327: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11327: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11327: Goal:
-11327: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11327: Order:
-11327: kbo
-11327: Leaf order:
-11327: inverse 2 1 0
-11327: divide 7 2 0
-11327: c3 2 0 2 2,2
-11327: multiply 5 2 4 0,2
-11327: b3 2 0 2 2,1,2
-11327: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11328: Facts:
-11328: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11328: Id : 3, {_}:
- multiply ?7 ?8 =>= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11328: Goal:
-11328: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11328: Order:
-11328: lpo
-11328: Leaf order:
-11328: inverse 2 1 0
-11328: divide 7 2 0
-11328: c3 2 0 2 2,2
-11328: multiply 5 2 4 0,2
-11328: b3 2 0 2 2,1,2
-11328: a3 2 0 2 1,1,2
-Statistics :
-Max weight : 52
-Found proof, 38.615883s
-% SZS status Unsatisfiable for GRP471-1.p
-% SZS output start CNFRefutation for GRP471-1.p
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
-Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
-Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
-Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
-Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
-Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
-Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
-Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
-Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
-Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
-Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
-Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
-Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
-Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
-Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
-Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
-Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
-Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
-Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
-Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
-Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
-Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
-Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
-Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
-Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
-Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
-Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
-Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
-Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
-Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
-Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
-Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
-Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
-Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
-Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
-Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
-Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
-Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
-Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
-Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
-Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
-Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
-Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
-Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
-Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
-Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
-Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
-Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
-Id : 17, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (divide (divide ?76 ?77) (inverse (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78)))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Super 2 with 15 at 2,2,1,1,2
-Id : 66361, {_}: divide (inverse (divide ?259836 (divide ?259837 ?259838))) (divide (multiply (divide ?259839 ?259840) (divide ?259840 (divide ?259838 (multiply (divide (divide ?259841 ?259842) ?259843) (divide ?259843 (divide ?259839 (divide ?259842 ?259841))))))) ?259836) =>= ?259837 [259843, 259842, 259841, 259840, 259839, 259838, 259837, 259836] by Demod 17 with 3 at 1,2,2
-Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
-Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
-Id : 13153, {_}: inverse (inverse (multiply (multiply ?68629 ?68630) (inverse (multiply (divide ?68631 ?68632) ?68633)))) =<= multiply ?68629 (divide (inverse (inverse ?68630)) (multiply ?68631 (multiply (inverse ?68632) ?68633))) [68633, 68632, 68631, 68630, 68629] by Super 12858 with 12807 at 2,3
-Id : 15503, {_}: inverse (inverse (divide (multiply ?81665 ?81666) (multiply ?81667 (multiply (inverse ?81668) ?81669)))) =<= multiply ?81665 (divide (inverse (inverse ?81666)) (multiply ?81667 (multiply (inverse ?81668) ?81669))) [81669, 81668, 81667, 81666, 81665] by Demod 13153 with 12807 at 1,1,2
-Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
-Id : 15524, {_}: inverse (inverse (divide (multiply ?81857 ?81858) (multiply (multiply (divide ?81859 ?81860) (divide (divide ?81860 ?81859) (divide (multiply (inverse ?81861) ?81862) ?81863))) (multiply (inverse ?81861) ?81862)))) =>= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81862, 81861, 81860, 81859, 81858, 81857] by Super 15503 with 6973 at 2,2,3
-Id : 15656, {_}: inverse (inverse (divide (multiply ?81857 ?81858) ?81863)) =<= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81858, 81857] by Demod 15524 with 6973 at 2,1,1,2
-Id : 23797, {_}: divide (divide ?119374 (divide (inverse ?119375) (divide (inverse (inverse ?119376)) ?119377))) ?119378 =<= multiply (inverse (inverse (divide (multiply ?119374 ?119376) ?119377))) (inverse (divide ?119378 ?119375)) [119378, 119377, 119376, 119375, 119374] by Super 9552 with 15656 at 1,3
-Id : 23859, {_}: divide (divide (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) (divide (inverse ?119934) (divide (inverse (inverse ?119932)) ?119935))) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Super 23797 with 7157 at 1,1,1,1,3
-Id : 13062, {_}: inverse (inverse (divide (divide ?67961 ?67962) (multiply ?67963 (multiply (inverse ?67964) ?67965)))) =>= multiply ?67961 (multiply (inverse ?67962) (inverse (multiply (divide ?67963 ?67964) ?67965))) [67965, 67964, 67963, 67962, 67961] by Super 12770 with 12807 at 1,1,2
-Id : 16664, {_}: inverse (inverse (divide (divide ?87645 ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649)))) =>= multiply ?87645 (divide (inverse ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649))) [87649, 87648, 87647, 87646, 87645] by Demod 13062 with 12807 at 2,3
-Id : 16690, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =<= multiply ?87882 (divide (inverse ?87883) (multiply (multiply (divide ?87885 ?87886) (divide (divide ?87886 ?87885) (divide (multiply (inverse ?87887) ?87888) ?87884))) (multiply (inverse ?87887) ?87888))) [87888, 87887, 87886, 87885, 87884, 87883, 87882] by Super 16664 with 6973 at 2,1,1,2
-Id : 16778, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =>= multiply ?87882 (divide (inverse ?87883) ?87884) [87884, 87883, 87882] by Demod 16690 with 6973 at 2,2,3
-Id : 16836, {_}: multiply ?88530 (inverse (divide (divide ?88531 ?88532) ?88533)) =>= divide ?88530 (multiply ?88531 (divide (inverse ?88532) ?88533)) [88533, 88532, 88531, 88530] by Super 3 with 16778 at 2,3
-Id : 16941, {_}: divide (divide ?89130 (divide (inverse ?89131) ?89132)) (divide ?89133 ?89134) =<= divide (multiply ?89130 ?89132) (multiply ?89133 (divide (inverse ?89134) ?89131)) [89134, 89133, 89132, 89131, 89130] by Super 9552 with 16836 at 3
-Id : 17721, {_}: divide (inverse ?92223) (multiply (divide ?92224 ?92225) (divide (divide ?92225 ?92224) (divide ?92223 (divide (divide ?92226 (divide (inverse ?92227) ?92228)) (divide ?92229 ?92230))))) =>= divide (multiply ?92229 (divide (inverse ?92230) ?92227)) (multiply ?92226 ?92228) [92230, 92229, 92228, 92227, 92226, 92225, 92224, 92223] by Super 362 with 16941 at 2,2,2,2,2
-Id : 18088, {_}: divide (divide ?94725 ?94726) (divide ?94727 (divide (inverse ?94728) ?94729)) =<= divide (multiply ?94725 (divide (inverse ?94726) ?94728)) (multiply ?94727 ?94729) [94729, 94728, 94727, 94726, 94725] by Demod 17721 with 362 at 2
-Id : 18882, {_}: divide (divide ?99448 ?99449) (divide ?99450 (divide (inverse (inverse ?99451)) ?99452)) =>= divide (multiply ?99448 (multiply (inverse ?99449) ?99451)) (multiply ?99450 ?99452) [99452, 99451, 99450, 99449, 99448] by Super 18088 with 3 at 2,1,3
-Id : 18956, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =?= divide (multiply ?100120 (multiply (inverse (inverse ?100121)) ?100123)) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Super 18882 with 3 at 1,2
-Id : 19253, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =>= divide (inverse (inverse (multiply (multiply ?100120 ?100121) ?100123))) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Demod 18956 with 12858 at 1,3
-Id : 24073, {_}: divide (divide (inverse (inverse (multiply (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) ?119932))) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Demod 23859 with 19253 at 1,2
-Id : 24074, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =<= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24073 with 7157 at 1,1,1,1,2
-Id : 18174, {_}: divide (divide ?95484 (inverse ?95485)) (divide ?95486 (divide (inverse ?95487) ?95488)) =>= divide (inverse (inverse (divide (multiply ?95484 ?95485) ?95487))) (multiply ?95486 ?95488) [95488, 95487, 95486, 95485, 95484] by Super 18088 with 15656 at 1,3
-Id : 20071, {_}: divide (multiply ?105383 ?105384) (divide ?105385 (divide (inverse ?105386) ?105387)) =<= divide (inverse (inverse (divide (multiply ?105383 ?105384) ?105386))) (multiply ?105385 ?105387) [105387, 105386, 105385, 105384, 105383] by Demod 18174 with 3 at 1,2
-Id : 20108, {_}: divide (multiply (multiply (divide ?105694 ?105695) (divide (divide ?105695 ?105694) (divide ?105696 ?105697))) ?105696) (divide ?105698 (divide (inverse ?105699) ?105700)) =>= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697, 105696, 105695, 105694] by Super 20071 with 6973 at 1,1,1,1,3
-Id : 20428, {_}: divide ?105697 (divide ?105698 (divide (inverse ?105699) ?105700)) =<= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697] by Demod 20108 with 6973 at 1,2
-Id : 20476, {_}: inverse (inverse (divide (divide ?106039 (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043)) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Super 16778 with 20428 at 1,1,1,2
-Id : 20938, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Demod 20476 with 16778 at 2
-Id : 24149, {_}: inverse (inverse (multiply (multiply ?120312 (divide ?120313 ?120314)) (inverse (divide ?120315 ?120316)))) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120316, 120315, 120314, 120313, 120312] by Super 12858 with 24074 at 2,3
-Id : 24438, {_}: inverse (inverse (divide (divide ?120312 (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315)) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24149 with 9552 at 1,1,2
-Id : 24439, {_}: multiply ?120312 (divide (inverse (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24438 with 16778 at 2
-Id : 33216, {_}: inverse (divide (divide (inverse (inverse ?156723)) (multiply (inverse ?156724) ?156725)) ?156726) =<= multiply (multiply (divide (inverse ?156727) ?156728) (divide (multiply ?156728 ?156727) (multiply ?156729 (divide (inverse (divide (inverse ?156724) (divide ?156723 ?156725))) ?156726)))) ?156729 [156729, 156728, 156727, 156726, 156725, 156724, 156723] by Super 7337 with 24439 at 2,2,1,3
-Id : 33721, {_}: inverse (divide (divide (inverse (inverse ?158945)) (multiply (inverse ?158946) ?158947)) ?158948) =>= inverse (divide (inverse (divide (inverse ?158946) (divide ?158945 ?158947))) ?158948) [158948, 158947, 158946, 158945] by Demod 33216 with 7337 at 3
-Id : 33722, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =<= inverse (divide (inverse (divide (inverse (divide ?158954 (divide (divide ?158951 (divide (divide ?158955 ?158956) ?158954)) (divide ?158956 ?158955)))) (divide ?158950 ?158952))) ?158953) [158956, 158955, 158954, 158953, 158952, 158951, 158950] by Super 33721 with 53 at 1,2,1,1,2
-Id : 34010, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =>= inverse (divide (inverse (divide ?158951 (divide ?158950 ?158952))) ?158953) [158953, 158952, 158951, 158950] by Demod 33722 with 53 at 1,1,1,1,3
-Id : 34077, {_}: inverse (inverse (divide (inverse (divide ?159790 (divide ?159791 ?159792))) ?159793)) =<= multiply (inverse (inverse ?159791)) (divide (inverse (multiply ?159790 ?159792)) ?159793) [159793, 159792, 159791, 159790] by Super 16778 with 34010 at 1,2
-Id : 34441, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= inverse (inverse (divide (inverse (divide ?106040 (divide (divide ?106039 ?106041) ?106042))) ?106043)) [106043, 106042, 106041, 106040, 106039] by Demod 20938 with 34077 at 3
-Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
-Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
-Id : 43649, {_}: multiply ?191130 (divide (inverse (divide ?191131 (divide (inverse ?191132) (multiply (divide ?191133 ?191134) (divide ?191134 (divide ?191135 (multiply (divide (divide ?191136 ?191137) ?191138) (divide ?191138 (divide ?191133 (divide ?191137 ?191136)))))))))) (divide ?191135 ?191131)) =>= inverse (inverse (divide ?191130 ?191132)) [191138, 191137, 191136, 191135, 191134, 191133, 191132, 191131, 191130] by Super 34441 with 38 at 1,1,3
-Id : 44429, {_}: multiply ?191130 (inverse ?191132) =<= inverse (inverse (divide ?191130 ?191132)) [191132, 191130] by Demod 43649 with 38 at 2,2
-Id : 44886, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (multiply ?119933 (inverse ?119935)) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24074 with 44429 at 1,3
-Id : 44891, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (divide (inverse ?119934) (inverse ?119935))) ?119936 [119936, 119935, 119934, 119933] by Demod 44886 with 9552 at 3
-Id : 44892, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (multiply (inverse ?119934) ?119935)) ?119936 [119936, 119935, 119934, 119933] by Demod 44891 with 3 at 2,1,3
-Id : 66804, {_}: divide (inverse (divide ?265003 (divide (divide ?265004 (multiply (inverse ?265005) ?265006)) ?265007))) (divide (multiply (divide ?265008 ?265009) (divide ?265009 (divide ?265007 (multiply (divide (divide ?265010 ?265011) ?265012) (divide ?265012 (divide ?265008 (divide ?265011 ?265010))))))) ?265003) =>= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265012, 265011, 265010, 265009, 265008, 265007, 265006, 265005, 265004, 265003] by Super 66361 with 44892 at 2,1,1,2
-Id : 39, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (multiply (divide ?76 ?77) (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Demod 17 with 3 at 1,2,2
-Id : 67572, {_}: divide ?265004 (multiply (inverse ?265005) ?265006) =<= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265006, 265005, 265004] by Demod 66804 with 39 at 2
-Id : 67796, {_}: divide (inverse (divide ?266802 (divide ?266803 (multiply (inverse ?266804) ?266805)))) (divide (divide (inverse ?266805) (inverse ?266804)) ?266802) =>= inverse (inverse ?266803) [266805, 266804, 266803, 266802] by Super 12 with 67572 at 2,1,1,2
-Id : 68093, {_}: ?266803 =<= inverse (inverse ?266803) [266803] by Demod 67796 with 12 at 2
-Id : 68404, {_}: multiply (multiply ?67174 ?67175) ?67176 =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 68093 at 2
-Id : 68405, {_}: multiply (multiply ?67174 ?67175) ?67176 =?= multiply ?67174 (multiply ?67175 ?67176) [67176, 67175, 67174] by Demod 68404 with 68093 at 1,2,3
-Id : 68861, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 68405 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP471-1.p
-11326: solved GRP471-1.p in 19.353208 using nrkbo
-11326: status Unsatisfiable for GRP471-1.p
-NO CLASH, using fixed ground order
-11333: Facts:
-11333: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11333: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11333: Goal:
-11333: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11333: Order:
-11333: nrkbo
-11333: Leaf order:
-11333: divide 7 2 0
-11333: b1 2 0 2 1,1,3
-11333: multiply 3 2 2 0,2
-11333: inverse 4 1 2 0,1,2
-11333: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11334: Facts:
-11334: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11334: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11334: Goal:
-11334: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11334: Order:
-11334: kbo
-11334: Leaf order:
-11334: divide 7 2 0
-11334: b1 2 0 2 1,1,3
-11334: multiply 3 2 2 0,2
-11334: inverse 4 1 2 0,1,2
-11334: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11335: Facts:
-11335: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11335: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11335: Goal:
-11335: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11335: Order:
-11335: lpo
-11335: Leaf order:
-11335: divide 7 2 0
-11335: b1 2 0 2 1,1,3
-11335: multiply 3 2 2 0,2
-11335: inverse 4 1 2 0,1,2
-11335: a1 2 0 2 1,1,2
-% SZS status Timeout for GRP475-1.p
-NO CLASH, using fixed ground order
-11373: Facts:
-11373: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11373: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11373: Goal:
-11373: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11373: Order:
-11373: nrkbo
-11373: Leaf order:
-11373: divide 7 2 0
-11373: a2 2 0 2 2,2
-11373: multiply 3 2 2 0,2
-11373: inverse 3 1 1 0,1,1,2
-11373: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11374: Facts:
-11374: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11374: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11374: Goal:
-11374: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11374: Order:
-11374: kbo
-11374: Leaf order:
-11374: divide 7 2 0
-11374: a2 2 0 2 2,2
-11374: multiply 3 2 2 0,2
-11374: inverse 3 1 1 0,1,1,2
-11374: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11375: Facts:
-11375: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11375: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11375: Goal:
-11375: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11375: Order:
-11375: lpo
-11375: Leaf order:
-11375: divide 7 2 0
-11375: a2 2 0 2 2,2
-11375: multiply 3 2 2 0,2
-11375: inverse 3 1 1 0,1,1,2
-11375: b2 2 0 2 1,1,1,2
-Statistics :
-Max weight : 49
-Found proof, 60.308770s
-% SZS status Unsatisfiable for GRP476-1.p
-% SZS output start CNFRefutation for GRP476-1.p
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
-Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
-Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
-Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
-Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
-Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
-Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
-Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
-Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
-Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
-Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
-Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
-Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
-Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
-Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
-Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
-Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
-Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
-Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
-Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
-Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
-Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
-Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
-Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
-Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
-Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
-Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
-Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
-Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
-Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
-Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
-Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
-Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
-Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
-Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
-Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
-Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
-Id : 36954, {_}: inverse (divide (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 36094 with 36681 at 1,1,2
-Id : 37568, {_}: divide ?167565 (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) =>= ?167565 [167567, 167566, 167565] by Demod 36954 with 37291 at 2
-Id : 33466, {_}: ?158075 =<= multiply (multiply ?158075 (divide ?158076 ?158077)) (divide ?158077 ?158076) [158077, 158076, 158075] by Demod 33087 with 2 at 2
-Id : 33531, {_}: ?158517 =<= multiply (multiply ?158517 (multiply ?158518 ?158519)) (divide (inverse ?158519) ?158518) [158519, 158518, 158517] by Super 33466 with 3 at 2,1,3
-Id : 36952, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (divide ?158518 (inverse ?158519)) [158519, 158518, 158517] by Demod 33531 with 36681 at 3
-Id : 36955, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (multiply ?158518 ?158519) [158519, 158518, 158517] by Demod 36952 with 3 at 2,3
-Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
-Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
-Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
-Id : 38144, {_}: ?175420 =<= divide (multiply ?175420 (multiply (divide ?175421 ?175422) ?175422)) ?175421 [175422, 175421, 175420] by Super 36955 with 36819 at 2,3
-Id : 38311, {_}: ?175420 =<= divide (multiply ?175420 ?175421) ?175421 [175421, 175420] by Demod 38144 with 36819 at 2,1,3
-Id : 38590, {_}: divide ?177333 (divide (divide (multiply ?177334 ?177335) ?177335) ?177334) =>= ?177333 [177335, 177334, 177333] by Super 37568 with 38311 at 2,2,2
-Id : 38627, {_}: divide ?177333 (divide ?177334 ?177334) =>= ?177333 [177334, 177333] by Demod 38590 with 38311 at 1,2,2
-Id : 41488, {_}: divide (divide ?193733 ?193733) ?193734 =>= inverse ?193734 [193734, 193733] by Super 37291 with 38627 at 1,3
-Id : 42000, {_}: multiply (divide ?195057 ?195057) ?195058 =>= inverse (inverse ?195058) [195058, 195057] by Super 3 with 41488 at 3
-Id : 38603, {_}: divide ?177417 (multiply ?177418 ?177417) =>= inverse ?177418 [177418, 177417] by Super 37291 with 38311 at 1,3
-Id : 40108, {_}: divide (multiply ?188666 ?188667) ?188667 =>= inverse (inverse ?188666) [188667, 188666] by Super 37291 with 38603 at 1,3
-Id : 40636, {_}: ?188666 =<= inverse (inverse ?188666) [188666] by Demod 40108 with 38311 at 2
-Id : 43036, {_}: multiply (divide ?197334 ?197334) ?197335 =>= ?197335 [197335, 197334] by Demod 42000 with 40636 at 3
-Id : 43063, {_}: multiply (multiply (inverse ?197470) ?197470) ?197471 =>= ?197471 [197471, 197470] by Super 43036 with 3 at 1,2
-Id : 47549, {_}: a2 =?= a2 [] by Demod 1 with 43063 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP476-1.p
-11374: solved GRP476-1.p in 30.053878 using kbo
-11374: status Unsatisfiable for GRP476-1.p
-NO CLASH, using fixed ground order
-11392: Facts:
-11392: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11392: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11392: Goal:
-11392: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11392: Order:
-11392: nrkbo
-11392: Leaf order:
-11392: inverse 2 1 0
-11392: divide 7 2 0
-11392: c3 2 0 2 2,2
-11392: multiply 5 2 4 0,2
-11392: b3 2 0 2 2,1,2
-11392: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11393: Facts:
-11393: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11393: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11393: Goal:
-11393: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11393: Order:
-11393: kbo
-11393: Leaf order:
-11393: inverse 2 1 0
-11393: divide 7 2 0
-11393: c3 2 0 2 2,2
-11393: multiply 5 2 4 0,2
-11393: b3 2 0 2 2,1,2
-11393: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11395: Facts:
-11395: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11395: Id : 3, {_}:
- multiply ?7 ?8 =>= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11395: Goal:
-11395: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11395: Order:
-11395: lpo
-11395: Leaf order:
-11395: inverse 2 1 0
-11395: divide 7 2 0
-11395: c3 2 0 2 2,2
-11395: multiply 5 2 4 0,2
-11395: b3 2 0 2 2,1,2
-11395: a3 2 0 2 1,1,2
-Statistics :
-Max weight : 49
-Found proof, 65.047626s
-% SZS status Unsatisfiable for GRP477-1.p
-% SZS output start CNFRefutation for GRP477-1.p
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
-Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
-Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
-Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
-Id : 2216, {_}: divide (divide (inverse (divide (divide (divide (inverse ?9957) ?9958) ?9959) ?9960)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9960, 9959, 9958, 9957] by Super 2201 with 3 at 2,1,2
-Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
-Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
-Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
-Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
-Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
-Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
-Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
-Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
-Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
-Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
-Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
-Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
-Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
-Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
-Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
-Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
-Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
-Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
-Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
-Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
-Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
-Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
-Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
-Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
-Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
-Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
-Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
-Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
-Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
-Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
-Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
-Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
-Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
-Id : 37631, {_}: divide (divide (divide ?9960 (divide (divide (inverse ?9957) ?9958) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9958, 9957, 9960] by Demod 2216 with 37291 at 1,1,2
-Id : 37745, {_}: divide ?174363 ?174364 =<= inverse (divide ?174364 ?174363) [174364, 174363] by Demod 37087 with 3370 at 2
-Id : 37810, {_}: divide (inverse ?174753) ?174754 =>= inverse (multiply ?174754 ?174753) [174754, 174753] by Super 37745 with 3 at 1,3
-Id : 38028, {_}: divide (divide (divide ?9960 (divide (inverse (multiply ?9958 ?9957)) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9957, 9958, 9960] by Demod 37631 with 37810 at 1,2,1,1,2
-Id : 38029, {_}: divide (divide (divide ?9960 (inverse (multiply ?9959 (multiply ?9958 ?9957)))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38028 with 37810 at 2,1,1,2
-Id : 38096, {_}: divide (divide (multiply ?9960 (multiply ?9959 (multiply ?9958 ?9957))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38029 with 3 at 1,1,2
-Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
-Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
-Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
-Id : 51854, {_}: divide (divide ?212601 (multiply ?212602 ?212603)) ?212604 =>= divide ?212601 (multiply ?212604 (multiply ?212602 ?212603)) [212604, 212603, 212602, 212601] by Super 38096 with 36819 at 1,1,2
-Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
-Id : 1822, {_}: multiply (divide (inverse (divide (divide (divide ?7521 ?7522) (inverse ?7523)) ?7524)) (divide ?7522 ?7521)) ?7523 =>= ?7524 [7524, 7523, 7522, 7521] by Super 18 with 20 at 1,2
-Id : 2348, {_}: multiply (divide (inverse (divide (multiply (divide ?10333 ?10334) ?10335) ?10336)) (divide ?10334 ?10333)) ?10335 =>= ?10336 [10336, 10335, 10334, 10333] by Demod 1822 with 3 at 1,1,1,1,2
-Id : 2690, {_}: multiply (divide (inverse (multiply (multiply (divide ?11645 ?11646) ?11647) ?11648)) (divide ?11646 ?11645)) ?11647 =>= inverse ?11648 [11648, 11647, 11646, 11645] by Super 2348 with 3 at 1,1,1,2
-Id : 2723, {_}: multiply (divide (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (divide (inverse ?11879) ?11878)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Super 2690 with 3 at 1,1,1,1,1,2
-Id : 38038, {_}: multiply (inverse (multiply (divide (inverse ?11879) ?11878) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11878, 11879] by Demod 2723 with 37810 at 1,2
-Id : 38039, {_}: multiply (inverse (multiply (inverse (multiply ?11878 ?11879)) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38038 with 37810 at 1,1,1,2
-Id : 38184, {_}: multiply (inverse ?175473) ?175474 =<= inverse (multiply (inverse ?175474) ?175473) [175474, 175473] by Super 3 with 37810 at 3
-Id : 38716, {_}: multiply (multiply (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (multiply ?11878 ?11879)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38039 with 38184 at 1,2
-Id : 51866, {_}: divide (divide ?212677 (inverse ?212678)) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Super 51854 with 38716 at 2,1,2
-Id : 52301, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Demod 51866 with 3 at 1,2
-Id : 52302, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (inverse ?212678)) [212679, 212678, 212677] by Demod 52301 with 38716 at 2,2,3
-Id : 38247, {_}: divide ?175863 (inverse ?175864) =<= inverse (inverse (multiply ?175863 ?175864)) [175864, 175863] by Super 37291 with 37810 at 1,3
-Id : 38843, {_}: multiply ?176435 ?176436 =<= inverse (inverse (multiply ?176435 ?176436)) [176436, 176435] by Demod 38247 with 3 at 2
-Id : 3670, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?16718) ?16719) ?16720) ?16721)) (multiply ?16719 ?16718)) ?16720 =>= ?16721 [16721, 16720, 16719, 16718] by Super 2348 with 3 at 2,1,2
-Id : 3706, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?16981) ?16982) ?16983) ?16984)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16984, 16983, 16982, 16981] by Super 3670 with 3 at 1,1,1,1,1,2
-Id : 37609, {_}: multiply (divide (divide ?16984 (multiply (multiply (inverse ?16981) ?16982) ?16983)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16983, 16982, 16981, 16984] by Demod 3706 with 37291 at 1,1,2
-Id : 38847, {_}: multiply (divide (divide ?176447 (multiply (multiply (inverse ?176448) ?176449) ?176450)) (multiply (inverse ?176449) ?176448)) ?176450 =>= inverse (inverse ?176447) [176450, 176449, 176448, 176447] by Super 38843 with 37609 at 1,1,3
-Id : 38880, {_}: ?176447 =<= inverse (inverse ?176447) [176447] by Demod 38847 with 37609 at 2
-Id : 40331, {_}: multiply ?187278 (inverse ?187279) =>= divide ?187278 ?187279 [187279, 187278] by Super 3 with 38880 at 2,3
-Id : 52303, {_}: divide (multiply ?212677 ?212678) ?212679 =>= divide ?212677 (divide ?212679 ?212678) [212679, 212678, 212677] by Demod 52302 with 40331 at 2,3
-Id : 53261, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (divide (inverse ?214474) ?214473) [214474, 214473, 214472] by Super 3 with 52303 at 3
-Id : 53437, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (inverse (multiply ?214473 ?214474)) [214474, 214473, 214472] by Demod 53261 with 37810 at 2,3
-Id : 53438, {_}: multiply (multiply ?214472 ?214473) ?214474 =>= multiply ?214472 (multiply ?214473 ?214474) [214474, 214473, 214472] by Demod 53437 with 3 at 3
-Id : 53834, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 53438 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP477-1.p
-11393: solved GRP477-1.p in 32.410025 using kbo
-11393: status Unsatisfiable for GRP477-1.p
-NO CLASH, using fixed ground order
-11411: Facts:
-11411: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11411: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11411: Goal:
-11411: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11411: Order:
-11411: nrkbo
-11411: Leaf order:
-11411: divide 7 2 0
-11411: b1 2 0 2 1,1,3
-11411: multiply 3 2 2 0,2
-11411: inverse 4 1 2 0,1,2
-11411: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11412: Facts:
-11412: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11412: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11412: Goal:
-11412: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11412: Order:
-11412: kbo
-11412: Leaf order:
-11412: divide 7 2 0
-11412: b1 2 0 2 1,1,3
-11412: multiply 3 2 2 0,2
-11412: inverse 4 1 2 0,1,2
-11412: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11413: Facts:
-11413: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11413: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11413: Goal:
-11413: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-11413: Order:
-11413: lpo
-11413: Leaf order:
-11413: divide 7 2 0
-11413: b1 2 0 2 1,1,3
-11413: multiply 3 2 2 0,2
-11413: inverse 4 1 2 0,1,2
-11413: a1 2 0 2 1,1,2
-% SZS status Timeout for GRP478-1.p
-NO CLASH, using fixed ground order
-11446: Facts:
-11446: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11446: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11446: Goal:
-11446: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11446: Order:
-11446: nrkbo
-11446: Leaf order:
-11446: divide 7 2 0
-11446: a2 2 0 2 2,2
-11446: multiply 3 2 2 0,2
-11446: inverse 3 1 1 0,1,1,2
-11446: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11447: Facts:
-11447: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11447: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11447: Goal:
-11447: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11447: Order:
-11447: kbo
-11447: Leaf order:
-11447: divide 7 2 0
-11447: a2 2 0 2 2,2
-11447: multiply 3 2 2 0,2
-11447: inverse 3 1 1 0,1,1,2
-11447: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11448: Facts:
-11448: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11448: Id : 3, {_}:
- multiply ?7 ?8 =?= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11448: Goal:
-11448: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-11448: Order:
-11448: lpo
-11448: Leaf order:
-11448: divide 7 2 0
-11448: a2 2 0 2 2,2
-11448: multiply 3 2 2 0,2
-11448: inverse 3 1 1 0,1,1,2
-11448: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP479-1.p
-NO CLASH, using fixed ground order
-11491: Facts:
-NO CLASH, using fixed ground order
-11492: Facts:
-11492: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11492: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11492: Goal:
-11492: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11492: Order:
-11492: kbo
-11492: Leaf order:
-11492: inverse 2 1 0
-11492: divide 7 2 0
-11492: c3 2 0 2 2,2
-11492: multiply 5 2 4 0,2
-11492: b3 2 0 2 2,1,2
-11492: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11493: Facts:
-11493: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11493: Id : 3, {_}:
- multiply ?7 ?8 =>= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11493: Goal:
-11493: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11493: Order:
-11493: lpo
-11493: Leaf order:
-11493: inverse 2 1 0
-11493: divide 7 2 0
-11493: c3 2 0 2 2,2
-11493: multiply 5 2 4 0,2
-11493: b3 2 0 2 2,1,2
-11493: a3 2 0 2 1,1,2
-11491: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-11491: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-11491: Goal:
-11491: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-11491: Order:
-11491: nrkbo
-11491: Leaf order:
-11491: inverse 2 1 0
-11491: divide 7 2 0
-11491: c3 2 0 2 2,2
-11491: multiply 5 2 4 0,2
-11491: b3 2 0 2 2,1,2
-11491: a3 2 0 2 1,1,2
-Statistics :
-Max weight : 78
-Found proof, 69.885629s
-% SZS status Unsatisfiable for GRP480-1.p
-% SZS output start CNFRefutation for GRP480-1.p
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
-Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2
-Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2
-Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
-Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
-Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
-Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
-Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
-Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
-Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
-Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
-Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
-Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
-Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
-Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
-Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
-Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
-Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
-Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
-Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
-Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
-Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
-Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
-Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
-Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
-Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
-Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
-Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
-Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
-Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
-Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
-Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
-Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
-Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
-Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
-Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
-Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
-Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
-Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
-Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
-Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
-Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
-Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
-Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
-Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
-Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
-Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
-Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
-Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
-Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
-Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
-Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
-Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
-Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
-Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
-Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
-Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
-Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
-Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
-Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
-Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
-Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
-Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
-Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
-Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
-Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
-Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
-Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
-Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
-Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
-Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
-Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
-Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
-Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
-Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
-Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
-Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
-Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
-Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
-Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
-Id : 102474, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
-Id : 102475, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102474 with 101980 at 2,2
-Id : 102476, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102475 at 2,3
-Id : 102520, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102476 with 101980 at 2,3
-Id : 102785, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102520 with 102475 at 1,2
-Id : 102786, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102785 with 102475 at 3
-Id : 104734, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102786 at 1,2
-Id : 104735, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104734 with 102786 at 3
-Id : 104736, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 212] by Demod 104735 with 100849 at 2,1,2
-Id : 104737, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104736 with 100849 at 2,3
-Id : 104738, {_}: multiply (multiply ?212 ?211) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104737 with 3 at 1,2
-Id : 104739, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) ?215 [215, 213, 211, 212] by Demod 104738 with 3 at 3
-Id : 104774, {_}: multiply (multiply ?542474 ?542475) ?542476 =<= multiply (divide ?542474 (divide ?542477 (multiply ?542475 ?542476))) ?542477 [542477, 542476, 542475, 542474] by Demod 104738 with 3 at 3
-Id : 104783, {_}: multiply (multiply ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Super 104774 with 101386 at 2,2,1,3
-Id : 102917, {_}: multiply ?539648 (divide ?539649 ?539650) =>= divide ?539648 (divide ?539650 ?539649) [539650, 539649, 539648] by Super 102475 with 102786 at 2,2
-Id : 104878, {_}: multiply (divide ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Demod 104783 with 102917 at 1,2
-Id : 104879, {_}: multiply ?542524 ?542526 =<= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542524] by Demod 104878 with 93111 at 1,2
-Id : 107171, {_}: multiply (multiply ?212 ?211) ?213 =?= multiply ?212 (multiply ?211 ?213) [213, 211, 212] by Demod 104739 with 104879 at 3
-Id : 107392, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 107171 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP480-1.p
-11491: solved GRP480-1.p in 34.906181 using nrkbo
-11491: status Unsatisfiable for GRP480-1.p
-NO CLASH, using fixed ground order
-11510: Facts:
-11510: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11510: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11510: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11510: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11510: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11510: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11510: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11510: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11510: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-11510: Goal:
-11510: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-11510: Order:
-11510: nrkbo
-11510: Leaf order:
-11510: meet 17 2 4 0,2
-11510: join 19 2 4 0,2,2
-11510: c 2 0 2 2,2,2
-11510: b 4 0 4 1,2,2
-11510: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-11511: Facts:
-11511: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11511: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11511: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11511: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11511: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11511: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11511: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11511: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11511: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-11511: Goal:
-11511: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-11511: Order:
-11511: kbo
-11511: Leaf order:
-11511: meet 17 2 4 0,2
-11511: join 19 2 4 0,2,2
-11511: c 2 0 2 2,2,2
-11511: b 4 0 4 1,2,2
-11511: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-11512: Facts:
-11512: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11512: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11512: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11512: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11512: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11512: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11512: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11512: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11512: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-11512: Goal:
-11512: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-11512: Order:
-11512: lpo
-11512: Leaf order:
-11512: meet 17 2 4 0,2
-11512: join 19 2 4 0,2,2
-11512: c 2 0 2 2,2,2
-11512: b 4 0 4 1,2,2
-11512: a 4 0 4 1,2
-% SZS status Timeout for LAT168-1.p
-NO CLASH, using fixed ground order
-11539: Facts:
-11539: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11539: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11539: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11539: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11539: Goal:
-11539: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-11539: Order:
-11539: nrkbo
-11539: Leaf order:
-11539: not 2 1 0
-11539: truth 4 0 1 3
-11539: implies 18 2 5 0,2
-11539: b 3 0 3 2,1,1,2
-11539: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-11540: Facts:
-11540: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11540: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11540: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11540: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11540: Goal:
-11540: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-11540: Order:
-11540: kbo
-11540: Leaf order:
-11540: not 2 1 0
-11540: truth 4 0 1 3
-11540: implies 18 2 5 0,2
-11540: b 3 0 3 2,1,1,2
-11540: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-11541: Facts:
-11541: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11541: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11541: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11541: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11541: Goal:
-11541: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-11541: Order:
-11541: lpo
-11541: Leaf order:
-11541: not 2 1 0
-11541: truth 4 0 1 3
-11541: implies 18 2 5 0,2
-11541: b 3 0 3 2,1,1,2
-11541: a 3 0 3 1,1,1,2
-% SZS status Timeout for LCL109-2.p
-NO CLASH, using fixed ground order
-11558: Facts:
-11558: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11558: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11558: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11558: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11558: Goal:
-11558: Id : 1, {_}:
- implies x (implies y z) =>= implies y (implies x z)
- [] by prove_wajsberg_lemma
-11558: Order:
-11558: nrkbo
-11558: Leaf order:
-11558: not 2 1 0
-11558: truth 3 0 0
-11558: implies 17 2 4 0,2
-11558: z 2 0 2 2,2,2
-11558: y 2 0 2 1,2,2
-11558: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11559: Facts:
-11559: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11559: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11559: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11559: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11559: Goal:
-11559: Id : 1, {_}:
- implies x (implies y z) =>= implies y (implies x z)
- [] by prove_wajsberg_lemma
-11559: Order:
-11559: kbo
-11559: Leaf order:
-11559: not 2 1 0
-11559: truth 3 0 0
-11559: implies 17 2 4 0,2
-11559: z 2 0 2 2,2,2
-11559: y 2 0 2 1,2,2
-11559: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11560: Facts:
-11560: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11560: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11560: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11560: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11560: Goal:
-11560: Id : 1, {_}:
- implies x (implies y z) =>= implies y (implies x z)
- [] by prove_wajsberg_lemma
-11560: Order:
-11560: lpo
-11560: Leaf order:
-11560: not 2 1 0
-11560: truth 3 0 0
-11560: implies 17 2 4 0,2
-11560: z 2 0 2 2,2,2
-11560: y 2 0 2 1,2,2
-11560: x 2 0 2 1,2
-% SZS status Timeout for LCL138-1.p
-NO CLASH, using fixed ground order
-11593: Facts:
-11593: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11593: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11593: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11593: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11593: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-11593: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-11593: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-11593: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-11593: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-11593: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-11593: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-11593: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-11593: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-11593: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-11593: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-11593: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-11593: Goal:
-11593: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-11593: Order:
-11593: nrkbo
-11593: Leaf order:
-11593: falsehood 1 0 0
-11593: and_star 7 2 0
-11593: and 9 2 0
-11593: or 10 2 0
-11593: not 12 1 0
-11593: implies 14 2 0
-11593: xor 7 2 4 0,2
-11593: y 2 0 2 2,2,2
-11593: truth 6 0 2 1,2,2
-11593: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11594: Facts:
-11594: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11594: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11594: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11594: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11594: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-11594: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-11594: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-11594: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-11594: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-11594: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-11594: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-11594: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-11594: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-11594: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-11594: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-11594: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-11594: Goal:
-11594: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-11594: Order:
-11594: kbo
-11594: Leaf order:
-11594: falsehood 1 0 0
-11594: and_star 7 2 0
-11594: and 9 2 0
-11594: or 10 2 0
-11594: not 12 1 0
-11594: implies 14 2 0
-11594: xor 7 2 4 0,2
-11594: y 2 0 2 2,2,2
-11594: truth 6 0 2 1,2,2
-11594: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11595: Facts:
-11595: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-11595: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-11595: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-11595: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-11595: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-11595: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-11595: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-11595: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-11595: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-11595: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-11595: Id : 12, {_}:
- xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-11595: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-11595: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-11595: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-11595: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-11595: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-11595: Goal:
-11595: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-11595: Order:
-11595: lpo
-11595: Leaf order:
-11595: falsehood 1 0 0
-11595: and_star 7 2 0
-11595: and 9 2 0
-11595: or 10 2 0
-11595: not 12 1 0
-11595: implies 14 2 0
-11595: xor 7 2 4 0,2
-11595: y 2 0 2 2,2,2
-11595: truth 6 0 2 1,2,2
-11595: x 2 0 2 1,2
-Statistics :
-Max weight : 25
-Found proof, 7.279985s
-% SZS status Unsatisfiable for LCL159-1.p
-% SZS output start CNFRefutation for LCL159-1.p
-Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
-Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
-Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112
-Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
-Id : 17, {_}: not truth =>= falsehood [] by false_definition
-Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
-Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
-Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
-Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
-Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
-Id : 12, {_}: xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
-Id : 207, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
-Id : 212, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 207 at 1,3
-Id : 213, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 212 with 207 at 2,3
-Id : 219, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 207 at 2
-Id : 220, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 219 with 207 at 3
-Id : 240, {_}: or truth ?463 =<= implies falsehood ?463 [463] by Super 6 with 17 at 1,3
-Id : 286, {_}: implies (implies ?477 falsehood) falsehood =>= implies (or truth ?477) ?477 [477] by Super 4 with 240 at 1,3
-Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
-Id : 784, {_}: implies (implies ?990 truth) (implies ?991 (implies ?990 ?991)) =>= truth [991, 990] by Super 20 with 2 at 1,2,2
-Id : 785, {_}: implies (implies truth truth) (implies ?993 ?993) =>= truth [993] by Super 784 with 2 at 2,2,2
-Id : 818, {_}: implies truth (implies ?993 ?993) =>= truth [993] by Demod 785 with 2 at 1,2
-Id : 819, {_}: implies ?993 ?993 =>= truth [993] by Demod 818 with 2 at 2
-Id : 870, {_}: implies (implies (implies ?1070 ?1070) ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071, 1070] by Super 22 with 819 at 2,1,2,2
-Id : 898, {_}: implies (implies truth ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071] by Demod 870 with 819 at 1,1,2
-Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3
-Id : 864, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 819 at 3
-Id : 899, {_}: implies (implies truth ?1071) truth =>= truth [1071] by Demod 898 with 864 at 2,2
-Id : 900, {_}: implies ?1071 truth =>= truth [1071] by Demod 899 with 2 at 1,2
-Id : 980, {_}: or ?1117 truth =>= truth [1117] by Super 6 with 900 at 3
-Id : 1078, {_}: or truth ?1157 =>= truth [1157] by Super 8 with 980 at 3
-Id : 1116, {_}: implies (implies ?477 falsehood) falsehood =>= implies truth ?477 [477] by Demod 286 with 1078 at 1,3
-Id : 1117, {_}: implies (implies ?477 falsehood) falsehood =>= ?477 [477] by Demod 1116 with 2 at 3
-Id : 218, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 207 at 2
-Id : 239, {_}: and_star truth ?461 =<= not (or falsehood (not ?461)) [461] by Super 218 with 17 at 1,1,3
-Id : 517, {_}: or (or falsehood (not ?805)) ?806 =<= implies (and_star truth ?805) ?806 [806, 805] by Super 6 with 239 at 1,3
-Id : 1565, {_}: or falsehood (or (not ?1468) ?1469) =<= implies (and_star truth ?1468) ?1469 [1469, 1468] by Demod 517 with 7 at 2
-Id : 1566, {_}: or falsehood (or (not ?1471) ?1472) =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Super 1565 with 220 at 1,3
-Id : 525, {_}: or falsehood (or (not ?805) ?806) =<= implies (and_star truth ?805) ?806 [806, 805] by Demod 517 with 7 at 2
-Id : 520, {_}: and_star truth ?814 =<= not (or falsehood (not ?814)) [814] by Super 218 with 17 at 1,1,3
-Id : 521, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 520 with 17 at 2,1,3
-Id : 564, {_}: or (or falsehood falsehood) ?828 =<= implies (and_star truth truth) ?828 [828] by Super 6 with 521 at 1,3
-Id : 589, {_}: or falsehood (or falsehood ?828) =<= implies (and_star truth truth) ?828 [828] by Demod 564 with 7 at 2
-Id : 1273, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 1117 with 589 at 1,2
-Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
-Id : 241, {_}: implies (or ?465 falsehood) (implies truth ?465) =>= truth [465] by Super 69 with 17 at 2,1,2
-Id : 260, {_}: implies (or ?465 falsehood) ?465 =>= truth [465] by Demod 241 with 2 at 2,2
-Id : 1322, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 1117 with 260 at 1,2
-Id : 1344, {_}: falsehood =<= or falsehood falsehood [] by Demod 1322 with 2 at 2
-Id : 1375, {_}: or falsehood ?1348 =<= or falsehood (or falsehood ?1348) [1348] by Super 7 with 1344 at 1,2
-Id : 2080, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 1273 with 1375 at 1,2
-Id : 2081, {_}: truth =<= and_star truth truth [] by Demod 2080 with 260 at 2
-Id : 2088, {_}: or falsehood (or (not truth) ?1976) =<= implies truth ?1976 [1976] by Super 525 with 2081 at 1,3
-Id : 2092, {_}: or falsehood (or falsehood ?1976) =<= implies truth ?1976 [1976] by Demod 2088 with 17 at 1,2,2
-Id : 2093, {_}: or falsehood (or falsehood ?1976) =>= ?1976 [1976] by Demod 2092 with 2 at 3
-Id : 2094, {_}: or falsehood ?1976 =>= ?1976 [1976] by Demod 2093 with 1375 at 2
-Id : 2619, {_}: or (not ?1471) ?1472 =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Demod 1566 with 2094 at 2
-Id : 2636, {_}: implies (or (not ?2581) falsehood) falsehood =>= and_star ?2581 truth [2581] by Super 1117 with 2619 at 1,2
-Id : 2658, {_}: implies (or falsehood (not ?2581)) falsehood =>= and_star ?2581 truth [2581] by Demod 2636 with 8 at 1,2
-Id : 2659, {_}: implies (not ?2581) falsehood =>= and_star ?2581 truth [2581] by Demod 2658 with 2094 at 1,2
-Id : 2660, {_}: or ?2581 falsehood =>= and_star ?2581 truth [2581] by Demod 2659 with 6 at 2
-Id : 1407, {_}: or falsehood ?1358 =<= or falsehood (or falsehood ?1358) [1358] by Super 7 with 1344 at 1,2
-Id : 1408, {_}: or falsehood ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Super 1407 with 8 at 2,3
-Id : 2132, {_}: ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Demod 1408 with 2094 at 2
-Id : 2133, {_}: ?1360 =<= or ?1360 falsehood [1360] by Demod 2132 with 2094 at 3
-Id : 2661, {_}: ?2581 =<= and_star ?2581 truth [2581] by Demod 2660 with 2133 at 2
-Id : 2708, {_}: or (not ?1471) ?1472 =<= implies ?1471 ?1472 [1472, 1471] by Demod 2619 with 2661 at 1,3
-Id : 2725, {_}: or (not (implies ?477 falsehood)) falsehood =>= ?477 [477] by Demod 1117 with 2708 at 2
-Id : 2726, {_}: or (not (or (not ?477) falsehood)) falsehood =>= ?477 [477] by Demod 2725 with 2708 at 1,1,2
-Id : 2767, {_}: or falsehood (not (or (not ?477) falsehood)) =>= ?477 [477] by Demod 2726 with 8 at 2
-Id : 2768, {_}: not (or (not ?477) falsehood) =>= ?477 [477] by Demod 2767 with 2094 at 2
-Id : 2769, {_}: not (or falsehood (not ?477)) =>= ?477 [477] by Demod 2768 with 8 at 1,2
-Id : 2770, {_}: not (not ?477) =>= ?477 [477] by Demod 2769 with 2094 at 1,2
-Id : 2131, {_}: and_star truth ?461 =<= not (not ?461) [461] by Demod 239 with 2094 at 1,3
-Id : 2771, {_}: and_star truth ?477 =>= ?477 [477] by Demod 2770 with 2131 at 2
-Id : 563, {_}: and_star (or falsehood falsehood) ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Super 218 with 521 at 1,1,3
-Id : 3108, {_}: and_star falsehood ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Demod 563 with 2094 at 1,2
-Id : 3109, {_}: and_star falsehood ?826 =<= not (or truth (not ?826)) [826] by Demod 3108 with 2771 at 1,1,3
-Id : 3110, {_}: and_star falsehood ?826 =?= not truth [826] by Demod 3109 with 1078 at 1,3
-Id : 3111, {_}: and_star falsehood ?826 =>= falsehood [826] by Demod 3110 with 17 at 3
-Id : 2777, {_}: ?461 =<= not (not ?461) [461] by Demod 2131 with 2771 at 2
-Id : 3185, {_}: or (and_star y x) (and_star (not y) (not x)) === or (and_star y x) (and_star (not y) (not x)) [] by Demod 3184 with 220 at 1,2
-Id : 3184, {_}: or (and_star x y) (and_star (not y) (not x)) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3183 with 8 at 2
-Id : 3183, {_}: or (and_star (not y) (not x)) (and_star x y) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3182 with 2777 at 2,2,2
-Id : 3182, {_}: or (and_star (not y) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3181 with 2094 at 1,1,2
-Id : 3181, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3180 with 8 at 3
-Id : 3180, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3179 with 2094 at 1,2,2,2
-Id : 3179, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3178 with 3111 at 1,1,1,2
-Id : 3178, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3177 with 2777 at 2,2,3
-Id : 3177, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3176 with 3111 at 1,1,2,2,2
-Id : 3176, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3175 with 220 at 1,1,1,2
-Id : 3175, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3174 with 2094 at 1,2,2,3
-Id : 3174, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (or falsehood (not x)))) [] by Demod 3173 with 2094 at 2,1,3
-Id : 3173, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3172 with 220 at 1,1,2,2,2
-Id : 3172, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3171 with 8 at 1,1,2
-Id : 3171, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3170 with 3111 at 1,1,2,2,3
-Id : 3170, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3169 with 3111 at 1,2,1,3
-Id : 3169, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3168 with 8 at 1,2,2,2
-Id : 3168, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3167 with 17 at 2,2,1,1,2
-Id : 3167, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3166 with 2771 at 2,1,2,2,3
-Id : 3166, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (and_star truth (not x))))) [] by Demod 3165 with 220 at 1,1,2,2,3
-Id : 3165, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3164 with 2771 at 2,2,1,3
-Id : 3164, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3163 with 220 at 1,2,1,3
-Id : 3163, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3162 with 17 at 2,2,1,2,2,2
-Id : 3162, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3161 with 220 at 2,1,1,2
-Id : 3161, {_}: or (and_star (or (not y) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3160 with 2771 at 1,1,1,2
-Id : 3160, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3159 with 220 at 2,1,2,2,3
-Id : 3159, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star (not x) truth)))) [] by Demod 3158 with 17 at 2,1,1,2,2,3
-Id : 3158, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3157 with 220 at 2,2,1,3
-Id : 3157, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3156 with 17 at 2,1,2,1,3
-Id : 3156, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3155 with 220 at 2,1,2,2,2
-Id : 3155, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3154 with 2771 at 1,1,2,2,2
-Id : 3154, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3153 with 220 at 1,2
-Id : 3153, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3152 with 213 at 1,2,2,3
-Id : 3152, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (xor x truth))) [] by Demod 3151 with 213 at 2,1,3
-Id : 3151, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3150 with 213 at 1,2,2,2
-Id : 3150, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3149 with 213 at 2,1,2
-Id : 3149, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3148 with 220 at 2,3
-Id : 3148, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star (not (xor x truth)) y) [] by Demod 3147 with 220 at 1,3
-Id : 3147, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3146 with 8 at 2
-Id : 3146, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3145 with 213 at 3
-Id : 3145, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= xor (xor x truth) y [] by Demod 1 with 213 at 2
-Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
-% SZS output end CNFRefutation for LCL159-1.p
-11595: solved LCL159-1.p in 3.608225 using lpo
-11595: status Unsatisfiable for LCL159-1.p
-NO CLASH, using fixed ground order
-11600: Facts:
-11600: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11600: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11600: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11600: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11600: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11600: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11600: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11600: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11600: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11600: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11600: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11600: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11600: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11600: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11600: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11600: Goal:
-11600: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-11600: Order:
-11600: nrkbo
-11600: Leaf order:
-11600: commutator 1 2 0
-11600: additive_inverse 6 1 0
-11600: multiply 22 2 0
-11600: additive_identity 8 0 0
-11600: associator 4 3 3 0,2
-11600: add 18 2 2 0,3,2
-11600: v 2 0 2 2,3,2
-11600: u 2 0 2 1,3,2
-11600: y 3 0 3 2,2
-11600: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-11601: Facts:
-11601: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11601: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11601: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11601: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11601: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11601: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11601: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11601: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11601: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11601: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11601: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11601: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11601: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11601: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11601: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11601: Goal:
-11601: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-11601: Order:
-11601: kbo
-11601: Leaf order:
-11601: commutator 1 2 0
-11601: additive_inverse 6 1 0
-11601: multiply 22 2 0
-11601: additive_identity 8 0 0
-11601: associator 4 3 3 0,2
-11601: add 18 2 2 0,3,2
-11601: v 2 0 2 2,3,2
-11601: u 2 0 2 1,3,2
-11601: y 3 0 3 2,2
-11601: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-11602: Facts:
-11602: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11602: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11602: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11602: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11602: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11602: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11602: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11602: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11602: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11602: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11602: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11602: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11602: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11602: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11602: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11602: Goal:
-11602: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-11602: Order:
-11602: lpo
-11602: Leaf order:
-11602: commutator 1 2 0
-11602: additive_inverse 6 1 0
-11602: multiply 22 2 0
-11602: additive_identity 8 0 0
-11602: associator 4 3 3 0,2
-11602: add 18 2 2 0,3,2
-11602: v 2 0 2 2,3,2
-11602: u 2 0 2 1,3,2
-11602: y 3 0 3 2,2
-11602: x 3 0 3 1,2
-% SZS status Timeout for RNG019-6.p
-NO CLASH, using fixed ground order
-11618: Facts:
-11618: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11618: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11618: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11618: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11618: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11618: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11618: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11618: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11618: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11618: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11618: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11618: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11618: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11618: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11618: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11618: Goal:
-11618: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-11618: Order:
-11618: nrkbo
-11618: Leaf order:
-11618: commutator 1 2 0
-11618: additive_inverse 6 1 0
-11618: multiply 22 2 0
-11618: additive_identity 8 0 0
-11618: associator 4 3 3 0,2
-11618: y 3 0 3 3,2
-11618: x 3 0 3 2,2
-11618: add 18 2 2 0,1,2
-11618: v 2 0 2 2,1,2
-11618: u 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11619: Facts:
-11619: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11619: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11619: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11619: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11619: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11619: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11619: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11619: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11619: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11619: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11619: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11619: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11619: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11619: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11619: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11619: Goal:
-11619: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-11619: Order:
-11619: kbo
-11619: Leaf order:
-11619: commutator 1 2 0
-11619: additive_inverse 6 1 0
-11619: multiply 22 2 0
-11619: additive_identity 8 0 0
-11619: associator 4 3 3 0,2
-11619: y 3 0 3 3,2
-11619: x 3 0 3 2,2
-11619: add 18 2 2 0,1,2
-11619: v 2 0 2 2,1,2
-11619: u 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11620: Facts:
-11620: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11620: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11620: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11620: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11620: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11620: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11620: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11620: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11620: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11620: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11620: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11620: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11620: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11620: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11620: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11620: Goal:
-11620: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-11620: Order:
-11620: lpo
-11620: Leaf order:
-11620: commutator 1 2 0
-11620: additive_inverse 6 1 0
-11620: multiply 22 2 0
-11620: additive_identity 8 0 0
-11620: associator 4 3 3 0,2
-11620: y 3 0 3 3,2
-11620: x 3 0 3 2,2
-11620: add 18 2 2 0,1,2
-11620: v 2 0 2 2,1,2
-11620: u 2 0 2 1,1,2
-% SZS status Timeout for RNG021-6.p
-NO CLASH, using fixed ground order
-11722: Facts:
-11722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11722: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11722: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11722: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11722: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11722: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11722: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11722: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11722: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11722: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11722: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11722: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11722: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11722: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11722: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11722: Goal:
-11722: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-11722: Order:
-11722: nrkbo
-11722: Leaf order:
-11722: commutator 1 2 0
-11722: additive_inverse 6 1 0
-11722: multiply 22 2 0
-11722: add 16 2 0
-11722: additive_identity 9 0 1 3
-11722: associator 2 3 1 0,2
-11722: y 1 0 1 2,2
-11722: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11723: Facts:
-11723: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11723: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11723: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11723: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11723: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11723: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11723: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11723: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11723: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11723: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11723: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11723: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11723: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11723: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11723: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11723: Goal:
-11723: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-11723: Order:
-11723: kbo
-11723: Leaf order:
-11723: commutator 1 2 0
-11723: additive_inverse 6 1 0
-11723: multiply 22 2 0
-11723: add 16 2 0
-11723: additive_identity 9 0 1 3
-11723: associator 2 3 1 0,2
-11723: y 1 0 1 2,2
-11723: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-11724: Facts:
-11724: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11724: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11724: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11724: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11724: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11724: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11724: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11724: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11724: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11724: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11724: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11724: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11724: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11724: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11724: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11724: Goal:
-11724: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-11724: Order:
-11724: lpo
-11724: Leaf order:
-11724: commutator 1 2 0
-11724: additive_inverse 6 1 0
-11724: multiply 22 2 0
-11724: add 16 2 0
-11724: additive_identity 9 0 1 3
-11724: associator 2 3 1 0,2
-11724: y 1 0 1 2,2
-11724: x 2 0 2 1,2
-% SZS status Timeout for RNG025-6.p
-NO CLASH, using fixed ground order
-11740: Facts:
-11740: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-11740: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-11740: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-11740: Id : 5, {_}: add c c =>= c [] by idempotence
-11740: Goal:
-11740: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-11740: Order:
-11740: nrkbo
-11740: Leaf order:
-11740: c 3 0 0
-11740: add 13 2 3 0,2
-11740: negate 9 1 5 0,1,2
-11740: b 3 0 3 1,2,1,1,2
-11740: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11741: Facts:
-11741: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-11741: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-11741: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-11741: Id : 5, {_}: add c c =>= c [] by idempotence
-11741: Goal:
-11741: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-11741: Order:
-11741: kbo
-11741: Leaf order:
-11741: c 3 0 0
-11741: add 13 2 3 0,2
-11741: negate 9 1 5 0,1,2
-11741: b 3 0 3 1,2,1,1,2
-11741: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-11742: Facts:
-11742: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-11742: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-11742: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-11742: Id : 5, {_}: add c c =>= c [] by idempotence
-11742: Goal:
-11742: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-11742: Order:
-11742: lpo
-11742: Leaf order:
-11742: c 3 0 0
-11742: add 13 2 3 0,2
-11742: negate 9 1 5 0,1,2
-11742: b 3 0 3 1,2,1,1,2
-11742: a 2 0 2 1,1,1,2
-% SZS status Timeout for ROB005-1.p
-NO CLASH, using fixed ground order
-11769: Facts:
-11769: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-11769: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-11769: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-11769: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-11769: Goal:
-11769: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-11769: Order:
-11769: nrkbo
-11769: Leaf order:
-11769: inverse 2 1 0
-11769: multiply 9 3 1 0,2
-11769: x 3 0 3 2,2
-11769: y 1 0 1 1,2
-NO CLASH, using fixed ground order
-11770: Facts:
-11770: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-11770: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-11770: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-11770: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-11770: Goal:
-11770: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-11770: Order:
-11770: kbo
-11770: Leaf order:
-11770: inverse 2 1 0
-11770: multiply 9 3 1 0,2
-11770: x 3 0 3 2,2
-11770: y 1 0 1 1,2
-NO CLASH, using fixed ground order
-11771: Facts:
-11771: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-11771: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-11771: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-11771: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-11771: Goal:
-11771: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-11771: Order:
-11771: lpo
-11771: Leaf order:
-11771: inverse 2 1 0
-11771: multiply 9 3 1 0,2
-11771: x 3 0 3 2,2
-11771: y 1 0 1 1,2
-% SZS status Timeout for BOO019-1.p
-CLASH, statistics insufficient
-11791: Facts:
-11791: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11791: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11791: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-11791: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-11791: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-11791: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-11791: Goal:
-11791: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11791: Order:
-11791: nrkbo
-11791: Leaf order:
-11791: add 11 2 0
-11791: multiply 11 2 0
-11791: inverse 3 1 2 0,2
-11791: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-11792: Facts:
-11792: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11792: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11792: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-11792: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-11792: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-11792: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-11792: Goal:
-11792: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11792: Order:
-11792: kbo
-11792: Leaf order:
-11792: add 11 2 0
-11792: multiply 11 2 0
-11792: inverse 3 1 2 0,2
-11792: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-11793: Facts:
-11793: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11793: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11793: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-11793: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-11793: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-11793: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-11793: Goal:
-11793: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11793: Order:
-11793: lpo
-11793: Leaf order:
-11793: add 11 2 0
-11793: multiply 11 2 0
-11793: inverse 3 1 2 0,2
-11793: a 2 0 2 1,1,2
-% SZS status Timeout for BOO030-1.p
-CLASH, statistics insufficient
-11822: Facts:
-11822: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11822: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11822: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-11822: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-11822: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-11822: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-11822: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-11822: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-11822: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-11822: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-11822: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-11822: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-11822: Goal:
-11822: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11822: Order:
-11822: lpo
-11822: Leaf order:
-11822: add 21 2 0
-11822: multiply 21 2 0
-11822: inverse 4 1 2 0,2
-11822: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-11821: Facts:
-11821: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11821: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11821: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-11821: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-11821: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-11821: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-11821: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-11821: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-11821: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-11821: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-11821: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-11821: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-11821: Goal:
-11821: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11821: Order:
-11821: kbo
-11821: Leaf order:
-11821: add 21 2 0
-11821: multiply 21 2 0
-11821: inverse 4 1 2 0,2
-11821: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-11820: Facts:
-11820: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-11820: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-11820: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-11820: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-11820: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-11820: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-11820: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-11820: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-11820: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-11820: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-11820: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-11820: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-11820: Goal:
-11820: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11820: Order:
-11820: nrkbo
-11820: Leaf order:
-11820: add 21 2 0
-11820: multiply 21 2 0
-11820: inverse 4 1 2 0,2
-11820: a 2 0 2 1,1,2
-% SZS status Timeout for BOO032-1.p
-NO CLASH, using fixed ground order
-11838: Facts:
-11838: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-11838: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-11838: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-11838: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-11838: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-11838: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-11838: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-11838: Goal:
-11838: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11838: Order:
-11838: nrkbo
-11838: Leaf order:
-11838: add 15 2 0 multiply
-11838: multiply 16 2 0 add
-11838: inverse 3 1 2 0,2
-11838: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11839: Facts:
-11839: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-11839: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-11839: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-11839: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-11839: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-11839: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-11839: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-11839: Goal:
-11839: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11839: Order:
-11839: kbo
-11839: Leaf order:
-11839: add 15 2 0 multiply
-11839: multiply 16 2 0 add
-11839: inverse 3 1 2 0,2
-11839: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-11840: Facts:
-11840: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-11840: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-11840: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-11840: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-11840: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-11840: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-11840: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-11840: Goal:
-11840: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-11840: Order:
-11840: lpo
-11840: Leaf order:
-11840: add 15 2 0 multiply
-11840: multiply 16 2 0 add
-11840: inverse 3 1 2 0,2
-11840: a 2 0 2 1,1,2
-% SZS status Timeout for BOO033-1.p
-NO CLASH, using fixed ground order
-11868: Facts:
-11868: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-11868: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-11868: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-11868: Goal:
-11868: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-11868: Order:
-11868: nrkbo
-11868: Leaf order:
-11868: w 4 0 0
-11868: b 7 0 0
-11868: apply 20 2 3 0,2
-11868: fixed_pt 3 0 3 2,2
-11868: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-11869: Facts:
-11869: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-11869: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-11869: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-11869: Goal:
-11869: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-11869: Order:
-11869: kbo
-11869: Leaf order:
-11869: w 4 0 0
-11869: b 7 0 0
-11869: apply 20 2 3 0,2
-11869: fixed_pt 3 0 3 2,2
-11869: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-11870: Facts:
-11870: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-11870: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-11870: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-11870: Goal:
-11870: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-11870: Order:
-11870: lpo
-11870: Leaf order:
-11870: w 4 0 0
-11870: b 7 0 0
-11870: apply 20 2 3 0,2
-11870: fixed_pt 3 0 3 2,2
-11870: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL003-20.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-11889: Facts:
-11889: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-11889: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-11889: Goal:
-11889: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-11889: Order:
-11889: kbo
-11889: Leaf order:
-11889: y 3 0 3 2,2
-11889: x 3 0 3 2,1,2
-11889: apply 25 2 17 0,2
-11889: k 8 0 7 1,2,1,1,1,2
-11889: s 7 0 6 1,1,1,1,2
-11888: Facts:
-11888: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-11888: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-11888: Goal:
-11888: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-11888: Order:
-11888: nrkbo
-11888: Leaf order:
-11888: y 3 0 3 2,2
-11888: x 3 0 3 2,1,2
-11888: apply 25 2 17 0,2
-11888: k 8 0 7 1,2,1,1,1,2
-11888: s 7 0 6 1,1,1,1,2
-NO CLASH, using fixed ground order
-11890: Facts:
-11890: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-11890: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-11890: Goal:
-11890: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-11890: Order:
-11890: lpo
-11890: Leaf order:
-11890: y 3 0 3 2,2
-11890: x 3 0 3 2,1,2
-11890: apply 25 2 17 0,2
-11890: k 8 0 7 1,2,1,1,1,2
-11890: s 7 0 6 1,1,1,1,2
-Statistics :
-Max weight : 29
-Found proof, 0.014068s
-% SZS status Unsatisfiable for COL004-3.p
-% SZS output start CNFRefutation for COL004-3.p
-Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4
-Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2
-Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2
-Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2
-Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2
-Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2
-Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2
-Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2
-Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2
-Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2
-Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2
-Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator
-% SZS output end CNFRefutation for COL004-3.p
-11890: solved COL004-3.p in 0.020001 using lpo
-11890: status Unsatisfiable for COL004-3.p
-CLASH, statistics insufficient
-11895: Facts:
-11895: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11895: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-11895: Goal:
-11895: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-11895: Order:
-11895: nrkbo
-11895: Leaf order:
-11895: w 1 0 0
-11895: s 1 0 0
-11895: apply 11 2 1 0,3
-11895: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-11896: Facts:
-11896: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11896: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-11896: Goal:
-11896: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-11896: Order:
-11896: kbo
-11896: Leaf order:
-11896: w 1 0 0
-11896: s 1 0 0
-11896: apply 11 2 1 0,3
-11896: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-11897: Facts:
-11897: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11897: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-11897: Goal:
-11897: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-11897: Order:
-11897: lpo
-11897: Leaf order:
-11897: w 1 0 0
-11897: s 1 0 0
-11897: apply 11 2 1 0,3
-11897: combinator 1 0 1 1,3
-% SZS status Timeout for COL005-1.p
-CLASH, statistics insufficient
-11929: Facts:
-11929: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11929: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-11929: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-11929: Goal:
-11929: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11929: Order:
-11929: nrkbo
-11929: Leaf order:
-11929: v 1 0 0
-11929: m 1 0 0
-11929: b 1 0 0
-11929: apply 15 2 3 0,2
-11929: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11930: Facts:
-11930: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11930: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-11930: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-11930: Goal:
-11930: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11930: Order:
-11930: kbo
-11930: Leaf order:
-11930: v 1 0 0
-11930: m 1 0 0
-11930: b 1 0 0
-11930: apply 15 2 3 0,2
-11930: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11931: Facts:
-11931: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11931: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-11931: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-11931: Goal:
-11931: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11931: Order:
-11931: lpo
-11931: Leaf order:
-11931: v 1 0 0
-11931: m 1 0 0
-11931: b 1 0 0
-11931: apply 15 2 3 0,2
-11931: f 3 1 3 0,2,2
-Goal subsumed
-Statistics :
-Max weight : 78
-Found proof, 6.233757s
-% SZS status Unsatisfiable for COL038-1.p
-% SZS output start CNFRefutation for COL038-1.p
-Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49
-Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2
-Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2
-Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3
-Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3
-Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3
-Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3
-Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2
-Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3
-Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2
-Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3
-Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2
-Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2
-Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
-Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2
-Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3
-Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2
-Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3
-Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2
-Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3
-Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2
-Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3
-Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2
-Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3
-Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3
-Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2
-Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2
-Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3
-Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3
-Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL038-1.p
-11930: solved COL038-1.p in 3.116194 using kbo
-11930: status Unsatisfiable for COL038-1.p
-CLASH, statistics insufficient
-11936: Facts:
-11936: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11936: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-11936: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-11936: Goal:
-11936: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11936: Order:
-11936: nrkbo
-11936: Leaf order:
-11936: m 1 0 0
-11936: b 1 0 0
-11936: s 1 0 0
-11936: apply 16 2 3 0,2
-11936: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11937: Facts:
-11937: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11937: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-11937: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-11937: Goal:
-11937: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11937: Order:
-11937: kbo
-11937: Leaf order:
-11937: m 1 0 0
-11937: b 1 0 0
-11937: s 1 0 0
-11937: apply 16 2 3 0,2
-11937: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11938: Facts:
-11938: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-11938: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-11938: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-11938: Goal:
-11938: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-11938: Order:
-11938: lpo
-11938: Leaf order:
-11938: m 1 0 0
-11938: b 1 0 0
-11938: s 1 0 0
-11938: apply 16 2 3 0,2
-11938: f 3 1 3 0,2,2
-% SZS status Timeout for COL046-1.p
-CLASH, statistics insufficient
-11954: Facts:
-11954: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-11954: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-11954: Goal:
-11954: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-11954: Order:
-11954: nrkbo
-11954: Leaf order:
-11954: q 1 0 0
-11954: l 1 0 0
-11954: apply 12 2 3 0,2
-11954: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11955: Facts:
-11955: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-11955: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-11955: Goal:
-11955: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-11955: Order:
-11955: kbo
-11955: Leaf order:
-11955: q 1 0 0
-11955: l 1 0 0
-11955: apply 12 2 3 0,2
-11955: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-11956: Facts:
-11956: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-11956: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-11956: Goal:
-11956: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-11956: Order:
-11956: lpo
-11956: Leaf order:
-11956: q 1 0 0
-11956: l 1 0 0
-11956: apply 12 2 3 0,2
-11956: f 3 1 3 0,2,2
-% SZS status Timeout for COL047-1.p
-CLASH, statistics insufficient
-11983: Facts:
-11983: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11983: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11983: Goal:
-11983: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-11983: Order:
-11983: nrkbo
-11983: Leaf order:
-11983: t 1 0 0
-11983: b 1 0 0
-11983: h 2 1 2 0,2,2
-11983: g 2 1 2 0,2,1,2
-11983: apply 13 2 5 0,2
-11983: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11984: Facts:
-11984: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11984: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11984: Goal:
-11984: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-11984: Order:
-11984: kbo
-11984: Leaf order:
-11984: t 1 0 0
-11984: b 1 0 0
-11984: h 2 1 2 0,2,2
-11984: g 2 1 2 0,2,1,2
-11984: apply 13 2 5 0,2
-11984: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11985: Facts:
-11985: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11985: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11985: Goal:
-11985: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-11985: Order:
-11985: lpo
-11985: Leaf order:
-11985: t 1 0 0
-11985: b 1 0 0
-11985: h 2 1 2 0,2,2
-11985: g 2 1 2 0,2,1,2
-11985: apply 13 2 5 0,2
-11985: f 2 1 2 0,2,1,1,2
-Goal subsumed
-Statistics :
-Max weight : 76
-Found proof, 1.436300s
-% SZS status Unsatisfiable for COL060-1.p
-% SZS output start CNFRefutation for COL060-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2
-Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
-% SZS output end CNFRefutation for COL060-1.p
-11983: solved COL060-1.p in 0.376023 using nrkbo
-11983: status Unsatisfiable for COL060-1.p
-CLASH, statistics insufficient
-11990: Facts:
-11990: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11990: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11990: Goal:
-11990: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-11990: Order:
-11990: nrkbo
-11990: Leaf order:
-11990: t 1 0 0
-11990: b 1 0 0
-11990: h 2 1 2 0,2,2
-11990: g 2 1 2 0,2,1,2
-11990: apply 13 2 5 0,2
-11990: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11991: Facts:
-11991: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11991: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11991: Goal:
-11991: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-11991: Order:
-11991: kbo
-11991: Leaf order:
-11991: t 1 0 0
-11991: b 1 0 0
-11991: h 2 1 2 0,2,2
-11991: g 2 1 2 0,2,1,2
-11991: apply 13 2 5 0,2
-11991: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11992: Facts:
-11992: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11992: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11992: Goal:
-11992: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-11992: Order:
-11992: lpo
-11992: Leaf order:
-11992: t 1 0 0
-11992: b 1 0 0
-11992: h 2 1 2 0,2,2
-11992: g 2 1 2 0,2,1,2
-11992: apply 13 2 5 0,2
-11992: f 2 1 2 0,2,1,1,2
-Goal subsumed
-Statistics :
-Max weight : 76
-Found proof, 2.573692s
-% SZS status Unsatisfiable for COL061-1.p
-% SZS output start CNFRefutation for COL061-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2
-Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
-% SZS output end CNFRefutation for COL061-1.p
-11990: solved COL061-1.p in 0.344021 using nrkbo
-11990: status Unsatisfiable for COL061-1.p
-CLASH, statistics insufficient
-11997: Facts:
-11997: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11997: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11997: Goal:
-11997: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-11997: Order:
-11997: nrkbo
-11997: Leaf order:
-11997: t 1 0 0
-11997: b 1 0 0
-11997: h 2 1 2 0,2,2
-11997: g 2 1 2 0,2,1,2
-11997: apply 13 2 5 0,2
-11997: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11998: Facts:
-11998: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11998: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11998: Goal:
-11998: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-11998: Order:
-11998: kbo
-11998: Leaf order:
-11998: t 1 0 0
-11998: b 1 0 0
-11998: h 2 1 2 0,2,2
-11998: g 2 1 2 0,2,1,2
-11998: apply 13 2 5 0,2
-11998: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-11999: Facts:
-11999: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-11999: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-11999: Goal:
-11999: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-11999: Order:
-11999: lpo
-11999: Leaf order:
-11999: t 1 0 0
-11999: b 1 0 0
-11999: h 2 1 2 0,2,2
-11999: g 2 1 2 0,2,1,2
-11999: apply 13 2 5 0,2
-11999: f 2 1 2 0,2,1,1,2
-Goal subsumed
-Statistics :
-Max weight : 100
-Found proof, 3.178698s
-% SZS status Unsatisfiable for COL062-1.p
-% SZS output start CNFRefutation for COL062-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2
-Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2
-Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2
-Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1
-% SZS output end CNFRefutation for COL062-1.p
-11997: solved COL062-1.p in 1.812113 using nrkbo
-11997: status Unsatisfiable for COL062-1.p
-CLASH, statistics insufficient
-12004: Facts:
-12004: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-CLASH, statistics insufficient
-12006: Facts:
-12006: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-12006: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-12006: Goal:
-12006: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-12006: Order:
-12006: lpo
-12006: Leaf order:
-12006: q 1 0 0
-12006: n 1 0 0
-12006: apply 14 2 3 0,2
-12006: f 3 1 3 0,2,2
-12004: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-12004: Goal:
-12004: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-12004: Order:
-12004: nrkbo
-12004: Leaf order:
-12004: q 1 0 0
-12004: n 1 0 0
-12004: apply 14 2 3 0,2
-12004: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-12005: Facts:
-12005: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-12005: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-12005: Goal:
-12005: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-12005: Order:
-12005: kbo
-12005: Leaf order:
-12005: q 1 0 0
-12005: n 1 0 0
-12005: apply 14 2 3 0,2
-12005: f 3 1 3 0,2,2
-% SZS status Timeout for COL071-1.p
-CLASH, statistics insufficient
-12093: Facts:
-12093: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-12093: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-12093: Goal:
-12093: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-12093: Order:
-12093: nrkbo
-12093: Leaf order:
-12093: b 1 0 0
-12093: n1 1 0 0
-12093: apply 14 2 3 0,2
-12093: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-12094: Facts:
-12094: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-12094: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-12094: Goal:
-12094: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-12094: Order:
-12094: kbo
-12094: Leaf order:
-12094: b 1 0 0
-12094: n1 1 0 0
-12094: apply 14 2 3 0,2
-12094: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-12095: Facts:
-12095: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-12095: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-12095: Goal:
-12095: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-12095: Order:
-12095: lpo
-12095: Leaf order:
-12095: b 1 0 0
-12095: n1 1 0 0
-12095: apply 14 2 3 0,2
-12095: f 3 1 3 0,2,2
-% SZS status Timeout for COL073-1.p
-NO CLASH, using fixed ground order
-12117: Facts:
-12117: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12117: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12117: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12117: Id : 5, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-12117: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-12117: Goal:
-12117: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-12117: Order:
-12117: nrkbo
-12117: Leaf order:
-12117: inverse 3 1 0
-12117: identity 2 0 0
-12117: multiply 11 2 2 0,2
-12117: commutator 7 2 2 0,2,2
-12117: c 2 0 2 2,2,2
-12117: b 2 0 2 1,2,2
-12117: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-12118: Facts:
-12118: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12118: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12118: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12118: Id : 5, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-12118: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =>=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-12118: Goal:
-12118: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-12118: Order:
-12118: kbo
-12118: Leaf order:
-12118: inverse 3 1 0
-12118: identity 2 0 0
-12118: multiply 11 2 2 0,2
-12118: commutator 7 2 2 0,2,2
-12118: c 2 0 2 2,2,2
-12118: b 2 0 2 1,2,2
-12118: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-12119: Facts:
-12119: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12119: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12119: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12119: Id : 5, {_}:
- commutator ?10 ?11
- =>=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-12119: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =>=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-12119: Goal:
-12119: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-12119: Order:
-12119: lpo
-12119: Leaf order:
-12119: inverse 3 1 0
-12119: identity 2 0 0
-12119: multiply 11 2 2 0,2
-12119: commutator 7 2 2 0,2,2
-12119: c 2 0 2 2,2,2
-12119: b 2 0 2 1,2,2
-12119: a 2 0 2 1,2
-% SZS status Timeout for GRP024-5.p
-CLASH, statistics insufficient
-12145: Facts:
-12145: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12145: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12145: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12145: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-12145: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-12145: Id : 7, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-12145: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-12145: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-12145: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-CLASH, statistics insufficient
-12146: Facts:
-12146: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12146: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12146: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12146: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-12146: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-12146: Id : 7, {_}:
- inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-12146: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-12146: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-12146: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-12146: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-12146: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =<=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-12146: Id : 13, {_}:
- union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-12146: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-12146: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-12146: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =>=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-12146: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =>=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-12146: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =>=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-12146: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =>=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-12146: Id : 20, {_}:
- positive_part ?56 =>= union ?56 identity
- [56] by positive_part ?56
-12146: Id : 21, {_}:
- negative_part ?58 =>= intersection ?58 identity
- [58] by negative_part ?58
-12146: Goal:
-12146: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-12146: Order:
-12146: lpo
-12146: Leaf order:
-12146: union 14 2 0
-12146: intersection 14 2 0
-12146: inverse 7 1 0
-12146: identity 6 0 0
-12146: multiply 21 2 1 0,2
-12146: negative_part 2 1 1 0,2,2
-12146: positive_part 2 1 1 0,1,2
-12146: a 3 0 3 1,1,2
-12145: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-12145: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =<=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-12145: Id : 13, {_}:
- union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-12145: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-12145: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-12145: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-12145: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-12145: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-12145: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-12145: Id : 20, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
-12145: Id : 21, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-12145: Goal:
-12145: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-12145: Order:
-12145: kbo
-12145: Leaf order:
-12145: union 14 2 0
-12145: intersection 14 2 0
-12145: inverse 7 1 0
-12145: identity 6 0 0
-12145: multiply 21 2 1 0,2
-12145: negative_part 2 1 1 0,2,2
-12145: positive_part 2 1 1 0,1,2
-12145: a 3 0 3 1,1,2
-CLASH, statistics insufficient
-12144: Facts:
-12144: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12144: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12144: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12144: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-12144: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-12144: Id : 7, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-12144: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-12144: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-12144: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-12144: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-12144: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-12144: Id : 13, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-12144: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-12144: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-12144: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-12144: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-12144: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-12144: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-12144: Id : 20, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
-12144: Id : 21, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-12144: Goal:
-12144: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-12144: Order:
-12144: nrkbo
-12144: Leaf order:
-12144: union 14 2 0
-12144: intersection 14 2 0
-12144: inverse 7 1 0
-12144: identity 6 0 0
-12144: multiply 21 2 1 0,2
-12144: negative_part 2 1 1 0,2,2
-12144: positive_part 2 1 1 0,1,2
-12144: a 3 0 3 1,1,2
-Statistics :
-Max weight : 15
-Found proof, 17.397670s
-% SZS status Unsatisfiable for GRP114-1.p
-% SZS output start CNFRefutation for GRP114-1.p
-Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =<= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
-Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
-Id : 13, {_}: union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
-Id : 235, {_}: multiply (union ?499 ?500) ?501 =<= union (multiply ?499 ?501) (multiply ?500 ?501) [501, 500, 499] by multiply_union2 ?499 ?500 ?501
-Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
-Id : 195, {_}: multiply ?427 (intersection ?428 ?429) =<= intersection (multiply ?427 ?428) (multiply ?427 ?429) [429, 428, 427] by multiply_intersection1 ?427 ?428 ?429
-Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
-Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
-Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-Id : 7, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
-Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
-Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
-Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-Id : 48, {_}: inverse (multiply ?104 ?105) =<= multiply (inverse ?105) (inverse ?104) [105, 104] by inverse_product_lemma ?104 ?105
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =>= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69
-Id : 28, {_}: multiply identity ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Super 26 with 3 at 1,2
-Id : 32, {_}: ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Demod 28 with 2 at 2
-Id : 50, {_}: inverse (multiply (inverse ?109) ?110) =>= multiply (inverse ?110) ?109 [110, 109] by Super 48 with 6 at 2,3
-Id : 49, {_}: inverse (multiply identity ?107) =<= multiply (inverse ?107) identity [107] by Super 48 with 5 at 2,3
-Id : 835, {_}: inverse ?1371 =<= multiply (inverse ?1371) identity [1371] by Demod 49 with 2 at 1,2
-Id : 841, {_}: inverse (inverse ?1382) =<= multiply ?1382 identity [1382] by Super 835 with 6 at 1,3
-Id : 864, {_}: ?1382 =<= multiply ?1382 identity [1382] by Demod 841 with 6 at 2
-Id : 881, {_}: multiply ?1419 (union ?1420 identity) =?= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Super 16 with 864 at 2,3
-Id : 900, {_}: multiply ?1419 (positive_part ?1420) =<= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Demod 881 with 20 at 2,2
-Id : 2897, {_}: multiply ?3964 (positive_part ?3965) =<= union ?3964 (multiply ?3964 ?3965) [3965, 3964] by Demod 900 with 11 at 3
-Id : 2901, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union (inverse ?3975) identity [3975] by Super 2897 with 3 at 2,3
-Id : 2938, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union identity (inverse ?3975) [3975] by Demod 2901 with 11 at 3
-Id : 296, {_}: union identity ?627 =>= positive_part ?627 [627] by Super 11 with 20 at 3
-Id : 2939, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= positive_part (inverse ?3975) [3975] by Demod 2938 with 296 at 3
-Id : 2958, {_}: inverse (positive_part (inverse ?4028)) =<= multiply (inverse (positive_part ?4028)) ?4028 [4028] by Super 50 with 2939 at 1,2
-Id : 3609, {_}: ?4904 =<= multiply (inverse (inverse (positive_part ?4904))) (inverse (positive_part (inverse ?4904))) [4904] by Super 32 with 2958 at 2,3
-Id : 3661, {_}: ?4904 =<= inverse (multiply (positive_part (inverse ?4904)) (inverse (positive_part ?4904))) [4904] by Demod 3609 with 7 at 3
-Id : 52, {_}: inverse (multiply ?114 (inverse ?115)) =>= multiply ?115 (inverse ?114) [115, 114] by Super 48 with 6 at 1,3
-Id : 3662, {_}: ?4904 =<= multiply (positive_part ?4904) (inverse (positive_part (inverse ?4904))) [4904] by Demod 3661 with 52 at 3
-Id : 875, {_}: multiply ?1405 (intersection ?1406 identity) =?= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Super 17 with 864 at 2,3
-Id : 906, {_}: multiply ?1405 (negative_part ?1406) =<= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Demod 875 with 21 at 2,2
-Id : 3727, {_}: multiply ?5043 (negative_part ?5044) =<= intersection ?5043 (multiply ?5043 ?5044) [5044, 5043] by Demod 906 with 10 at 3
-Id : 40, {_}: multiply ?89 (inverse ?89) =>= identity [89] by Super 3 with 6 at 1,2
-Id : 3734, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= intersection ?5063 identity [5063] by Super 3727 with 40 at 2,3
-Id : 3782, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 3734 with 21 at 3
-Id : 201, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= intersection identity (multiply (inverse ?449) ?450) [450, 449] by Super 195 with 3 at 1,3
-Id : 311, {_}: intersection identity ?654 =>= negative_part ?654 [654] by Super 10 with 21 at 3
-Id : 8114, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= negative_part (multiply (inverse ?449) ?450) [450, 449] by Demod 201 with 311 at 3
-Id : 135, {_}: intersection ?38 (union ?37 ?38) =>= ?38 [37, 38] by Demod 15 with 10 at 2
-Id : 701, {_}: intersection ?1238 (positive_part ?1238) =>= ?1238 [1238] by Super 135 with 296 at 2,2
-Id : 241, {_}: multiply (union (inverse ?521) ?522) ?521 =>= union identity (multiply ?522 ?521) [522, 521] by Super 235 with 3 at 1,3
-Id : 8575, {_}: multiply (union (inverse ?10997) ?10998) ?10997 =>= positive_part (multiply ?10998 ?10997) [10998, 10997] by Demod 241 with 296 at 3
-Id : 699, {_}: union identity (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Super 13 with 296 at 1,3
-Id : 716, {_}: positive_part (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 699 with 296 at 2
-Id : 299, {_}: union ?634 (union ?635 identity) =>= positive_part (union ?634 ?635) [635, 634] by Super 13 with 20 at 3
-Id : 307, {_}: union ?634 (positive_part ?635) =<= positive_part (union ?634 ?635) [635, 634] by Demod 299 with 20 at 2,2
-Id : 1223, {_}: union ?1233 (positive_part ?1234) =<= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 716 with 307 at 2
-Id : 2971, {_}: multiply (inverse ?4064) (positive_part ?4064) =>= positive_part (inverse ?4064) [4064] by Demod 2938 with 296 at 3
-Id : 121, {_}: union ?35 (intersection ?34 ?35) =>= ?35 [34, 35] by Demod 14 with 11 at 2
-Id : 700, {_}: positive_part (intersection ?1236 identity) =>= identity [1236] by Super 121 with 296 at 2
-Id : 715, {_}: positive_part (negative_part ?1236) =>= identity [1236] by Demod 700 with 21 at 1,2
-Id : 2976, {_}: multiply (inverse (negative_part ?4073)) identity =>= positive_part (inverse (negative_part ?4073)) [4073] by Super 2971 with 715 at 2,2
-Id : 3014, {_}: inverse (negative_part ?4073) =<= positive_part (inverse (negative_part ?4073)) [4073] by Demod 2976 with 864 at 2
-Id : 3035, {_}: union (inverse (negative_part ?4112)) (positive_part ?4113) =>= union (inverse (negative_part ?4112)) ?4113 [4113, 4112] by Super 1223 with 3014 at 1,3
-Id : 8597, {_}: multiply (union (inverse (negative_part ?11063)) ?11064) (negative_part ?11063) =>= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11064, 11063] by Super 8575 with 3035 at 1,2
-Id : 8560, {_}: multiply (union (inverse ?521) ?522) ?521 =>= positive_part (multiply ?522 ?521) [522, 521] by Demod 241 with 296 at 3
-Id : 8643, {_}: positive_part (multiply ?11064 (negative_part ?11063)) =<= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11063, 11064] by Demod 8597 with 8560 at 2
-Id : 907, {_}: multiply ?1405 (negative_part ?1406) =<= intersection ?1405 (multiply ?1405 ?1406) [1406, 1405] by Demod 906 with 10 at 3
-Id : 8600, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part (multiply identity ?11072) [11072] by Super 8575 with 20 at 1,2
-Id : 8645, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part ?11072 [11072] by Demod 8600 with 2 at 1,3
-Id : 8660, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part (inverse ?11112)) (positive_part ?11112) [11112] by Super 907 with 8645 at 2,3
-Id : 8719, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part ?11112) (positive_part (inverse ?11112)) [11112] by Demod 8660 with 10 at 3
-Id : 9585, {_}: positive_part (multiply (inverse ?11973) (negative_part ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Super 8643 with 8719 at 1,3
-Id : 3731, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection (inverse ?5054) identity [5054] by Super 3727 with 3 at 2,3
-Id : 3776, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection identity (inverse ?5054) [5054] by Demod 3731 with 10 at 3
-Id : 3777, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= negative_part (inverse ?5054) [5054] by Demod 3776 with 311 at 3
-Id : 9660, {_}: positive_part (negative_part (inverse ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9585 with 3777 at 1,2
-Id : 9661, {_}: identity =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9660 with 715 at 2
-Id : 37105, {_}: intersection (intersection (positive_part ?38557) (positive_part (inverse ?38557))) identity =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Super 701 with 9661 at 2,2
-Id : 37338, {_}: intersection identity (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37105 with 10 at 2
-Id : 37339, {_}: negative_part (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37338 with 311 at 2
-Id : 314, {_}: intersection ?661 (intersection ?662 identity) =>= negative_part (intersection ?661 ?662) [662, 661] by Super 12 with 21 at 3
-Id : 321, {_}: intersection ?661 (negative_part ?662) =<= negative_part (intersection ?661 ?662) [662, 661] by Demod 314 with 21 at 2,2
-Id : 37340, {_}: intersection (positive_part ?38557) (negative_part (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37339 with 321 at 2
-Id : 743, {_}: intersection identity (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Super 12 with 311 at 1,3
-Id : 757, {_}: negative_part (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Demod 743 with 311 at 2
-Id : 1432, {_}: intersection ?2159 (negative_part ?2160) =<= intersection (negative_part ?2159) ?2160 [2160, 2159] by Demod 757 with 321 at 2
-Id : 738, {_}: negative_part (union ?1265 identity) =>= identity [1265] by Super 135 with 311 at 2
-Id : 761, {_}: negative_part (positive_part ?1265) =>= identity [1265] by Demod 738 with 20 at 1,2
-Id : 1437, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= intersection identity ?2174 [2174, 2173] by Super 1432 with 761 at 1,3
-Id : 1472, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= negative_part ?2174 [2174, 2173] by Demod 1437 with 311 at 3
-Id : 37341, {_}: negative_part (positive_part (inverse ?38557)) =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37340 with 1472 at 2
-Id : 37342, {_}: identity =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37341 with 761 at 2
-Id : 37637, {_}: multiply (inverse (positive_part ?38828)) identity =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Super 8114 with 37342 at 2,2
-Id : 37769, {_}: inverse (positive_part ?38828) =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Demod 37637 with 864 at 2
-Id : 8675, {_}: multiply (positive_part (inverse ?11150)) ?11150 =>= positive_part ?11150 [11150] by Demod 8600 with 2 at 1,3
-Id : 8679, {_}: multiply (positive_part ?11157) (inverse ?11157) =>= positive_part (inverse ?11157) [11157] by Super 8675 with 6 at 1,1,2
-Id : 8754, {_}: inverse ?11202 =<= multiply (inverse (positive_part ?11202)) (positive_part (inverse ?11202)) [11202] by Super 32 with 8679 at 2,3
-Id : 37770, {_}: inverse (positive_part ?38828) =<= negative_part (inverse ?38828) [38828] by Demod 37769 with 8754 at 1,3
-Id : 37939, {_}: multiply ?5063 (inverse (positive_part ?5063)) =>= negative_part ?5063 [5063] by Demod 3782 with 37770 at 2,2
-Id : 8672, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part (inverse (inverse ?11144)))) [11144] by Super 52 with 8645 at 1,2
-Id : 8705, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part ?11144)) [11144] by Demod 8672 with 6 at 1,1,2,3
-Id : 37967, {_}: inverse (positive_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 37939 with 8705 at 2
-Id : 37970, {_}: ?4904 =<= multiply (positive_part ?4904) (negative_part ?4904) [4904] by Demod 3662 with 37967 at 2,3
-Id : 38259, {_}: a =?= a [] by Demod 1 with 37970 at 2
-Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
-% SZS output end CNFRefutation for GRP114-1.p
-12145: solved GRP114-1.p in 5.996374 using kbo
-12145: status Unsatisfiable for GRP114-1.p
-NO CLASH, using fixed ground order
-12157: Facts:
-12157: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12157: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12157: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12157: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12157: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12157: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12157: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12157: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12157: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12157: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12157: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12157: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12157: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12157: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12157: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12157: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-12157: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-12157: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-12157: Goal:
-12157: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-12157: Order:
-12157: nrkbo
-12157: Leaf order:
-12157: inverse 7 1 0
-12157: multiply 21 2 1 0,3
-12157: greatest_lower_bound 14 2 1 0,2,3
-12157: least_upper_bound 14 2 1 0,1,3
-12157: identity 6 0 2 2,1,3
-12157: a 3 0 3 2
-NO CLASH, using fixed ground order
-12158: Facts:
-12158: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12158: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12158: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12158: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12158: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12158: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12158: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12158: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12158: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12158: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12158: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12158: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12158: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12158: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12158: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12158: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-12158: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-12158: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-12158: Goal:
-12158: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-12158: Order:
-12158: kbo
-12158: Leaf order:
-12158: inverse 7 1 0
-12158: multiply 21 2 1 0,3
-12158: greatest_lower_bound 14 2 1 0,2,3
-12158: least_upper_bound 14 2 1 0,1,3
-12158: identity 6 0 2 2,1,3
-12158: a 3 0 3 2
-NO CLASH, using fixed ground order
-12159: Facts:
-12159: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12159: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12159: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12159: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12159: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12159: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12159: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12159: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12159: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12159: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12159: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12159: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12159: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12159: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12159: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12159: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-12159: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-12159: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-12159: Goal:
-12159: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-12159: Order:
-12159: lpo
-12159: Leaf order:
-12159: inverse 7 1 0
-12159: multiply 21 2 1 0,3
-12159: greatest_lower_bound 14 2 1 0,2,3
-12159: least_upper_bound 14 2 1 0,1,3
-12159: identity 6 0 2 2,1,3
-12159: a 3 0 3 2
-% SZS status Timeout for GRP167-4.p
-NO CLASH, using fixed ground order
-12195: Facts:
-12195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12195: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12195: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12195: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12195: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12195: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12195: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12195: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12195: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12195: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12195: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12195: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12195: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12195: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12195: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12195: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-12195: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-12195: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-12195: Goal:
-12195: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-12195: Order:
-12195: nrkbo
-12195: Leaf order:
-12195: least_upper_bound 13 2 0
-12195: inverse 1 1 0
-12195: identity 8 0 0
-12195: greatest_lower_bound 21 2 5 0,2
-12195: multiply 21 2 3 0,2,1,2
-12195: c 4 0 3 2,2,1,2
-12195: b 4 0 3 1,2,1,2
-12195: a 5 0 4 1,1,2
-NO CLASH, using fixed ground order
-12196: Facts:
-12196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12196: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12196: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12196: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12196: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12196: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12196: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12196: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12196: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12196: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12196: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12196: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12196: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12196: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12196: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12196: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-12196: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-12196: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-12196: Goal:
-12196: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-12196: Order:
-12196: kbo
-12196: Leaf order:
-12196: least_upper_bound 13 2 0
-12196: inverse 1 1 0
-12196: identity 8 0 0
-12196: greatest_lower_bound 21 2 5 0,2
-12196: multiply 21 2 3 0,2,1,2
-12196: c 4 0 3 2,2,1,2
-12196: b 4 0 3 1,2,1,2
-12196: a 5 0 4 1,1,2
-NO CLASH, using fixed ground order
-12197: Facts:
-12197: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12197: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12197: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12197: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12197: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12197: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12197: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12197: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12197: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12197: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12197: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12197: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12197: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12197: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12197: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12197: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-12197: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-12197: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-12197: Goal:
-12197: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-12197: Order:
-12197: lpo
-12197: Leaf order:
-12197: least_upper_bound 13 2 0
-12197: inverse 1 1 0
-12197: identity 8 0 0
-12197: greatest_lower_bound 21 2 5 0,2
-12197: multiply 21 2 3 0,2,1,2
-12197: c 4 0 3 2,2,1,2
-12197: b 4 0 3 1,2,1,2
-12197: a 5 0 4 1,1,2
-% SZS status Timeout for GRP177-2.p
-NO CLASH, using fixed ground order
-12224: Facts:
-12224: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12224: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12224: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12224: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12224: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12224: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12224: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12224: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12224: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12224: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12224: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12224: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12224: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12224: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12224: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12224: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-12224: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-12224: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-12224: Goal:
-12224: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-12224: Order:
-12224: nrkbo
-12224: Leaf order:
-12224: multiply 20 2 0
-12224: greatest_lower_bound 14 2 1 0,1,3
-12224: least_upper_bound 14 2 1 0,2
-12224: identity 6 0 2 2,2
-12224: inverse 9 1 2 0,1,2
-12224: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12225: Facts:
-12225: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12225: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12225: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12225: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12225: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12225: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12225: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12225: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12225: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-NO CLASH, using fixed ground order
-12226: Facts:
-12226: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12226: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12226: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12226: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12226: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12226: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12226: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12226: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12226: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12226: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12226: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12226: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12226: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12226: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12226: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12226: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-12226: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-12226: Id : 19, {_}:
- inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-12226: Goal:
-12226: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-12226: Order:
-12226: lpo
-12226: Leaf order:
-12226: multiply 20 2 0
-12226: greatest_lower_bound 14 2 1 0,1,3
-12226: least_upper_bound 14 2 1 0,2
-12226: identity 6 0 2 2,2
-12226: inverse 9 1 2 0,1,2
-12226: a 2 0 2 1,1,2
-12225: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12225: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12225: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12225: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12225: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12225: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12225: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-12225: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-12225: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-12225: Goal:
-12225: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-12225: Order:
-12225: kbo
-12225: Leaf order:
-12225: multiply 20 2 0
-12225: greatest_lower_bound 14 2 1 0,1,3
-12225: least_upper_bound 14 2 1 0,2
-12225: identity 6 0 2 2,2
-12225: inverse 9 1 2 0,1,2
-12225: a 2 0 2 1,1,2
-% SZS status Timeout for GRP179-3.p
-NO CLASH, using fixed ground order
-12243: Facts:
-12243: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12243: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12243: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12243: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12243: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12243: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12243: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12243: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12243: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12243: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12243: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12243: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12243: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12243: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12243: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12243: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-12243: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-12243: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-12243: Goal:
-12243: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-12243: Order:
-12243: nrkbo
-12243: Leaf order:
-12243: identity 4 0 0
-12243: least_upper_bound 14 2 1 0,3
-12243: multiply 22 2 2 0,2
-12243: inverse 8 1 1 0,1,2,2
-12243: greatest_lower_bound 14 2 1 0,1,1,2,2
-12243: b 3 0 3 2,1,1,2,2
-12243: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-12244: Facts:
-12244: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12244: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12244: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12244: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12244: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12244: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12244: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12244: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12244: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12244: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12244: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12244: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12244: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12244: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12244: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12244: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-12244: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-12244: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-12244: Goal:
-12244: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-12244: Order:
-12244: kbo
-12244: Leaf order:
-12244: identity 4 0 0
-12244: least_upper_bound 14 2 1 0,3
-12244: multiply 22 2 2 0,2
-12244: inverse 8 1 1 0,1,2,2
-12244: greatest_lower_bound 14 2 1 0,1,1,2,2
-12244: b 3 0 3 2,1,1,2,2
-12244: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-12245: Facts:
-12245: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12245: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12245: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12245: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12245: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12245: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12245: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12245: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12245: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12245: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12245: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12245: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12245: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12245: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12245: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12245: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-12245: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-12245: Id : 19, {_}:
- inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-12245: Goal:
-12245: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-12245: Order:
-12245: lpo
-12245: Leaf order:
-12245: identity 4 0 0
-12245: least_upper_bound 14 2 1 0,3
-12245: multiply 22 2 2 0,2
-12245: inverse 8 1 1 0,1,2,2
-12245: greatest_lower_bound 14 2 1 0,1,1,2,2
-12245: b 3 0 3 2,1,1,2,2
-12245: a 3 0 3 1,2
-% SZS status Timeout for GRP180-2.p
-CLASH, statistics insufficient
-12274: Facts:
-12274: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12274: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12274: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12274: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12274: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12274: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12274: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12274: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12274: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12274: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12274: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12274: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12274: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12274: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12274: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12274: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-12274: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-12274: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-12274: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-12274: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-12274: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-12274: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-12274: Goal:
-12274: Id : 1, {_}: a =>= b [] by prove_p12x
-12274: Order:
-12274: nrkbo
-12274: Leaf order:
-12274: c 4 0 0
-12274: least_upper_bound 17 2 0
-12274: greatest_lower_bound 17 2 0
-12274: inverse 13 1 0
-12274: multiply 20 2 0
-12274: identity 4 0 0
-12274: b 3 0 1 3
-12274: a 3 0 1 2
-CLASH, statistics insufficient
-12275: Facts:
-12275: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12275: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12275: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12275: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12275: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12275: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12275: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12275: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12275: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12275: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12275: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12275: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12275: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12275: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12275: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12275: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-12275: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-12275: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-12275: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-12275: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-12275: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-12275: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-12275: Goal:
-12275: Id : 1, {_}: a =>= b [] by prove_p12x
-12275: Order:
-12275: kbo
-12275: Leaf order:
-12275: c 4 0 0
-12275: least_upper_bound 17 2 0
-12275: greatest_lower_bound 17 2 0
-12275: inverse 13 1 0
-12275: multiply 20 2 0
-12275: identity 4 0 0
-12275: b 3 0 1 3
-12275: a 3 0 1 2
-CLASH, statistics insufficient
-12276: Facts:
-12276: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12276: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12276: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12276: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12276: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12276: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12276: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12276: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12276: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12276: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12276: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12276: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12276: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12276: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12276: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12276: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-12276: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-12276: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-12276: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-12276: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-12276: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =>=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-12276: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =>=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-12276: Goal:
-12276: Id : 1, {_}: a =>= b [] by prove_p12x
-12276: Order:
-12276: lpo
-12276: Leaf order:
-12276: c 4 0 0
-12276: least_upper_bound 17 2 0
-12276: greatest_lower_bound 17 2 0
-12276: inverse 13 1 0
-12276: multiply 20 2 0
-12276: identity 4 0 0
-12276: b 3 0 1 3
-12276: a 3 0 1 2
-Statistics :
-Max weight : 16
-Found proof, 22.107626s
-% SZS status Unsatisfiable for GRP181-4.p
-% SZS output start CNFRefutation for GRP181-4.p
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
-Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588
-Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930
-Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517
-Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846
-Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3
-Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3
-Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3
-Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2
-Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3
-Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2
-Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3
-Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2
-Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3
-Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3
-Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3
-Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2
-Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3
-Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3
-Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3
-Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3
-Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3
-Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3
-Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2
-Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2
-Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3
-Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2
-Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3
-Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2
-Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3
-Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2
-Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2
-Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3
-Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3
-Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2
-Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3
-Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2
-Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3
-Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2
-Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2
-Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2
-Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3
-Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3
-Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2
-Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2
-Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3
-Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2
-Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3
-Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2
-Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3
-Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2
-Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2
-Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2
-Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3
-Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2
-Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2
-Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2
-Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2
-Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3
-Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2
-Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3
-Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3
-Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2
-Id : 1, {_}: a =>= b [] by prove_p12x
-% SZS output end CNFRefutation for GRP181-4.p
-12274: solved GRP181-4.p in 8.100505 using nrkbo
-12274: status Unsatisfiable for GRP181-4.p
-NO CLASH, using fixed ground order
-12282: Facts:
-12282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12282: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12282: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12282: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12282: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12282: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12282: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12282: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12282: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12282: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12282: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12282: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12282: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12282: Goal:
-12282: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-12282: Order:
-12282: kbo
-12282: Leaf order:
-12282: multiply 18 2 0
-12282: inverse 2 1 1 0,2,2
-12282: greatest_lower_bound 15 2 2 0,2
-12282: least_upper_bound 14 2 1 0,1,2
-12282: identity 5 0 3 2,1,2
-12282: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12283: Facts:
-12283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12283: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12283: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12283: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12283: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12283: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12283: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12283: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12283: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12283: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12283: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12283: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12283: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12283: Goal:
-12283: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-12283: Order:
-12283: lpo
-12283: Leaf order:
-12283: multiply 18 2 0
-12283: inverse 2 1 1 0,2,2
-12283: greatest_lower_bound 15 2 2 0,2
-12283: least_upper_bound 14 2 1 0,1,2
-12283: identity 5 0 3 2,1,2
-12283: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12281: Facts:
-12281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12281: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12281: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12281: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12281: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12281: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12281: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12281: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12281: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12281: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12281: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12281: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12281: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12281: Goal:
-12281: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-12281: Order:
-12281: nrkbo
-12281: Leaf order:
-12281: multiply 18 2 0
-12281: inverse 2 1 1 0,2,2
-12281: greatest_lower_bound 15 2 2 0,2
-12281: least_upper_bound 14 2 1 0,1,2
-12281: identity 5 0 3 2,1,2
-12281: a 2 0 2 1,1,2
-% SZS status Timeout for GRP183-1.p
-NO CLASH, using fixed ground order
-12310: Facts:
-12310: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12310: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12310: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12310: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12310: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12310: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12310: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12310: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12310: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12310: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12310: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12310: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12310: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12310: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12310: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12310: Goal:
-12310: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12310: Order:
-12310: nrkbo
-12310: Leaf order:
-12310: multiply 18 2 0
-12310: greatest_lower_bound 14 2 1 0,2
-12310: inverse 2 1 1 0,1,2,2
-12310: least_upper_bound 15 2 2 0,1,2
-12310: identity 5 0 3 2,1,2
-12310: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12311: Facts:
-12311: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12311: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12311: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12311: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12311: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12311: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12311: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12311: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12311: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12311: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12311: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12311: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12311: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12311: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12311: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12311: Goal:
-12311: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12311: Order:
-12311: kbo
-12311: Leaf order:
-12311: multiply 18 2 0
-12311: greatest_lower_bound 14 2 1 0,2
-12311: inverse 2 1 1 0,1,2,2
-12311: least_upper_bound 15 2 2 0,1,2
-12311: identity 5 0 3 2,1,2
-12311: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12312: Facts:
-12312: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12312: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12312: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12312: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12312: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12312: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12312: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12312: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12312: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12312: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12312: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12312: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12312: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12312: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12312: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12312: Goal:
-12312: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12312: Order:
-12312: lpo
-12312: Leaf order:
-12312: multiply 18 2 0
-12312: greatest_lower_bound 14 2 1 0,2
-12312: inverse 2 1 1 0,1,2,2
-12312: least_upper_bound 15 2 2 0,1,2
-12312: identity 5 0 3 2,1,2
-12312: a 2 0 2 1,1,2
-% SZS status Timeout for GRP183-3.p
-NO CLASH, using fixed ground order
-12349: Facts:
-12349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12349: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12349: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12349: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12349: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12349: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12349: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12349: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12349: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12349: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12349: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12349: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12349: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12349: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-12349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-12349: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-12349: Goal:
-12349: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12349: Order:
-12349: nrkbo
-12349: Leaf order:
-12349: multiply 20 2 0
-12349: greatest_lower_bound 14 2 1 0,2
-12349: inverse 8 1 1 0,1,2,2
-12349: least_upper_bound 15 2 2 0,1,2
-12349: identity 7 0 3 2,1,2
-12349: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12350: Facts:
-12350: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12350: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12350: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12350: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12350: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12350: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12350: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12350: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12350: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12350: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12350: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12350: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12350: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12350: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12350: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12350: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-12350: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-12350: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-12350: Goal:
-12350: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12350: Order:
-12350: kbo
-12350: Leaf order:
-12350: multiply 20 2 0
-12350: greatest_lower_bound 14 2 1 0,2
-12350: inverse 8 1 1 0,1,2,2
-12350: least_upper_bound 15 2 2 0,1,2
-12350: identity 7 0 3 2,1,2
-12350: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12351: Facts:
-12351: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12351: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12351: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12351: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12351: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12351: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12351: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12351: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12351: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12351: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12351: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12351: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12351: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12351: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12351: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12351: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-12351: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-12351: Id : 19, {_}:
- inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-12351: Goal:
-12351: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-12351: Order:
-12351: lpo
-12351: Leaf order:
-12351: multiply 20 2 0
-12351: greatest_lower_bound 14 2 1 0,2
-12351: inverse 8 1 1 0,1,2,2
-12351: least_upper_bound 15 2 2 0,1,2
-12351: identity 7 0 3 2,1,2
-12351: a 2 0 2 1,1,2
-% SZS status Timeout for GRP183-4.p
-NO CLASH, using fixed ground order
-12378: Facts:
-12378: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12378: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12378: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12378: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12378: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12378: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12378: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12378: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12378: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12378: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12378: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12378: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12378: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12378: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12378: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12378: Goal:
-12378: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-12378: Order:
-12378: nrkbo
-12378: Leaf order:
-12378: multiply 20 2 2 0,2
-12378: inverse 3 1 2 0,2,2
-12378: greatest_lower_bound 15 2 2 0,1,2,2
-12378: least_upper_bound 15 2 2 0,1,2
-12378: identity 6 0 4 2,1,2
-12378: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-12379: Facts:
-12379: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12379: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12379: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12379: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12379: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12379: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12379: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12379: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12379: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12379: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12379: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12379: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12379: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12379: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12379: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12379: Goal:
-12379: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-12379: Order:
-12379: kbo
-12379: Leaf order:
-12379: multiply 20 2 2 0,2
-12379: inverse 3 1 2 0,2,2
-12379: greatest_lower_bound 15 2 2 0,1,2,2
-12379: least_upper_bound 15 2 2 0,1,2
-12379: identity 6 0 4 2,1,2
-12379: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-12380: Facts:
-12380: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12380: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12380: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12380: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12380: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12380: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12380: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12380: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12380: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12380: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12380: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12380: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12380: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12380: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12380: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12380: Goal:
-12380: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-12380: Order:
-12380: lpo
-12380: Leaf order:
-12380: multiply 20 2 2 0,2
-12380: inverse 3 1 2 0,2,2
-12380: greatest_lower_bound 15 2 2 0,1,2,2
-12380: least_upper_bound 15 2 2 0,1,2
-12380: identity 6 0 4 2,1,2
-12380: a 4 0 4 1,1,2
-% SZS status Timeout for GRP184-1.p
-NO CLASH, using fixed ground order
-12396: Facts:
-12396: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12396: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12396: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12396: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12396: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12396: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12396: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12396: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12396: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12396: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12396: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12396: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12396: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12396: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12396: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12396: Goal:
-12396: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-12396: Order:
-12396: nrkbo
-12396: Leaf order:
-12396: multiply 20 2 2 0,2
-12396: inverse 3 1 2 0,2,2
-12396: greatest_lower_bound 15 2 2 0,1,2,2
-12396: least_upper_bound 15 2 2 0,1,2
-12396: identity 6 0 4 2,1,2
-12396: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-12397: Facts:
-12397: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12397: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12397: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12397: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12397: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12397: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12397: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12397: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12397: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12397: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12397: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12397: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12397: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12397: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12397: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12397: Goal:
-12397: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-12397: Order:
-12397: kbo
-12397: Leaf order:
-12397: multiply 20 2 2 0,2
-12397: inverse 3 1 2 0,2,2
-12397: greatest_lower_bound 15 2 2 0,1,2,2
-12397: least_upper_bound 15 2 2 0,1,2
-12397: identity 6 0 4 2,1,2
-12397: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-12398: Facts:
-12398: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12398: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12398: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12398: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12398: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12398: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12398: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12398: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12398: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12398: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12398: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12398: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12398: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12398: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12398: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12398: Goal:
-12398: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-12398: Order:
-12398: lpo
-12398: Leaf order:
-12398: multiply 20 2 2 0,2
-12398: inverse 3 1 2 0,2,2
-12398: greatest_lower_bound 15 2 2 0,1,2,2
-12398: least_upper_bound 15 2 2 0,1,2
-12398: identity 6 0 4 2,1,2
-12398: a 4 0 4 1,1,2
-% SZS status Timeout for GRP184-3.p
-NO CLASH, using fixed ground order
-12794: Facts:
-12794: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12794: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12794: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12794: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12794: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12794: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12794: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12794: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12794: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12794: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12794: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12794: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12794: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12794: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12794: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12794: Goal:
-12794: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12794: Order:
-12794: nrkbo
-12794: Leaf order:
-12794: inverse 1 1 0
-12794: greatest_lower_bound 14 2 1 0,2
-12794: least_upper_bound 17 2 4 0,1,2
-12794: identity 6 0 4 2,1,2
-12794: multiply 21 2 3 0,1,1,2
-12794: b 3 0 3 2,1,1,2
-12794: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-12795: Facts:
-12795: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12795: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12795: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12795: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12795: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12795: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12795: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12795: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12795: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12795: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-NO CLASH, using fixed ground order
-12796: Facts:
-12796: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12796: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12796: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12796: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12796: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12796: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12796: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12796: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12796: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12796: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12796: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12795: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12795: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12795: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12795: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12795: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12795: Goal:
-12795: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12795: Order:
-12795: kbo
-12795: Leaf order:
-12795: inverse 1 1 0
-12795: greatest_lower_bound 14 2 1 0,2
-12795: least_upper_bound 17 2 4 0,1,2
-12795: identity 6 0 4 2,1,2
-12795: multiply 21 2 3 0,1,1,2
-12795: b 3 0 3 2,1,1,2
-12795: a 3 0 3 1,1,1,2
-12796: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12796: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12796: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12796: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12796: Goal:
-12796: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12796: Order:
-12796: lpo
-12796: Leaf order:
-12796: inverse 1 1 0
-12796: greatest_lower_bound 14 2 1 0,2
-12796: least_upper_bound 17 2 4 0,1,2
-12796: identity 6 0 4 2,1,2
-12796: multiply 21 2 3 0,1,1,2
-12796: b 3 0 3 2,1,1,2
-12796: a 3 0 3 1,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 1.752071s
-% SZS status Unsatisfiable for GRP185-3.p
-% SZS output start CNFRefutation for GRP185-3.p
-Id : 120, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
-Id : 436, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
-Id : 438, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 436 with 3 at 2,3
-Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
-Id : 444, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 436 with 27 at 2,3
-Id : 599, {_}: ?599 =<= multiply ?599 identity [599] by Demod 438 with 444 at 3
-Id : 63, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
-Id : 894, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 120 with 6 at 2,2
-Id : 901, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 894 with 8 at 2,2
-Id : 2450, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2449 with 901 at 2
-Id : 2449, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2448 with 2 at 1,2,2,2,2
-Id : 2448, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2447 with 2 at 1,2,2,2
-Id : 2447, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2446 with 63 at 2,2,2
-Id : 2446, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2445 with 599 at 1,2,2
-Id : 2445, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2444 with 8 at 2,2
-Id : 2444, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2443 with 15 at 2,2,2
-Id : 2443, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2442 with 15 at 1,2,2
-Id : 2442, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2441 with 6 at 2,2
-Id : 2441, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2440 with 6 at 3
-Id : 2440, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2439 with 13 at 2,2
-Id : 2439, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
-% SZS output end CNFRefutation for GRP185-3.p
-12796: solved GRP185-3.p in 0.64804 using lpo
-12796: status Unsatisfiable for GRP185-3.p
-NO CLASH, using fixed ground order
-12801: Facts:
-12801: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12801: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12801: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12801: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12801: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12801: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12801: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12801: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12801: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12801: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12801: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12801: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12801: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12801: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12801: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12801: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-12801: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-12801: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-12801: Goal:
-12801: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12801: Order:
-12801: nrkbo
-12801: Leaf order:
-12801: inverse 7 1 0
-12801: greatest_lower_bound 14 2 1 0,2
-12801: least_upper_bound 17 2 4 0,1,2
-12801: identity 8 0 4 2,1,2
-12801: multiply 23 2 3 0,1,1,2
-12801: b 3 0 3 2,1,1,2
-12801: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-12802: Facts:
-12802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12802: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12802: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12802: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12802: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12802: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12802: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12802: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12802: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12802: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12802: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12802: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12802: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12802: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-12802: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-12802: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-12802: Goal:
-12802: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12802: Order:
-12802: kbo
-12802: Leaf order:
-12802: inverse 7 1 0
-12802: greatest_lower_bound 14 2 1 0,2
-12802: least_upper_bound 17 2 4 0,1,2
-12802: identity 8 0 4 2,1,2
-12802: multiply 23 2 3 0,1,1,2
-12802: b 3 0 3 2,1,1,2
-12802: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-12803: Facts:
-12803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12803: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12803: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12803: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12803: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12803: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12803: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12803: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12803: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12803: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12803: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12803: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12803: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12803: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-12803: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-12803: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-12803: Goal:
-12803: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-12803: Order:
-12803: lpo
-12803: Leaf order:
-12803: inverse 7 1 0
-12803: greatest_lower_bound 14 2 1 0,2
-12803: least_upper_bound 17 2 4 0,1,2
-12803: identity 8 0 4 2,1,2
-12803: multiply 23 2 3 0,1,1,2
-12803: b 3 0 3 2,1,1,2
-12803: a 3 0 3 1,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 2.993705s
-% SZS status Unsatisfiable for GRP185-4.p
-% SZS output start CNFRefutation for GRP185-4.p
-Id : 123, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-Id : 382, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 383, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 382 with 17 at 2,3
-Id : 422, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 383 with 2 at 1,2
-Id : 424, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 422 with 18 at 1,3
-Id : 432, {_}: ?572 =<= multiply ?572 identity [572] by Demod 424 with 18 at 2
-Id : 66, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3
-Id : 766, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 123 with 6 at 2,2
-Id : 773, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 766 with 8 at 2,2
-Id : 4003, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 4002 with 773 at 2
-Id : 4002, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4001 with 2 at 1,2,2,2,2
-Id : 4001, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4000 with 2 at 1,2,2,2
-Id : 4000, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3999 with 66 at 2,2,2
-Id : 3999, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3998 with 432 at 1,2,2
-Id : 3998, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3997 with 8 at 2,2
-Id : 3997, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 3996 with 15 at 2,2,2
-Id : 3996, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3995 with 15 at 1,2,2
-Id : 3995, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3994 with 6 at 2,2
-Id : 3994, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 3993 with 6 at 3
-Id : 3993, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 3992 with 13 at 2,2
-Id : 3992, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
-% SZS output end CNFRefutation for GRP185-4.p
-12803: solved GRP185-4.p in 0.988061 using lpo
-12803: status Unsatisfiable for GRP185-4.p
-NO CLASH, using fixed ground order
-12808: Facts:
-12808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12808: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12808: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12808: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12808: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12808: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12808: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12808: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12808: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12808: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12808: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12808: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12808: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12808: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-12808: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-12808: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-12808: Goal:
-12808: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-12808: Order:
-12808: nrkbo
-12808: Leaf order:
-12808: greatest_lower_bound 14 2 1 0,1,2,3
-12808: inverse 9 1 2 0,2,3
-12808: least_upper_bound 14 2 1 0,2
-12808: identity 5 0 1 2,2
-12808: multiply 22 2 2 0,1,2
-12808: b 2 0 2 2,1,2
-12808: a 3 0 3 1,1,2
-NO CLASH, using fixed ground order
-12809: Facts:
-12809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12809: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12809: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12809: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12809: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12809: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12809: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12809: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12809: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12809: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12809: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12809: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12809: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12809: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-12809: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-12809: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-12809: Goal:
-12809: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-12809: Order:
-12809: kbo
-12809: Leaf order:
-12809: greatest_lower_bound 14 2 1 0,1,2,3
-12809: inverse 9 1 2 0,2,3
-12809: least_upper_bound 14 2 1 0,2
-12809: identity 5 0 1 2,2
-12809: multiply 22 2 2 0,1,2
-12809: b 2 0 2 2,1,2
-12809: a 3 0 3 1,1,2
-NO CLASH, using fixed ground order
-12810: Facts:
-12810: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12810: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-12810: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-12810: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-12810: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-12810: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-12810: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-12810: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-12810: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-12810: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-12810: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-12810: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-12810: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-12810: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-12810: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-12810: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-12810: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-12810: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-12810: Goal:
-12810: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-12810: Order:
-12810: lpo
-12810: Leaf order:
-12810: greatest_lower_bound 14 2 1 0,1,2,3
-12810: inverse 9 1 2 0,2,3
-12810: least_upper_bound 14 2 1 0,2
-12810: identity 5 0 1 2,2
-12810: multiply 22 2 2 0,1,2
-12810: b 2 0 2 2,1,2
-12810: a 3 0 3 1,1,2
-% SZS status Timeout for GRP186-2.p
-NO CLASH, using fixed ground order
-12831: Facts:
-12831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12831: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-12831: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =?=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-12831: Goal:
-12831: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-12831: Order:
-12831: nrkbo
-12831: Leaf order:
-12831: left_inverse 1 1 0
-12831: identity 2 0 0
-12831: c 2 0 2 2,1,2
-12831: multiply 14 2 6 0,2
-12831: b 4 0 4 2,1,1,2
-12831: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-12833: Facts:
-12833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12833: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-12833: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =>=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-12833: Goal:
-12833: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-12833: Order:
-12833: lpo
-12833: Leaf order:
-12833: left_inverse 1 1 0
-12833: identity 2 0 0
-12833: c 2 0 2 2,1,2
-12833: multiply 14 2 6 0,2
-12833: b 4 0 4 2,1,1,2
-12833: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-12832: Facts:
-12832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12832: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-12832: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =>=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-12832: Goal:
-12832: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-12832: Order:
-12832: kbo
-12832: Leaf order:
-12832: left_inverse 1 1 0
-12832: identity 2 0 0
-12832: c 2 0 2 2,1,2
-12832: multiply 14 2 6 0,2
-12832: b 4 0 4 2,1,1,2
-12832: a 2 0 2 1,1,1,2
-% SZS status Timeout for GRP204-1.p
-CLASH, statistics insufficient
-12860: Facts:
-12860: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12860: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-12860: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-12860: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-12860: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-12860: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-12860: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-12860: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-12860: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-12860: Goal:
-12860: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-12860: Order:
-12860: nrkbo
-12860: Leaf order:
-12860: left_inverse 1 1 0
-12860: right_inverse 1 1 0
-12860: right_division 2 2 0
-12860: left_division 2 2 0
-12860: identity 4 0 0
-12860: multiply 20 2 6 0,2
-12860: z 2 0 2 2,1,2,2
-12860: y 2 0 2 1,1,2,2
-12860: x 4 0 4 1,2
-CLASH, statistics insufficient
-12861: Facts:
-12861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12861: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-12861: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-12861: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-12861: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-12861: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-12861: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-12861: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-12861: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-12861: Goal:
-12861: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-12861: Order:
-12861: kbo
-12861: Leaf order:
-12861: left_inverse 1 1 0
-12861: right_inverse 1 1 0
-12861: right_division 2 2 0
-12861: left_division 2 2 0
-12861: identity 4 0 0
-12861: multiply 20 2 6 0,2
-12861: z 2 0 2 2,1,2,2
-12861: y 2 0 2 1,1,2,2
-12861: x 4 0 4 1,2
-CLASH, statistics insufficient
-12862: Facts:
-12862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-12862: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-12862: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-12862: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-12862: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-12862: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-12862: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-12862: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-12862: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-12862: Goal:
-12862: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-12862: Order:
-12862: lpo
-12862: Leaf order:
-12862: left_inverse 1 1 0
-12862: right_inverse 1 1 0
-12862: right_division 2 2 0
-12862: left_division 2 2 0
-12862: identity 4 0 0
-12862: multiply 20 2 6 0,2
-12862: z 2 0 2 2,1,2,2
-12862: y 2 0 2 1,1,2,2
-12862: x 4 0 4 1,2
-Statistics :
-Max weight : 20
-Found proof, 29.150598s
-% SZS status Unsatisfiable for GRP205-1.p
-% SZS output start CNFRefutation for GRP205-1.p
-Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
-Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
-Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
-Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2
-Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
-Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
-Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
-Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
-Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
-Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2
-Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2
-Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2
-Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2
-Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2
-Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3
-Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
-Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
-Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2
-Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2
-Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2
-Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2
-Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2
-Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3
-Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2
-Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3
-Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2
-Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
-Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2
-Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
-Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3
-Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3
-Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2
-Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2
-Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3
-Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2
-Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2
-Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3
-Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3
-Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3
-Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3
-Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3
-Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2
-Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2
-Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2
-Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3
-Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3
-Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2
-Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2
-Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3
-Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2
-Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3
-Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2
-Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2
-Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3
-Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2
-Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3
-Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2
-Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3
-Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2
-Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3
-Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3
-Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2
-Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2
-Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3
-Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2
-Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3
-Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2
-Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3
-Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3
-Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3
-Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2
-Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3
-Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3
-Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2
-Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3
-Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2
-Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2
-Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3
-Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3
-Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
-Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
-Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3
-Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2
-Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2
-Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2
-Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2
-Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2
-Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3
-Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2
-Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3
-Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2
-Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3
-Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2
-Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3
-Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3
-Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2
-Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2
-Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3
-Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2
-Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
-Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2
-Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3
-Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2
-Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3
-Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2
-Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3
-Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2
-Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2
-Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3
-Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2
-Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3
-Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2
-Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3
-Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2
-Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2
-Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3
-Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3
-Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2
-Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2
-Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2
-Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3
-Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2
-Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2
-Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3
-Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2
-Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3
-Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3
-Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2
-Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2
-Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2
-Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3
-Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2
-Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3
-Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3
-Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3
-Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3
-Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4
-% SZS output end CNFRefutation for GRP205-1.p
-12861: solved GRP205-1.p in 14.652915 using kbo
-12861: status Unsatisfiable for GRP205-1.p
-NO CLASH, using fixed ground order
-12867: Facts:
-12867: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-12867: Goal:
-12867: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-12867: Order:
-12867: nrkbo
-12867: Leaf order:
-12867: u 2 0 2 1,1,2,1,2,1,2,2
-12867: multiply 12 2 6 0,2
-12867: inverse 6 1 3 0,2,2
-12867: z 2 0 2 1,1,1,2,1,2,2
-12867: y 2 0 2 1,1,2,2
-12867: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-12868: Facts:
-12868: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-12868: Goal:
-12868: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-12868: Order:
-12868: kbo
-12868: Leaf order:
-12868: u 2 0 2 1,1,2,1,2,1,2,2
-12868: multiply 12 2 6 0,2
-12868: inverse 6 1 3 0,2,2
-12868: z 2 0 2 1,1,1,2,1,2,2
-12868: y 2 0 2 1,1,2,2
-12868: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-12869: Facts:
-12869: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-12869: Goal:
-12869: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-12869: Order:
-12869: lpo
-12869: Leaf order:
-12869: u 2 0 2 1,1,2,1,2,1,2,2
-12869: multiply 12 2 6 0,2
-12869: inverse 6 1 3 0,2,2
-12869: z 2 0 2 1,1,1,2,1,2,2
-12869: y 2 0 2 1,1,2,2
-12869: x 2 0 2 1,2
-% SZS status Timeout for GRP207-1.p
-Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
-NO CLASH, using fixed ground order
-12900: Facts:
-12900: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12900: Goal:
-12900: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12900: Order:
-12900: nrkbo
-12900: Leaf order:
-12900: inverse 7 1 0
-12900: c3 2 0 2 2,2
-12900: multiply 10 2 4 0,2
-12900: b3 2 0 2 2,1,2
-12900: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12901: Facts:
-12901: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12901: Goal:
-12901: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12901: Order:
-12901: kbo
-12901: Leaf order:
-12901: inverse 7 1 0
-12901: c3 2 0 2 2,2
-12901: multiply 10 2 4 0,2
-12901: b3 2 0 2 2,1,2
-12901: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12902: Facts:
-12902: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12902: Goal:
-12902: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12902: Order:
-12902: lpo
-12902: Leaf order:
-12902: inverse 7 1 0
-12902: c3 2 0 2 2,2
-12902: multiply 10 2 4 0,2
-12902: b3 2 0 2 2,1,2
-12902: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP420-1.p
-NO CLASH, using fixed ground order
-12949: Facts:
-12949: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12949: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-12949: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-12949: Goal:
-12949: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12949: Order:
-12949: nrkbo
-12949: Leaf order:
-12949: inverse 1 1 0
-12949: divide 13 2 0
-12949: c3 2 0 2 2,2
-12949: multiply 5 2 4 0,2
-12949: b3 2 0 2 2,1,2
-12949: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12950: Facts:
-12950: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12950: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-12950: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-12950: Goal:
-12950: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12950: Order:
-12950: kbo
-12950: Leaf order:
-12950: inverse 1 1 0
-12950: divide 13 2 0
-12950: c3 2 0 2 2,2
-12950: multiply 5 2 4 0,2
-12950: b3 2 0 2 2,1,2
-12950: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-12951: Facts:
-12951: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-12951: Id : 3, {_}:
- multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-12951: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-12951: Goal:
-12951: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-12951: Order:
-12951: lpo
-12951: Leaf order:
-12951: inverse 1 1 0
-12951: divide 13 2 0
-12951: c3 2 0 2 2,2
-12951: multiply 5 2 4 0,2
-12951: b3 2 0 2 2,1,2
-12951: a3 2 0 2 1,1,2
-Statistics :
-Max weight : 38
-Found proof, 2.410071s
-% SZS status Unsatisfiable for GRP453-1.p
-% SZS output start CNFRefutation for GRP453-1.p
-Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
-Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
-Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
-Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
-Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
-Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
-Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
-Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
-Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
-Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
-Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
-Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
-Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
-Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
-Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
-Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2
-Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2
-Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2
-Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
-Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3
-Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2
-Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2
-Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3
-Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
-Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2
-Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3
-Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3
-Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3
-Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2
-Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3
-Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2
-Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2
-Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2
-Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2
-Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3
-Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3
-Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2
-Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2
-Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2
-Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2
-Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2
-Id : 2653, {_}: inverse (inverse ?5844) =<= divide (multiply ?5844 (inverse (inverse ?5845))) ?5845 [5845, 5844] by Demod 1854 with 29 at 1,3
-Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
-Id : 2679, {_}: inverse (inverse (inverse (inverse (divide ?5935 ?5935)))) =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Super 2653 with 224 at 1,3
-Id : 2732, {_}: divide ?5935 ?5935 =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Demod 2679 with 1559 at 2
-Id : 2733, {_}: divide ?5935 ?5935 =?= divide ?5936 ?5936 [5936, 5935] by Demod 2732 with 1559 at 1,3
-Id : 2794, {_}: divide (inverse (divide ?6115 (divide (inverse ?6116) (divide (inverse ?6115) ?6117)))) ?6117 =?= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6117, 6116, 6115] by Super 145 with 2733 at 2,1,3
-Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
-Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
-Id : 2869, {_}: inverse ?6116 =<= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6116] by Demod 2794 with 31 at 2
-Id : 2925, {_}: divide ?6471 (divide ?6472 ?6472) =>= inverse (inverse (inverse (inverse ?6471))) [6472, 6471] by Super 1559 with 2869 at 1,1,1,3
-Id : 2977, {_}: divide ?6471 (divide ?6472 ?6472) =>= ?6471 [6472, 6471] by Demod 2925 with 1559 at 3
-Id : 3050, {_}: divide (inverse (divide ?6728 ?6729)) (divide ?6730 ?6730) =>= inverse (inverse (multiply ?6729 (inverse ?6728))) [6730, 6729, 6728] by Super 250 with 2977 at 2,1,1,3
-Id : 3110, {_}: inverse (divide ?6728 ?6729) =<= inverse (inverse (multiply ?6729 (inverse ?6728))) [6729, 6728] by Demod 3050 with 2977 at 2
-Id : 3383, {_}: inverse (divide ?7439 ?7440) =<= divide (inverse (inverse ?7440)) ?7439 [7440, 7439] by Demod 3110 with 936 at 3
-Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2
-Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3
-Id : 3111, {_}: inverse (divide ?6728 ?6729) =<= divide (inverse (inverse ?6729)) ?6728 [6729, 6728] by Demod 3110 with 936 at 3
-Id : 3340, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3111 at 1,1,3
-Id : 3404, {_}: inverse (divide ?7516 (inverse (divide ?7517 ?7518))) =>= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Super 3383 with 3340 at 1,3
-Id : 3497, {_}: inverse (multiply ?7516 (divide ?7517 ?7518)) =<= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Demod 3404 with 29 at 1,2
-Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
-Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
-Id : 3338, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3111 at 3
-Id : 3343, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3338 with 29 at 1,3
-Id : 3051, {_}: multiply ?6732 (divide ?6733 ?6733) =>= inverse (inverse ?6732) [6733, 6732] by Super 1825 with 2977 at 1,2
-Id : 3711, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3343 with 3051 at 1,3
-Id : 3714, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3711 at 2,2
-Id : 4200, {_}: inverse (multiply ?8647 (divide ?8648 ?8649)) =>= divide (divide ?8649 ?8648) ?8647 [8649, 8648, 8647] by Demod 3497 with 3714 at 1,3
-Id : 3401, {_}: inverse (divide ?7505 (inverse (inverse ?7506))) =>= divide ?7506 ?7505 [7506, 7505] by Super 3383 with 1559 at 1,3
-Id : 3496, {_}: inverse (multiply ?7505 (inverse ?7506)) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3401 with 29 at 1,2
-Id : 3715, {_}: inverse (divide ?7505 ?7506) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3496 with 3714 at 1,2
-Id : 3725, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3715 at 1,2
-Id : 3337, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3111 at 2
-Id : 3721, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3337 with 3715 at 2
-Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2
-Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2
-Id : 3717, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3714 at 2
-Id : 3737, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3721 with 3717 at 2
-Id : 3738, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3725 with 3737 at 3
-Id : 4230, {_}: inverse (divide (divide ?8777 ?8778) ?8779) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8779, 8778, 8777] by Super 4200 with 3738 at 1,2
-Id : 4280, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8778, 8777, 8779] by Demod 4230 with 3715 at 2
-Id : 4281, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (multiply ?8779 ?8778) ?8777 [8778, 8777, 8779] by Demod 4280 with 29 at 1,3
-Id : 4962, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (divide (inverse ?10175) ?10174) [10175, 10174, 10173] by Super 29 with 4281 at 3
-Id : 4205, {_}: inverse (multiply ?8667 ?8668) =<= divide (divide (divide ?8669 ?8669) ?8668) ?8667 [8669, 8668, 8667] by Super 4200 with 2977 at 2,1,2
-Id : 4245, {_}: inverse (multiply ?8667 ?8668) =<= divide (inverse ?8668) ?8667 [8668, 8667] by Demod 4205 with 4 at 1,3
-Id : 5005, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (inverse (multiply ?10174 ?10175)) [10175, 10174, 10173] by Demod 4962 with 4245 at 2,3
-Id : 5006, {_}: multiply (multiply ?10173 ?10174) ?10175 =>= multiply ?10173 (multiply ?10174 ?10175) [10175, 10174, 10173] by Demod 5005 with 29 at 3
-Id : 5130, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 5006 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP453-1.p
-12950: solved GRP453-1.p in 1.216075 using kbo
-12950: status Unsatisfiable for GRP453-1.p
-Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
-NO CLASH, using fixed ground order
-12960: Facts:
-12960: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-12960: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-12960: Goal:
-12960: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-12960: Order:
-12960: nrkbo
-12960: Leaf order:
-12960: meet 4 2 0
-12960: c 2 0 2 2,2
-12960: join 7 2 4 0,2
-12960: b 2 0 2 2,1,2
-12960: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-12962: Facts:
-12962: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-12962: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-12962: Goal:
-12962: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-12962: Order:
-12962: lpo
-12962: Leaf order:
-12962: meet 4 2 0
-12962: c 2 0 2 2,2
-12962: join 7 2 4 0,2
-12962: b 2 0 2 2,1,2
-12962: a 2 0 2 1,1,2
-12961: Facts:
-12961: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-12961: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-12961: Goal:
-12961: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-12961: Order:
-12961: kbo
-12961: Leaf order:
-12961: meet 4 2 0
-12961: c 2 0 2 2,2
-12961: join 7 2 4 0,2
-12961: b 2 0 2 2,1,2
-12961: a 2 0 2 1,1,2
-Statistics :
-Max weight : 22
-Found proof, 37.088774s
-% SZS status Unsatisfiable for LAT007-1.p
-% SZS output start CNFRefutation for LAT007-1.p
-Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7
-Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20
-Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3
-Id : 122, {_}: meet (meet ?274 ?275) (meet ?275 (join ?276 ?274)) =>= meet ?274 ?275 [276, 275, 274] by Super 2 with 3 at 2,2
-Id : 132, {_}: meet (meet ?317 ?318) ?318 =>= meet ?317 ?318 [318, 317] by Super 122 with 2 at 2,2
-Id : 166, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =<= join (meet ?382 ?380) (meet ?381 ?380) [382, 381, 380] by Super 3 with 132 at 1,3
-Id : 405, {_}: meet ?915 (join ?916 (meet ?917 ?915)) =>= meet ?915 (join ?916 ?917) [917, 916, 915] by Demod 166 with 3 at 3
-Id : 419, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =?= meet ?974 (join (meet ?976 ?974) ?975) [976, 975, 974] by Super 405 with 3 at 2,2
-Id : 165, {_}: meet ?376 (join (meet ?377 ?376) ?378) =<= join (meet ?378 ?376) (meet ?377 ?376) [378, 377, 376] by Super 3 with 132 at 2,3
-Id : 187, {_}: meet ?376 (join (meet ?377 ?376) ?378) =>= meet ?376 (join ?377 ?378) [378, 377, 376] by Demod 165 with 3 at 3
-Id : 473, {_}: meet ?1062 (meet ?1062 (join ?1063 ?1064)) =>= meet ?1062 (join ?1064 ?1063) [1064, 1063, 1062] by Demod 419 with 187 at 3
-Id : 484, {_}: meet ?1111 ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Super 473 with 2 at 2,2
-Id : 590, {_}: meet (join ?1333 ?1334) (join ?1333 ?1334) =>= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Super 8 with 484 at 1,3
-Id : 593, {_}: meet ?1344 ?1344 =>= ?1344 [1344] by Super 2 with 484 at 2
-Id : 2478, {_}: join ?1333 ?1334 =<= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Demod 590 with 593 at 2
-Id : 2479, {_}: join ?1333 ?1334 =?= join ?1334 ?1333 [1334, 1333] by Demod 2478 with 593 at 1,3
-Id : 639, {_}: meet ?1436 (join ?1437 ?1436) =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Super 3 with 593 at 1,3
-Id : 631, {_}: ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Demod 484 with 593 at 2
-Id : 669, {_}: ?1436 =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Demod 639 with 631 at 2
-Id : 53, {_}: meet (join ?112 ?113) (join ?112 ?114) =<= join (meet ?114 (join ?112 ?113)) ?112 [114, 113, 112] by Super 7 with 2 at 2,3
-Id : 62, {_}: meet (join ?150 ?151) (join ?150 ?150) =>= join ?150 ?150 [151, 150] by Super 53 with 2 at 1,3
-Id : 57, {_}: meet (join (meet ?128 ?129) (meet ?130 ?129)) (join (meet ?128 ?129) ?131) =>= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 130, 129, 128] by Super 53 with 3 at 2,1,3
-Id : 73, {_}: meet (meet ?129 (join ?130 ?128)) (join (meet ?128 ?129) ?131) =<= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 128, 130, 129] by Demod 57 with 3 at 1,2
-Id : 642, {_}: meet (meet ?1444 (join ?1445 ?1444)) (join (meet ?1444 ?1444) ?1446) =>= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1446, 1445, 1444] by Super 73 with 593 at 2,3
-Id : 657, {_}: meet ?1444 (join (meet ?1444 ?1444) ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 642 with 631 at 1,2
-Id : 658, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 657 with 593 at 1,2,2
-Id : 659, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 658 with 631 at 2,1,3
-Id : 699, {_}: ?1517 =<= join (meet ?1518 ?1517) ?1517 [1518, 1517] by Demod 659 with 2 at 2
-Id : 711, {_}: ?1557 =<= join ?1557 ?1557 [1557] by Super 699 with 593 at 1,3
-Id : 744, {_}: meet (join ?150 ?151) ?150 =>= join ?150 ?150 [151, 150] by Demod 62 with 711 at 2,2
-Id : 745, {_}: meet (join ?150 ?151) ?150 =>= ?150 [151, 150] by Demod 744 with 711 at 3
-Id : 713, {_}: join ?1562 ?1563 =<= join ?1563 (join ?1562 ?1563) [1563, 1562] by Super 699 with 631 at 1,3
-Id : 1157, {_}: meet (join ?2329 ?2330) ?2330 =>= ?2330 [2330, 2329] by Super 745 with 713 at 1,2
-Id : 1688, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= join (meet ?3264 ?3262) ?3262 [3264, 3263, 3262] by Super 3 with 1157 at 2,3
-Id : 660, {_}: ?1444 =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 659 with 2 at 2
-Id : 1738, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= ?3262 [3264, 3263, 3262] by Demod 1688 with 660 at 3
-Id : 4104, {_}: join (join ?7363 ?7364) ?7365 =<= join (join (join ?7363 ?7364) ?7365) ?7364 [7365, 7364, 7363] by Super 669 with 1738 at 2,3
-Id : 9885, {_}: join (join ?18104 ?18105) ?18106 =<= join ?18105 (join (join ?18104 ?18105) ?18106) [18106, 18105, 18104] by Demod 4104 with 2479 at 3
-Id : 9889, {_}: join (join ?18120 ?18121) ?18122 =<= join ?18121 (join (join ?18121 ?18120) ?18122) [18122, 18121, 18120] by Super 9885 with 2479 at 1,2,3
-Id : 4118, {_}: meet ?7422 (join (join ?7423 ?7422) ?7424) =>= ?7422 [7424, 7423, 7422] by Demod 1688 with 660 at 3
-Id : 4122, {_}: meet ?7438 (join (join ?7438 ?7439) ?7440) =>= ?7438 [7440, 7439, 7438] by Super 4118 with 2479 at 1,2,2
-Id : 9604, {_}: join (join ?17475 ?17476) ?17477 =<= join (join (join ?17475 ?17476) ?17477) ?17475 [17477, 17476, 17475] by Super 669 with 4122 at 2,3
-Id : 9740, {_}: join (join ?17475 ?17476) ?17477 =<= join ?17475 (join (join ?17475 ?17476) ?17477) [17477, 17476, 17475] by Demod 9604 with 2479 at 3
-Id : 16688, {_}: join (join ?18120 ?18121) ?18122 =?= join (join ?18121 ?18120) ?18122 [18122, 18121, 18120] by Demod 9889 with 9740 at 3
-Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3
-Id : 753, {_}: meet ?1599 (join ?1600 ?1600) =>= meet ?1600 ?1599 [1600, 1599] by Super 3 with 711 at 3
-Id : 773, {_}: meet ?1599 ?1600 =?= meet ?1600 ?1599 [1600, 1599] by Demod 753 with 711 at 2,2
-Id : 2380, {_}: meet (join ?4513 ?4514) (join ?4515 ?4513) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4515, 4514, 4513] by Super 9 with 773 at 2,3
-Id : 2506, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =<= join ?4784 (meet ?4786 (join ?4785 ?4784)) [4786, 4785, 4784] by Super 9 with 2479 at 2,2,3
-Id : 1153, {_}: meet (join ?2312 (join ?2313 ?2312)) (join ?2314 ?2312) =>= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2313, 2312] by Super 9 with 713 at 2,2,3
-Id : 1191, {_}: meet (join ?2313 ?2312) (join ?2314 ?2312) =<= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2312, 2313] by Demod 1153 with 713 at 1,2
-Id : 5434, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =?= meet (join ?4785 ?4784) (join ?4786 ?4784) [4786, 4785, 4784] by Demod 2506 with 1191 at 3
-Id : 455, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =>= meet ?974 (join ?976 ?975) [976, 975, 974] by Demod 419 with 187 at 3
-Id : 757, {_}: meet ?1611 (meet ?1611 ?1612) =?= meet ?1611 (join ?1612 ?1612) [1612, 1611] by Super 455 with 711 at 2,2,2
-Id : 767, {_}: meet ?1611 (meet ?1611 ?1612) =>= meet ?1611 ?1612 [1612, 1611] by Demod 757 with 711 at 2,3
-Id : 1239, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =<= join (meet ?2428 (meet ?2426 ?2427)) (meet ?2426 ?2427) [2428, 2427, 2426] by Super 3 with 767 at 2,3
-Id : 1275, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =>= meet ?2426 ?2427 [2428, 2427, 2426] by Demod 1239 with 660 at 3
-Id : 30976, {_}: meet (join ?55510 ?55511) (join (meet ?55510 ?55512) ?55511) =>= join ?55511 (meet ?55510 ?55512) [55512, 55511, 55510] by Super 1191 with 1275 at 2,3
-Id : 30986, {_}: meet (join ?55551 ?55552) (join (meet ?55553 ?55551) ?55552) =>= join ?55552 (meet ?55551 ?55553) [55553, 55552, 55551] by Super 30976 with 773 at 1,2,2
-Id : 3010, {_}: meet (join ?5441 ?5442) (join ?5443 ?5442) =<= join ?5442 (meet ?5443 (join ?5441 ?5442)) [5443, 5442, 5441] by Demod 1153 with 713 at 1,2
-Id : 3031, {_}: meet (join (meet ?5530 ?5531) ?5532) (join ?5531 ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5532, 5531, 5530] by Super 3010 with 187 at 2,3
-Id : 3109, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5530, 5532, 5531] by Demod 3031 with 773 at 2
-Id : 3110, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= meet (join ?5530 ?5532) (join ?5531 ?5532) [5530, 5532, 5531] by Demod 3109 with 1191 at 3
-Id : 31246, {_}: meet (join ?55553 ?55552) (join ?55551 ?55552) =>= join ?55552 (meet ?55551 ?55553) [55551, 55552, 55553] by Demod 30986 with 3110 at 2
-Id : 31561, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =>= join ?4784 (meet ?4786 ?4785) [4786, 4785, 4784] by Demod 5434 with 31246 at 3
-Id : 31569, {_}: join ?4513 (meet ?4515 ?4514) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4514, 4515, 4513] by Demod 2380 with 31561 at 2
-Id : 31659, {_}: join ?56550 (meet (join ?56551 ?56552) ?56552) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56552, 56551, 56550] by Super 31569 with 31246 at 2,3
-Id : 31781, {_}: join ?56550 (meet ?56552 (join ?56551 ?56552)) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31659 with 773 at 2,2
-Id : 32533, {_}: join ?58368 ?58369 =<= join ?58368 (join ?58369 (meet ?58370 ?58368)) [58370, 58369, 58368] by Demod 31781 with 631 at 2,2
-Id : 32536, {_}: join (join ?58380 ?58381) ?58382 =<= join (join ?58380 ?58381) (join ?58382 ?58380) [58382, 58381, 58380] by Super 32533 with 2 at 2,2,3
-Id : 35660, {_}: join (join ?62824 ?62825) (join ?62825 ?62826) =>= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Super 2479 with 32536 at 3
-Id : 188, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =>= meet ?380 (join ?381 ?382) [382, 381, 380] by Demod 166 with 3 at 3
-Id : 1695, {_}: meet ?3292 (join ?3293 ?3292) =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Super 188 with 1157 at 2,2,2
-Id : 1732, {_}: ?3292 =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Demod 1695 with 631 at 2
-Id : 3955, {_}: join ?7063 (join ?7064 ?7065) =<= join (join ?7063 (join ?7064 ?7065)) ?7065 [7065, 7064, 7063] by Super 669 with 1732 at 2,3
-Id : 9413, {_}: join ?17183 (join ?17184 ?17185) =<= join ?17185 (join ?17183 (join ?17184 ?17185)) [17185, 17184, 17183] by Demod 3955 with 2479 at 3
-Id : 9417, {_}: join ?17199 (join ?17200 ?17201) =<= join ?17201 (join ?17199 (join ?17201 ?17200)) [17201, 17200, 17199] by Super 9413 with 2479 at 2,2,3
-Id : 3974, {_}: ?7142 =<= meet ?7142 (join ?7143 (join ?7144 ?7142)) [7144, 7143, 7142] by Demod 1695 with 631 at 2
-Id : 3978, {_}: ?7158 =<= meet ?7158 (join ?7159 (join ?7158 ?7160)) [7160, 7159, 7158] by Super 3974 with 2479 at 2,2,3
-Id : 8662, {_}: join ?15620 (join ?15621 ?15622) =<= join (join ?15620 (join ?15621 ?15622)) ?15621 [15622, 15621, 15620] by Super 669 with 3978 at 2,3
-Id : 8767, {_}: join ?15620 (join ?15621 ?15622) =<= join ?15621 (join ?15620 (join ?15621 ?15622)) [15622, 15621, 15620] by Demod 8662 with 2479 at 3
-Id : 15553, {_}: join ?17199 (join ?17200 ?17201) =?= join ?17199 (join ?17201 ?17200) [17201, 17200, 17199] by Demod 9417 with 8767 at 3
-Id : 31782, {_}: join ?56550 ?56552 =<= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31781 with 631 at 2,2
-Id : 35263, {_}: join ?62192 (join (meet ?62193 ?62192) ?62194) =>= join ?62192 ?62194 [62194, 62193, 62192] by Super 15553 with 31782 at 3
-Id : 35296, {_}: join (join ?62350 ?62351) (join ?62351 ?62352) =>= join (join ?62350 ?62351) ?62352 [62352, 62351, 62350] by Super 35263 with 631 at 1,2,2
-Id : 38052, {_}: join (join ?62824 ?62825) ?62826 =?= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Demod 35660 with 35296 at 2
-Id : 38125, {_}: join ?67897 (join ?67898 ?67899) =<= join (join ?67899 ?67897) ?67898 [67899, 67898, 67897] by Super 2479 with 38052 at 3
-Id : 38567, {_}: join ?18121 (join ?18122 ?18120) =<= join (join ?18121 ?18120) ?18122 [18120, 18122, 18121] by Demod 16688 with 38125 at 2
-Id : 38568, {_}: join ?18121 (join ?18122 ?18120) =?= join ?18120 (join ?18122 ?18121) [18120, 18122, 18121] by Demod 38567 with 38125 at 3
-Id : 39014, {_}: join c (join b a) =?= join c (join b a) [] by Demod 39013 with 2479 at 2,2
-Id : 39013, {_}: join c (join a b) =?= join c (join b a) [] by Demod 39012 with 38568 at 3
-Id : 39012, {_}: join c (join a b) =<= join a (join b c) [] by Demod 1 with 2479 at 2
-Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join
-% SZS output end CNFRefutation for LAT007-1.p
-12961: solved LAT007-1.p in 17.645102 using kbo
-12961: status Unsatisfiable for LAT007-1.p
-NO CLASH, using fixed ground order
-12978: Facts:
-12978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-12978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-12978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-12978: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-12978: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-12978: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-12978: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-12978: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-12978: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-12978: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-12978: Goal:
-12978: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-12978: Order:
-12978: nrkbo
-12978: Leaf order:
-12978: n0 1 0 0
-12978: n1 2 0 1 3
-12978: join 20 2 8 0,2
-12978: meet 15 2 6 0,1,1,1,2
-12978: complement 18 1 9 0,1,2
-12978: b 6 0 6 1,2,1,1,1,2
-12978: a 9 0 9 1,1,1,1,2
-NO CLASH, using fixed ground order
-12979: Facts:
-12979: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-12979: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-12979: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-12979: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-12979: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-12979: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-12979: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-12979: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-12979: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-12979: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-12979: Goal:
-12979: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-12979: Order:
-12979: kbo
-12979: Leaf order:
-12979: n0 1 0 0
-12979: n1 2 0 1 3
-12979: join 20 2 8 0,2
-12979: meet 15 2 6 0,1,1,1,2
-12979: complement 18 1 9 0,1,2
-12979: b 6 0 6 1,2,1,1,1,2
-12979: a 9 0 9 1,1,1,1,2
-NO CLASH, using fixed ground order
-12980: Facts:
-12980: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-12980: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-12980: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-12980: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-12980: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-12980: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-12980: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-12980: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-12980: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-12980: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-12980: Goal:
-12980: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-12980: Order:
-12980: lpo
-12980: Leaf order:
-12980: n0 1 0 0
-12980: n1 2 0 1 3
-12980: join 20 2 8 0,2
-12980: meet 15 2 6 0,1,1,1,2
-12980: complement 18 1 9 0,1,2
-12980: b 6 0 6 1,2,1,1,1,2
-12980: a 9 0 9 1,1,1,1,2
-% SZS status Timeout for LAT016-1.p
-NO CLASH, using fixed ground order
-12998: Facts:
-12998: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-12998: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-NO CLASH, using fixed ground order
-12999: Facts:
-12999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-12999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-12999: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-12999: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-12999: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-12999: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-12999: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-NO CLASH, using fixed ground order
-13000: Facts:
-13000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13000: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-13000: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-13000: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-13000: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-13000: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-13000: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-13000: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-13000: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-13000: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-12998: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-12999: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-12998: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-13000: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-13000: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-13000: Goal:
-13000: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-13000: Order:
-13000: lpo
-13000: Leaf order:
-13000: join 19 2 0
-13000: meet2 14 2 1 0,3
-13000: meet 14 2 1 0,2
-13000: b 2 0 2 2,2
-13000: a 2 0 2 1,2
-12998: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-12998: Id : 7, {_}:
- join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-12998: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-12998: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-12998: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-12998: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-12998: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-12998: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-12998: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-12998: Goal:
-12998: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-12998: Order:
-12998: nrkbo
-12998: Leaf order:
-12998: join 19 2 0
-12998: meet2 14 2 1 0,3
-12998: meet 14 2 1 0,2
-12998: b 2 0 2 2,2
-12998: a 2 0 2 1,2
-12999: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-12999: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-12999: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-12999: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-12999: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-12999: Goal:
-12999: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-12999: Order:
-12999: kbo
-12999: Leaf order:
-12999: join 19 2 0
-12999: meet2 14 2 1 0,3
-12999: meet 14 2 1 0,2
-12999: b 2 0 2 2,2
-12999: a 2 0 2 1,2
-% SZS status Timeout for LAT024-1.p
-NO CLASH, using fixed ground order
-13029: Facts:
-13029: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13029: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13029: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13029: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13029: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13029: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13029: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-13029: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-13029: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-13029: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-13029: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-13029: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-13029: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-13029: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-13029: Goal:
-13029: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-13029: Order:
-13029: nrkbo
-13029: Leaf order:
-13029: join 13 2 0
-13029: meet2 9 2 1 0,3
-13029: meet 9 2 1 0,2
-13029: b 2 0 2 2,2
-13029: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-13030: Facts:
-13030: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13030: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13030: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13030: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13030: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13030: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13030: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-13030: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-13030: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-13030: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-13030: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-13030: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-13030: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-13030: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-13030: Goal:
-13030: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-13030: Order:
-13030: kbo
-13030: Leaf order:
-13030: join 13 2 0
-13030: meet2 9 2 1 0,3
-13030: meet 9 2 1 0,2
-13030: b 2 0 2 2,2
-13030: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-13031: Facts:
-13031: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13031: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13031: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13031: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13031: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13031: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13031: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-13031: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-13031: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-13031: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-13031: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-13031: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-13031: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-13031: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-13031: Goal:
-13031: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
-13031: Order:
-13031: lpo
-13031: Leaf order:
-13031: join 13 2 0
-13031: meet2 9 2 1 0,3
-13031: meet 9 2 1 0,2
-13031: b 2 0 2 2,2
-13031: a 2 0 2 1,2
-% SZS status Timeout for LAT025-1.p
-CLASH, statistics insufficient
-13057: Facts:
-13057: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13057: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13057: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13057: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13057: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13057: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13057: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13057: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13057: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13057: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13057: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13057: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13057: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13057: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-13057: Goal:
-13057: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-13057: Order:
-13057: nrkbo
-13057: Leaf order:
-13057: n0 1 0 0
-13057: n1 1 0 0
-13057: complement 10 1 0
-13057: meet 17 2 3 0,2
-13057: join 18 2 2 0,2,2
-13057: c 2 0 2 2,2,2
-13057: b 2 0 2 1,2,2
-13057: a 3 0 3 1,2
-CLASH, statistics insufficient
-13058: Facts:
-13058: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13058: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13058: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13058: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13058: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13058: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13058: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13058: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13058: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13058: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13058: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13058: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13058: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13058: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-13058: Goal:
-13058: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-13058: Order:
-13058: kbo
-13058: Leaf order:
-13058: n0 1 0 0
-13058: n1 1 0 0
-13058: complement 10 1 0
-13058: meet 17 2 3 0,2
-13058: join 18 2 2 0,2,2
-13058: c 2 0 2 2,2,2
-13058: b 2 0 2 1,2,2
-13058: a 3 0 3 1,2
-CLASH, statistics insufficient
-13059: Facts:
-13059: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13059: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13059: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13059: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13059: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13059: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13059: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13059: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13059: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13059: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13059: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13059: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13059: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13059: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-13059: Goal:
-13059: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-13059: Order:
-13059: lpo
-13059: Leaf order:
-13059: n0 1 0 0
-13059: n1 1 0 0
-13059: complement 10 1 0
-13059: meet 17 2 3 0,2
-13059: join 18 2 2 0,2,2
-13059: c 2 0 2 2,2,2
-13059: b 2 0 2 1,2,2
-13059: a 3 0 3 1,2
-% SZS status Timeout for LAT046-1.p
-NO CLASH, using fixed ground order
-13087: Facts:
-NO CLASH, using fixed ground order
-13088: Facts:
-13088: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13088: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13088: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13088: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13088: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13088: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13088: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13088: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13088: Goal:
-13088: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-13088: Order:
-13088: kbo
-13088: Leaf order:
-13088: meet 11 2 2 0,2,2
-13088: join 13 2 4 0,2
-13088: c 2 0 2 2,2,2,2
-13088: b 2 0 2 1,2,2
-13088: a 4 0 4 1,2
-13087: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13087: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13087: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13087: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13087: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13087: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13087: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13087: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13087: Goal:
-13087: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-13087: Order:
-13087: nrkbo
-13087: Leaf order:
-13087: meet 11 2 2 0,2,2
-13087: join 13 2 4 0,2
-13087: c 2 0 2 2,2,2,2
-13087: b 2 0 2 1,2,2
-13087: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-13089: Facts:
-13089: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13089: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13089: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13089: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13089: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13089: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13089: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13089: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13089: Goal:
-13089: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-13089: Order:
-13089: lpo
-13089: Leaf order:
-13089: meet 11 2 2 0,2,2
-13089: join 13 2 4 0,2
-13089: c 2 0 2 2,2,2,2
-13089: b 2 0 2 1,2,2
-13089: a 4 0 4 1,2
-% SZS status Timeout for LAT047-1.p
-NO CLASH, using fixed ground order
-13105: Facts:
-13105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13105: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13105: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13105: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13105: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13105: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13105: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13105: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13105: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13105: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13105: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-13105: Goal:
-13105: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-13105: Order:
-13105: nrkbo
-13105: Leaf order:
-13105: n0 1 0 0
-13105: n1 2 0 0
-13105: meet 15 2 1 0,2,2
-13105: join 18 2 3 0,2
-13105: b 2 0 2 2,2,2,2
-13105: complement 13 1 1 0,1,2,2
-13105: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-13106: Facts:
-13106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13106: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13106: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13106: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13106: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13106: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13106: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13106: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13106: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13106: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13106: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-13106: Goal:
-13106: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-13106: Order:
-13106: kbo
-13106: Leaf order:
-13106: n0 1 0 0
-13106: n1 2 0 0
-13106: meet 15 2 1 0,2,2
-13106: join 18 2 3 0,2
-13106: b 2 0 2 2,2,2,2
-13106: complement 13 1 1 0,1,2,2
-13106: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-13107: Facts:
-13107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13107: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13107: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13107: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13107: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13107: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13107: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13107: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13107: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13107: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13107: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-13107: Goal:
-13107: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-13107: Order:
-13107: lpo
-13107: Leaf order:
-13107: n0 1 0 0
-13107: n1 2 0 0
-13107: meet 15 2 1 0,2,2
-13107: join 18 2 3 0,2
-13107: b 2 0 2 2,2,2,2
-13107: complement 13 1 1 0,1,2,2
-13107: a 4 0 4 1,2
-% SZS status Timeout for LAT048-1.p
-NO CLASH, using fixed ground order
-13228: Facts:
-13228: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13228: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13228: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13228: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13228: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13228: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13228: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13228: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13228: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13228: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13228: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13228: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13228: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13228: Goal:
-13228: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-13228: Order:
-13228: nrkbo
-13228: Leaf order:
-13228: n0 1 0 0
-13228: n1 2 0 1 3
-13228: meet 14 2 2 0,1,2
-13228: join 15 2 3 0,2
-13228: b 3 0 3 2,2,1,2
-13228: complement 12 1 2 0,1,1,2
-13228: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-13229: Facts:
-13229: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13229: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13229: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13229: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13229: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13229: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13229: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13229: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13229: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13229: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13229: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13229: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13229: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13229: Goal:
-13229: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-13229: Order:
-13229: kbo
-13229: Leaf order:
-13229: n0 1 0 0
-13229: n1 2 0 1 3
-13229: meet 14 2 2 0,1,2
-13229: join 15 2 3 0,2
-13229: b 3 0 3 2,2,1,2
-13229: complement 12 1 2 0,1,1,2
-13229: a 3 0 3 1,1,1,2
-NO CLASH, using fixed ground order
-13230: Facts:
-13230: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13230: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13230: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13230: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13230: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13230: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13230: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13230: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13230: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13230: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13230: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13230: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13230: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13230: Goal:
-13230: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-13230: Order:
-13230: lpo
-13230: Leaf order:
-13230: n0 1 0 0
-13230: n1 2 0 1 3
-13230: meet 14 2 2 0,1,2
-13230: join 15 2 3 0,2
-13230: b 3 0 3 2,2,1,2
-13230: complement 12 1 2 0,1,1,2
-13230: a 3 0 3 1,1,1,2
-% SZS status Timeout for LAT049-1.p
-CLASH, statistics insufficient
-13579: Facts:
-13579: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13579: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13579: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13579: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13579: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13579: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13579: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13579: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13579: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13579: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13579: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13579: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13579: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13579: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-13579: Goal:
-13579: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-13579: Order:
-13579: nrkbo
-13579: Leaf order:
-13579: n0 1 0 0
-13579: n1 1 0 0
-13579: complement 11 1 0
-13579: meet 15 2 2 0,2,2
-13579: join 19 2 4 0,2
-13579: c 2 0 2 2,2,2,2
-13579: b 2 0 2 1,2,2
-13579: a 4 0 4 1,2
-CLASH, statistics insufficient
-13580: Facts:
-13580: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13580: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13580: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13580: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13580: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13580: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13580: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13580: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13580: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13580: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13580: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13580: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13580: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13580: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-13580: Goal:
-13580: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-13580: Order:
-13580: kbo
-13580: Leaf order:
-13580: n0 1 0 0
-13580: n1 1 0 0
-13580: complement 11 1 0
-13580: meet 15 2 2 0,2,2
-13580: join 19 2 4 0,2
-13580: c 2 0 2 2,2,2,2
-13580: b 2 0 2 1,2,2
-13580: a 4 0 4 1,2
-CLASH, statistics insufficient
-13582: Facts:
-13582: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13582: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13582: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13582: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13582: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13582: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13582: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13582: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13582: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13582: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13582: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13582: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13582: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13582: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-13582: Goal:
-13582: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-13582: Order:
-13582: lpo
-13582: Leaf order:
-13582: n0 1 0 0
-13582: n1 1 0 0
-13582: complement 11 1 0
-13582: meet 15 2 2 0,2,2
-13582: join 19 2 4 0,2
-13582: c 2 0 2 2,2,2,2
-13582: b 2 0 2 1,2,2
-13582: a 4 0 4 1,2
-% SZS status Timeout for LAT050-1.p
-CLASH, statistics insufficient
-13811: Facts:
-13811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13811: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13811: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13811: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13811: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13811: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13811: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13811: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13811: Goal:
-13811: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13811: Order:
-13811: nrkbo
-13811: Leaf order:
-13811: n0 1 0 0
-13811: n1 1 0 0
-13811: meet 11 2 1 0,3
-13811: complement 7 1 3 0,2
-13811: join 11 2 1 0,1,2
-13811: b 2 0 2 2,1,2
-13811: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-13812: Facts:
-13812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13812: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13812: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13812: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13812: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13812: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13812: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13812: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13812: Goal:
-13812: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13812: Order:
-13812: kbo
-13812: Leaf order:
-13812: n0 1 0 0
-13812: n1 1 0 0
-13812: meet 11 2 1 0,3
-13812: complement 7 1 3 0,2
-13812: join 11 2 1 0,1,2
-13812: b 2 0 2 2,1,2
-13812: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-13813: Facts:
-13813: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13813: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13813: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13813: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13813: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13813: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13813: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13813: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13813: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13813: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13813: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13813: Goal:
-13813: Id : 1, {_}:
- complement (join a b) =>= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13813: Order:
-13813: lpo
-13813: Leaf order:
-13813: n0 1 0 0
-13813: n1 1 0 0
-13813: meet 11 2 1 0,3
-13813: complement 7 1 3 0,2
-13813: join 11 2 1 0,1,2
-13813: b 2 0 2 2,1,2
-13813: a 2 0 2 1,1,2
-% SZS status Timeout for LAT051-1.p
-CLASH, statistics insufficient
-13839: Facts:
-13839: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13839: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13839: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13839: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13839: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13839: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13839: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13839: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13839: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13839: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13839: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13839: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-13839: Goal:
-13839: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13839: Order:
-13839: nrkbo
-13839: Leaf order:
-13839: n0 1 0 0
-13839: n1 1 0 0
-13839: meet 13 2 1 0,3
-13839: complement 7 1 3 0,2
-13839: join 15 2 1 0,1,2
-13839: b 2 0 2 2,1,2
-13839: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-13840: Facts:
-13840: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13840: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13840: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13840: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13840: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13840: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13840: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13840: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13840: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13840: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13840: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13840: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-13840: Goal:
-13840: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13840: Order:
-13840: kbo
-13840: Leaf order:
-13840: n0 1 0 0
-13840: n1 1 0 0
-13840: meet 13 2 1 0,3
-13840: complement 7 1 3 0,2
-13840: join 15 2 1 0,1,2
-13840: b 2 0 2 2,1,2
-13840: a 2 0 2 1,1,2
-CLASH, statistics insufficient
-13841: Facts:
-13841: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13841: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13841: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13841: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13841: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13841: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13841: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13841: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13841: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-13841: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-13841: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-13841: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-13841: Goal:
-13841: Id : 1, {_}:
- complement (join a b) =>= meet (complement a) (complement b)
- [] by prove_compatibility_law
-13841: Order:
-13841: lpo
-13841: Leaf order:
-13841: n0 1 0 0
-13841: n1 1 0 0
-13841: meet 13 2 1 0,3
-13841: complement 7 1 3 0,2
-13841: join 15 2 1 0,1,2
-13841: b 2 0 2 2,1,2
-13841: a 2 0 2 1,1,2
-% SZS status Timeout for LAT052-1.p
-CLASH, statistics insufficient
-13871: Facts:
-13871: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13871: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13871: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13871: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13871: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13871: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13871: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13871: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13871: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13871: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13871: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13871: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13871: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13871: Goal:
-13871: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-13871: Order:
-13871: nrkbo
-13871: Leaf order:
-13871: n0 1 0 0
-13871: n1 1 0 0
-13871: join 19 2 7 0,2
-13871: meet 19 2 7 0,2,2
-13871: complement 21 1 11 0,1,2,2
-13871: b 7 0 7 1,1,2,2
-13871: a 9 0 9 1,2
-CLASH, statistics insufficient
-13872: Facts:
-13872: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13872: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13872: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13872: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13872: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13872: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13872: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13872: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13872: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13872: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13872: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13872: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13872: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13872: Goal:
-13872: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-13872: Order:
-13872: kbo
-13872: Leaf order:
-13872: n0 1 0 0
-13872: n1 1 0 0
-13872: join 19 2 7 0,2
-13872: meet 19 2 7 0,2,2
-13872: complement 21 1 11 0,1,2,2
-13872: b 7 0 7 1,1,2,2
-13872: a 9 0 9 1,2
-CLASH, statistics insufficient
-13873: Facts:
-13873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13873: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13873: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13873: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13873: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13873: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-13873: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-13873: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-13873: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-13873: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-13873: Goal:
-13873: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-13873: Order:
-13873: lpo
-13873: Leaf order:
-13873: n0 1 0 0
-13873: n1 1 0 0
-13873: join 19 2 7 0,2
-13873: meet 19 2 7 0,2,2
-13873: complement 21 1 11 0,1,2,2
-13873: b 7 0 7 1,1,2,2
-13873: a 9 0 9 1,2
-% SZS status Timeout for LAT054-1.p
-CLASH, statistics insufficient
-13890: Facts:
-13890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13890: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13890: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13890: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13890: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13890: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13890: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13890: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13890: Goal:
-13890: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-13890: Order:
-13890: nrkbo
-13890: Leaf order:
-13890: n0 1 0 0
-13890: n1 1 0 0
-13890: meet 17 2 6 0,2
-13890: join 15 2 4 0,1,2
-13890: complement 11 1 6 0,2,1,2
-13890: b 6 0 6 1,2,1,2
-13890: a 6 0 6 1,1,2
-CLASH, statistics insufficient
-13891: Facts:
-13891: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13891: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13891: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13891: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13891: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13891: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13891: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13891: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13891: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13891: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13891: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13891: Goal:
-13891: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-13891: Order:
-13891: kbo
-13891: Leaf order:
-13891: n0 1 0 0
-13891: n1 1 0 0
-13891: meet 17 2 6 0,2
-13891: join 15 2 4 0,1,2
-13891: complement 11 1 6 0,2,1,2
-13891: b 6 0 6 1,2,1,2
-13891: a 6 0 6 1,1,2
-CLASH, statistics insufficient
-13892: Facts:
-13892: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13892: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13892: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13892: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13892: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13892: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13892: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13892: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13892: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13892: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13892: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13892: Goal:
-13892: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-13892: Order:
-13892: lpo
-13892: Leaf order:
-13892: n0 1 0 0
-13892: n1 1 0 0
-13892: meet 17 2 6 0,2
-13892: join 15 2 4 0,1,2
-13892: complement 11 1 6 0,2,1,2
-13892: b 6 0 6 1,2,1,2
-13892: a 6 0 6 1,1,2
-% SZS status Timeout for LAT062-1.p
-CLASH, statistics insufficient
-13921: Facts:
-13921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13921: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13921: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13921: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13921: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13921: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13921: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13921: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13921: Goal:
-CLASH, statistics insufficient
-CLASH, statistics insufficient
-13921: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-13921: Order:
-13921: nrkbo
-13921: Leaf order:
-13921: n0 1 0 0
-13921: n1 1 0 0
-13921: join 14 2 3 0,2,2
-13921: meet 16 2 5 0,2
-13921: complement 7 1 2 0,1,2,2,2,2
-13921: b 3 0 3 1,2,2
-13921: a 7 0 7 1,2
-13923: Facts:
-13923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13923: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13923: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13923: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13923: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13923: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13923: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13923: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13923: Goal:
-13923: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-13923: Order:
-13923: lpo
-13923: Leaf order:
-13923: n0 1 0 0
-13923: n1 1 0 0
-13923: join 14 2 3 0,2,2
-13923: meet 16 2 5 0,2
-13923: complement 7 1 2 0,1,2,2,2,2
-13923: b 3 0 3 1,2,2
-13923: a 7 0 7 1,2
-13922: Facts:
-13922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13922: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13922: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13922: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13922: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13922: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-13922: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-13922: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-13922: Goal:
-13922: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-13922: Order:
-13922: kbo
-13922: Leaf order:
-13922: n0 1 0 0
-13922: n1 1 0 0
-13922: join 14 2 3 0,2,2
-13922: meet 16 2 5 0,2
-13922: complement 7 1 2 0,1,2,2,2,2
-13922: b 3 0 3 1,2,2
-13922: a 7 0 7 1,2
-% SZS status Timeout for LAT063-1.p
-NO CLASH, using fixed ground order
-13955: Facts:
-13955: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13955: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13955: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13955: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13955: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13955: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13955: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13955: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13955: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-13955: Goal:
-13955: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-13955: Order:
-13955: nrkbo
-13955: Leaf order:
-13955: join 17 2 4 0,2,2
-13955: meet 21 2 6 0,2
-13955: c 3 0 3 2,2,2,2
-13955: b 4 0 4 1,2,2
-13955: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-13956: Facts:
-13956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13956: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13956: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13956: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13956: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13956: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-13956: Goal:
-13956: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-13956: Order:
-13956: kbo
-13956: Leaf order:
-13956: join 17 2 4 0,2,2
-13956: meet 21 2 6 0,2
-13956: c 3 0 3 2,2,2,2
-13956: b 4 0 4 1,2,2
-13956: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-13957: Facts:
-13957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13957: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13957: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13957: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13957: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13957: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-13957: Goal:
-13957: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-13957: Order:
-13957: lpo
-13957: Leaf order:
-13957: join 17 2 4 0,2,2
-13957: meet 21 2 6 0,2
-13957: c 3 0 3 2,2,2,2
-13957: b 4 0 4 1,2,2
-13957: a 5 0 5 1,2
-% SZS status Timeout for LAT098-1.p
-NO CLASH, using fixed ground order
-13999: Facts:
-13999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13999: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13999: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13999: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13999: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13999: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13999: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13999: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-13999: Goal:
-13999: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-13999: Order:
-13999: nrkbo
-13999: Leaf order:
-13999: meet 20 2 5 0,2
-13999: join 18 2 5 0,2,2
-13999: d 3 0 3 2,2,2,2,2
-13999: c 2 0 2 1,2,2,2,2
-13999: b 3 0 3 1,2,2
-13999: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14000: Facts:
-14000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14000: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14000: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14000: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14000: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14000: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14000: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14000: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-14000: Goal:
-14000: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-14000: Order:
-14000: kbo
-14000: Leaf order:
-14000: meet 20 2 5 0,2
-14000: join 18 2 5 0,2,2
-14000: d 3 0 3 2,2,2,2,2
-14000: c 2 0 2 1,2,2,2,2
-14000: b 3 0 3 1,2,2
-14000: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14001: Facts:
-14001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14001: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14001: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14001: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14001: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14001: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14001: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14001: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-14001: Goal:
-14001: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-14001: Order:
-14001: lpo
-14001: Leaf order:
-14001: meet 20 2 5 0,2
-14001: join 18 2 5 0,2,2
-14001: d 3 0 3 2,2,2,2,2
-14001: c 2 0 2 1,2,2,2,2
-14001: b 3 0 3 1,2,2
-14001: a 4 0 4 1,2
-% SZS status Timeout for LAT100-1.p
-NO CLASH, using fixed ground order
-14017: Facts:
-14017: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14017: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14017: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14017: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14017: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14017: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14017: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14017: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14017: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-14017: Goal:
-14017: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14017: Order:
-14017: nrkbo
-14017: Leaf order:
-14017: join 16 2 3 0,2,2
-14017: meet 20 2 5 0,2
-14017: c 3 0 3 2,2,2,2
-14017: b 3 0 3 1,2,2
-14017: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14018: Facts:
-14018: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14018: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14018: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14018: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14018: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14018: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14018: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14018: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14018: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-14018: Goal:
-14018: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14018: Order:
-14018: kbo
-14018: Leaf order:
-14018: join 16 2 3 0,2,2
-14018: meet 20 2 5 0,2
-14018: c 3 0 3 2,2,2,2
-14018: b 3 0 3 1,2,2
-14018: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14019: Facts:
-14019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14019: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14019: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14019: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14019: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14019: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-14019: Goal:
-14019: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14019: Order:
-14019: lpo
-14019: Leaf order:
-14019: join 16 2 3 0,2,2
-14019: meet 20 2 5 0,2
-14019: c 3 0 3 2,2,2,2
-14019: b 3 0 3 1,2,2
-14019: a 4 0 4 1,2
-% SZS status Timeout for LAT101-1.p
-NO CLASH, using fixed ground order
-14050: Facts:
-14050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14050: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14050: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14050: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14050: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14050: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-14050: Goal:
-14050: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-14050: Order:
-14050: nrkbo
-14050: Leaf order:
-14050: meet 20 2 5 0,2
-14050: join 18 2 5 0,2,2
-14050: d 3 0 3 2,2,2,2,2
-14050: c 2 0 2 1,2,2,2,2
-14050: b 3 0 3 1,2,2
-14050: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14051: Facts:
-14051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14051: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14051: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14051: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14051: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14051: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-14051: Goal:
-14051: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-14051: Order:
-14051: kbo
-14051: Leaf order:
-14051: meet 20 2 5 0,2
-14051: join 18 2 5 0,2,2
-14051: d 3 0 3 2,2,2,2,2
-14051: c 2 0 2 1,2,2,2,2
-14051: b 3 0 3 1,2,2
-14051: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14052: Facts:
-14052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14052: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14052: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14052: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14052: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14052: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-14052: Goal:
-14052: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-14052: Order:
-14052: lpo
-14052: Leaf order:
-14052: meet 20 2 5 0,2
-14052: join 18 2 5 0,2,2
-14052: d 3 0 3 2,2,2,2,2
-14052: c 2 0 2 1,2,2,2,2
-14052: b 3 0 3 1,2,2
-14052: a 4 0 4 1,2
-% SZS status Timeout for LAT102-1.p
-NO CLASH, using fixed ground order
-14140: Facts:
-14140: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14140: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14140: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14140: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14140: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14140: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14140: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14140: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14140: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-14140: Goal:
-14140: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-14140: Order:
-14140: nrkbo
-14140: Leaf order:
-14140: join 16 2 4 0,2,2
-14140: meet 20 2 6 0,2
-14140: c 3 0 3 2,2,2,2
-14140: b 3 0 3 1,2,2
-14140: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-14141: Facts:
-14141: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14141: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14141: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14141: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14141: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14141: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14141: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14141: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14141: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-14141: Goal:
-14141: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-14141: Order:
-14141: kbo
-14141: Leaf order:
-14141: join 16 2 4 0,2,2
-14141: meet 20 2 6 0,2
-14141: c 3 0 3 2,2,2,2
-14141: b 3 0 3 1,2,2
-14141: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-14142: Facts:
-14142: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14142: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14142: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14142: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14142: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14142: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14142: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14142: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14142: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-14142: Goal:
-14142: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-14142: Order:
-14142: lpo
-14142: Leaf order:
-14142: join 16 2 4 0,2,2
-14142: meet 20 2 6 0,2
-14142: c 3 0 3 2,2,2,2
-14142: b 3 0 3 1,2,2
-14142: a 6 0 6 1,2
-% SZS status Timeout for LAT103-1.p
-NO CLASH, using fixed ground order
-14175: Facts:
-14175: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14175: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14175: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14175: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14175: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14175: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14175: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14175: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14175: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14175: Goal:
-14175: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14175: Order:
-14175: kbo
-14175: Leaf order:
-14175: join 17 2 4 0,2,2
-14175: meet 21 2 6 0,2
-14175: c 3 0 3 2,2,2,2
-14175: b 4 0 4 1,2,2
-14175: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-14176: Facts:
-14176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14176: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14176: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14176: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14176: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14176: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14176: Goal:
-14176: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14176: Order:
-14176: lpo
-14176: Leaf order:
-14176: join 17 2 4 0,2,2
-14176: meet 21 2 6 0,2
-14176: c 3 0 3 2,2,2,2
-14176: b 4 0 4 1,2,2
-14176: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-14174: Facts:
-14174: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14174: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14174: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14174: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14174: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14174: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14174: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14174: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14174: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14174: Goal:
-14174: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14174: Order:
-14174: nrkbo
-14174: Leaf order:
-14174: join 17 2 4 0,2,2
-14174: meet 21 2 6 0,2
-14174: c 3 0 3 2,2,2,2
-14174: b 4 0 4 1,2,2
-14174: a 5 0 5 1,2
-% SZS status Timeout for LAT104-1.p
-NO CLASH, using fixed ground order
-14193: Facts:
-14193: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14193: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14193: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14193: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14193: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14193: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14193: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14193: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14193: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14193: Goal:
-14193: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14193: Order:
-14193: nrkbo
-14193: Leaf order:
-14193: join 16 2 3 0,2,2
-14193: meet 20 2 5 0,2
-14193: c 3 0 3 2,2,2,2
-14193: b 3 0 3 1,2,2
-14193: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14194: Facts:
-14194: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14194: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14194: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14194: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14194: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14194: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14194: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14194: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14194: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14194: Goal:
-14194: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14194: Order:
-14194: kbo
-14194: Leaf order:
-14194: join 16 2 3 0,2,2
-14194: meet 20 2 5 0,2
-14194: c 3 0 3 2,2,2,2
-14194: b 3 0 3 1,2,2
-14194: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-14195: Facts:
-14195: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14195: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14195: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14195: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14195: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14195: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14195: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14195: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14195: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-14195: Goal:
-14195: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-14195: Order:
-14195: lpo
-14195: Leaf order:
-14195: join 16 2 3 0,2,2
-14195: meet 20 2 5 0,2
-14195: c 3 0 3 2,2,2,2
-14195: b 3 0 3 1,2,2
-14195: a 4 0 4 1,2
-% SZS status Timeout for LAT105-1.p
-NO CLASH, using fixed ground order
-14223: Facts:
-14223: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14223: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14223: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14223: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14223: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14223: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14223: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14223: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14223: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14223: Goal:
-14223: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14223: Order:
-14223: nrkbo
-14223: Leaf order:
-14223: join 17 2 4 0,2,2
-14223: meet 21 2 6 0,2
-14223: c 3 0 3 2,2,2,2
-14223: b 4 0 4 1,2,2
-14223: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-14224: Facts:
-14224: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14224: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14224: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14224: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14224: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14224: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14224: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14224: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14224: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14224: Goal:
-14224: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14224: Order:
-14224: kbo
-14224: Leaf order:
-NO CLASH, using fixed ground order
-14225: Facts:
-14225: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14225: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14225: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14225: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14225: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14225: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14225: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14225: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14225: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14225: Goal:
-14225: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-14225: Order:
-14225: lpo
-14225: Leaf order:
-14225: join 17 2 4 0,2,2
-14225: meet 21 2 6 0,2
-14225: c 3 0 3 2,2,2,2
-14225: b 4 0 4 1,2,2
-14225: a 5 0 5 1,2
-14224: join 17 2 4 0,2,2
-14224: meet 21 2 6 0,2
-14224: c 3 0 3 2,2,2,2
-14224: b 4 0 4 1,2,2
-14224: a 5 0 5 1,2
-% SZS status Timeout for LAT106-1.p
-NO CLASH, using fixed ground order
-14371: Facts:
-14371: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14371: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14371: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14371: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14371: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14371: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14371: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14371: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14371: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14371: Goal:
-14371: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =<=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-14371: Order:
-14371: nrkbo
-14371: Leaf order:
-14371: join 17 2 4 0,2,2
-14371: c 3 0 3 2,2,2,2
-14371: meet 22 2 7 0,2
-14371: b 4 0 4 2,1,2,2
-14371: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-14372: Facts:
-14372: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14372: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14372: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14372: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14372: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14372: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14372: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14372: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14372: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14372: Goal:
-14372: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =<=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-14372: Order:
-14372: kbo
-14372: Leaf order:
-14372: join 17 2 4 0,2,2
-14372: c 3 0 3 2,2,2,2
-14372: meet 22 2 7 0,2
-14372: b 4 0 4 2,1,2,2
-14372: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-14373: Facts:
-14373: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14373: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14373: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14373: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14373: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14373: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14373: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14373: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14373: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-14373: Goal:
-14373: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =>=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-14373: Order:
-14373: lpo
-14373: Leaf order:
-14373: join 17 2 4 0,2,2
-14373: c 3 0 3 2,2,2,2
-14373: meet 22 2 7 0,2
-14373: b 4 0 4 2,1,2,2
-14373: a 6 0 6 1,2
-% SZS status Timeout for LAT107-1.p
-NO CLASH, using fixed ground order
-15801: Facts:
-15801: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15801: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15801: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15801: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15801: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15801: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15801: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15801: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15801: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-15801: Goal:
-15801: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-15801: Order:
-15801: nrkbo
-15801: Leaf order:
-15801: meet 21 2 5 0,2
-15801: join 17 2 5 0,2,2
-15801: d 2 0 2 2,2,2,2,2
-15801: c 3 0 3 1,2,2,2
-15801: b 3 0 3 1,2,2
-15801: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-15804: Facts:
-15804: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15804: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15804: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15804: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15804: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15804: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15804: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15804: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15804: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-15804: Goal:
-15804: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-15804: Order:
-15804: kbo
-15804: Leaf order:
-15804: meet 21 2 5 0,2
-15804: join 17 2 5 0,2,2
-15804: d 2 0 2 2,2,2,2,2
-15804: c 3 0 3 1,2,2,2
-15804: b 3 0 3 1,2,2
-15804: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-15805: Facts:
-15805: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15805: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15805: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15805: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15805: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15805: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15805: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15805: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15805: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-15805: Goal:
-15805: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-15805: Order:
-15805: lpo
-15805: Leaf order:
-15805: meet 21 2 5 0,2
-15805: join 17 2 5 0,2,2
-15805: d 2 0 2 2,2,2,2,2
-15805: c 3 0 3 1,2,2,2
-15805: b 3 0 3 1,2,2
-15805: a 4 0 4 1,2
-% SZS status Timeout for LAT108-1.p
-NO CLASH, using fixed ground order
-17324: Facts:
-17324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17324: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17324: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17324: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17324: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17324: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-17324: Goal:
-17324: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-17324: Order:
-17324: lpo
-17324: Leaf order:
-17324: meet 19 2 5 0,2
-17324: join 19 2 5 0,2,2
-17324: d 2 0 2 2,2,2,2,2
-17324: c 3 0 3 1,2,2,2
-17324: b 3 0 3 1,2,2
-17324: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-17322: Facts:
-17322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17322: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17322: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17322: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17322: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17322: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-17322: Goal:
-17322: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-17322: Order:
-17322: nrkbo
-17322: Leaf order:
-17322: meet 19 2 5 0,2
-17322: join 19 2 5 0,2,2
-17322: d 2 0 2 2,2,2,2,2
-17322: c 3 0 3 1,2,2,2
-17322: b 3 0 3 1,2,2
-17322: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-17323: Facts:
-17323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17323: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17323: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17323: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17323: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17323: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-17323: Goal:
-17323: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-17323: Order:
-17323: kbo
-17323: Leaf order:
-17323: meet 19 2 5 0,2
-17323: join 19 2 5 0,2,2
-17323: d 2 0 2 2,2,2,2,2
-17323: c 3 0 3 1,2,2,2
-17323: b 3 0 3 1,2,2
-17323: a 4 0 4 1,2
-% SZS status Timeout for LAT109-1.p
-NO CLASH, using fixed ground order
-19002: Facts:
-19002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19002: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19002: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19002: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19002: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19002: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19002: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19002: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-19002: Goal:
-19002: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19002: Order:
-19002: nrkbo
-19002: Leaf order:
-19002: meet 21 2 5 0,2
-19002: join 17 2 5 0,2,2
-19002: d 2 0 2 2,2,2,2,2
-19002: c 3 0 3 1,2,2,2
-19002: b 3 0 3 1,2,2
-19002: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19008: Facts:
-19008: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19008: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19008: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19008: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19008: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19008: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19008: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19008: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19008: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-19008: Goal:
-19008: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19008: Order:
-19008: kbo
-19008: Leaf order:
-19008: meet 21 2 5 0,2
-19008: join 17 2 5 0,2,2
-19008: d 2 0 2 2,2,2,2,2
-19008: c 3 0 3 1,2,2,2
-19008: b 3 0 3 1,2,2
-19008: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19009: Facts:
-19009: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19009: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19009: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19009: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19009: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19009: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19009: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19009: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19009: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-19009: Goal:
-19009: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19009: Order:
-19009: lpo
-19009: Leaf order:
-19009: meet 21 2 5 0,2
-19009: join 17 2 5 0,2,2
-19009: d 2 0 2 2,2,2,2,2
-19009: c 3 0 3 1,2,2,2
-19009: b 3 0 3 1,2,2
-19009: a 4 0 4 1,2
-% SZS status Timeout for LAT111-1.p
-NO CLASH, using fixed ground order
-19496: Facts:
-19496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19496: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19496: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19496: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19496: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19496: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-19496: Goal:
-19496: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-19496: Order:
-19496: nrkbo
-19496: Leaf order:
-19496: meet 21 2 5 0,2
-19496: join 17 2 5 0,2,2
-19496: d 2 0 2 2,2,2,2,2
-19496: c 3 0 3 1,2,2,2
-19496: b 3 0 3 1,2,2
-19496: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19497: Facts:
-19497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19497: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19497: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19497: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19497: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19497: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-19497: Goal:
-19497: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-19497: Order:
-19497: kbo
-19497: Leaf order:
-19497: meet 21 2 5 0,2
-19497: join 17 2 5 0,2,2
-19497: d 2 0 2 2,2,2,2,2
-19497: c 3 0 3 1,2,2,2
-19497: b 3 0 3 1,2,2
-19497: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19498: Facts:
-19498: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19498: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19498: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19498: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19498: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19498: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19498: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19498: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19498: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-19498: Goal:
-19498: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-19498: Order:
-19498: lpo
-19498: Leaf order:
-19498: meet 21 2 5 0,2
-19498: join 17 2 5 0,2,2
-19498: d 2 0 2 2,2,2,2,2
-19498: c 3 0 3 1,2,2,2
-19498: b 3 0 3 1,2,2
-19498: a 4 0 4 1,2
-% SZS status Timeout for LAT112-1.p
-NO CLASH, using fixed ground order
-19529: Facts:
-19529: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19529: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19529: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19529: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19529: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19529: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19529: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19529: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19529: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-19529: Goal:
-19529: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19529: Order:
-19529: nrkbo
-19529: Leaf order:
-19529: meet 19 2 5 0,2
-19529: join 19 2 5 0,2,2
-19529: d 2 0 2 2,2,2,2,2
-19529: c 3 0 3 1,2,2,2
-19529: b 3 0 3 1,2,2
-19529: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19530: Facts:
-19530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19530: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19530: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19530: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19530: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19530: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-19530: Goal:
-19530: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19530: Order:
-19530: kbo
-19530: Leaf order:
-19530: meet 19 2 5 0,2
-19530: join 19 2 5 0,2,2
-19530: d 2 0 2 2,2,2,2,2
-19530: c 3 0 3 1,2,2,2
-19530: b 3 0 3 1,2,2
-19530: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19531: Facts:
-19531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19531: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19531: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19531: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19531: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19531: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-19531: Goal:
-19531: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-19531: Order:
-19531: lpo
-19531: Leaf order:
-19531: meet 19 2 5 0,2
-19531: join 19 2 5 0,2,2
-19531: d 2 0 2 2,2,2,2,2
-19531: c 3 0 3 1,2,2,2
-19531: b 3 0 3 1,2,2
-19531: a 4 0 4 1,2
-% SZS status Timeout for LAT113-1.p
-NO CLASH, using fixed ground order
-19568: Facts:
-19568: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19568: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19568: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19568: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19568: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19568: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19568: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19568: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19568: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19568: Goal:
-19568: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-19568: Order:
-19568: kbo
-19568: Leaf order:
-19568: join 19 2 5 0,2
-19568: c 2 0 2 2,2,2,2
-19568: meet 17 2 5 0,1,2
-19568: b 5 0 5 2,1,2
-19568: a 5 0 5 1,1,2
-NO CLASH, using fixed ground order
-19567: Facts:
-19567: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19567: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19567: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19567: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19567: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19567: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19567: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19567: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19567: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19567: Goal:
-19567: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-19567: Order:
-19567: nrkbo
-19567: Leaf order:
-19567: join 19 2 5 0,2
-19567: c 2 0 2 2,2,2,2
-19567: meet 17 2 5 0,1,2
-19567: b 5 0 5 2,1,2
-19567: a 5 0 5 1,1,2
-NO CLASH, using fixed ground order
-19569: Facts:
-19569: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19569: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19569: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19569: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19569: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19569: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19569: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19569: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19569: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19569: Goal:
-19569: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-19569: Order:
-19569: lpo
-19569: Leaf order:
-19569: join 19 2 5 0,2
-19569: c 2 0 2 2,2,2,2
-19569: meet 17 2 5 0,1,2
-19569: b 5 0 5 2,1,2
-19569: a 5 0 5 1,1,2
-% SZS status Timeout for LAT114-1.p
-NO CLASH, using fixed ground order
-19631: Facts:
-19631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19631: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19631: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19631: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19631: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19631: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19631: Goal:
-19631: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-19631: Order:
-19631: nrkbo
-19631: Leaf order:
-19631: meet 17 2 5 0,2
-19631: d 2 0 2 2,2,2,2
-19631: join 19 2 5 0,1,2,2
-19631: c 2 0 2 2,1,2,2
-19631: b 5 0 5 1,1,2,2
-19631: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-19632: Facts:
-19632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19632: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19632: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19632: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19632: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19632: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19632: Goal:
-19632: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-19632: Order:
-19632: kbo
-19632: Leaf order:
-19632: meet 17 2 5 0,2
-19632: d 2 0 2 2,2,2,2
-19632: join 19 2 5 0,1,2,2
-19632: c 2 0 2 2,1,2,2
-19632: b 5 0 5 1,1,2,2
-19632: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-19633: Facts:
-19633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19633: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19633: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19633: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19633: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19633: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19633: Goal:
-19633: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-19633: Order:
-19633: lpo
-19633: Leaf order:
-19633: meet 17 2 5 0,2
-19633: d 2 0 2 2,2,2,2
-19633: join 19 2 5 0,1,2,2
-19633: c 2 0 2 2,1,2,2
-19633: b 5 0 5 1,1,2,2
-19633: a 3 0 3 1,2
-% SZS status Timeout for LAT115-1.p
-NO CLASH, using fixed ground order
-19650: Facts:
-19650: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19650: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19650: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19650: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19650: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19650: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-NO CLASH, using fixed ground order
-19651: Facts:
-19651: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19651: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19651: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19651: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19651: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19651: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19651: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19651: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19651: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19651: Goal:
-19651: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-19651: Order:
-19651: kbo
-19651: Leaf order:
-19651: meet 17 2 5 0,2
-19651: d 2 0 2 2,2,2,2
-19651: join 19 2 5 0,1,2,2
-19651: c 2 0 2 2,1,2,2
-19651: b 5 0 5 1,1,2,2
-19651: a 3 0 3 1,2
-19650: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19650: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19650: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19650: Goal:
-19650: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-19650: Order:
-19650: nrkbo
-19650: Leaf order:
-19650: meet 17 2 5 0,2
-19650: d 2 0 2 2,2,2,2
-19650: join 19 2 5 0,1,2,2
-19650: c 2 0 2 2,1,2,2
-19650: b 5 0 5 1,1,2,2
-19650: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-19652: Facts:
-19652: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19652: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19652: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19652: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19652: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19652: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19652: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19652: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19652: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-19652: Goal:
-19652: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-19652: Order:
-19652: lpo
-19652: Leaf order:
-19652: meet 17 2 5 0,2
-19652: d 2 0 2 2,2,2,2
-19652: join 19 2 5 0,1,2,2
-19652: c 2 0 2 2,1,2,2
-19652: b 5 0 5 1,1,2,2
-19652: a 3 0 3 1,2
-% SZS status Timeout for LAT116-1.p
-NO CLASH, using fixed ground order
-19680: Facts:
-19680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19680: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19680: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19680: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19680: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19680: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-19680: Goal:
-19680: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19680: Order:
-19680: nrkbo
-19680: Leaf order:
-19680: meet 20 2 5 0,2
-19680: join 16 2 4 0,2,2
-19680: c 3 0 3 2,2,2
-19680: b 3 0 3 1,2,2
-19680: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19681: Facts:
-19681: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19681: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19681: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19681: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19681: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19681: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19681: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19681: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19681: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-19681: Goal:
-19681: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19681: Order:
-19681: kbo
-19681: Leaf order:
-19681: meet 20 2 5 0,2
-19681: join 16 2 4 0,2,2
-19681: c 3 0 3 2,2,2
-19681: b 3 0 3 1,2,2
-19681: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19682: Facts:
-19682: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19682: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19682: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19682: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19682: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19682: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19682: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19682: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19682: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-19682: Goal:
-19682: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19682: Order:
-19682: lpo
-19682: Leaf order:
-19682: meet 20 2 5 0,2
-19682: join 16 2 4 0,2,2
-19682: c 3 0 3 2,2,2
-19682: b 3 0 3 1,2,2
-19682: a 5 0 5 1,2
-% SZS status Timeout for LAT117-1.p
-NO CLASH, using fixed ground order
-19698: Facts:
-19698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19698: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19698: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19698: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19698: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19698: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-19698: Goal:
-19698: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-19698: Order:
-19698: nrkbo
-19698: Leaf order:
-19698: join 17 2 4 0,2,2
-19698: meet 20 2 6 0,2
-19698: c 3 0 3 2,2,2,2
-19698: b 4 0 4 1,2,2
-19698: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19699: Facts:
-19699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19699: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19699: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19699: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19699: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19699: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-19699: Goal:
-19699: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-19699: Order:
-19699: kbo
-19699: Leaf order:
-19699: join 17 2 4 0,2,2
-19699: meet 20 2 6 0,2
-19699: c 3 0 3 2,2,2,2
-19699: b 4 0 4 1,2,2
-19699: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19700: Facts:
-19700: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19700: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19700: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19700: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19700: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19700: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19700: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19700: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19700: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-19700: Goal:
-19700: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-19700: Order:
-19700: lpo
-19700: Leaf order:
-19700: join 17 2 4 0,2,2
-19700: meet 20 2 6 0,2
-19700: c 3 0 3 2,2,2,2
-19700: b 4 0 4 1,2,2
-19700: a 5 0 5 1,2
-% SZS status Timeout for LAT119-1.p
-NO CLASH, using fixed ground order
-19732: Facts:
-19732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19732: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19732: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19732: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19732: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19732: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-19732: Goal:
-19732: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-19732: Order:
-19732: nrkbo
-19732: Leaf order:
-19732: meet 16 2 4 0,2
-19732: join 18 2 4 0,2,2
-19732: c 2 0 2 2,2,2
-19732: b 4 0 4 1,2,2
-19732: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19733: Facts:
-19733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19733: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19733: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19733: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19733: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19733: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-19733: Goal:
-19733: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-19733: Order:
-19733: kbo
-19733: Leaf order:
-19733: meet 16 2 4 0,2
-19733: join 18 2 4 0,2,2
-19733: c 2 0 2 2,2,2
-19733: b 4 0 4 1,2,2
-19733: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19734: Facts:
-19734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19734: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19734: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19734: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19734: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19734: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-19734: Goal:
-19734: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-19734: Order:
-19734: lpo
-19734: Leaf order:
-19734: meet 16 2 4 0,2
-19734: join 18 2 4 0,2,2
-19734: c 2 0 2 2,2,2
-19734: b 4 0 4 1,2,2
-19734: a 4 0 4 1,2
-% SZS status Timeout for LAT120-1.p
-NO CLASH, using fixed ground order
-19750: Facts:
-19750: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19750: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19750: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19750: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19750: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19750: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19750: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19750: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19750: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-19750: Goal:
-19750: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19750: Order:
-19750: nrkbo
-19750: Leaf order:
-19750: meet 16 2 3 0,2,2
-19750: join 20 2 5 0,2
-19750: c 3 0 3 2,2,2,2
-19750: b 3 0 3 1,2,2
-19750: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19751: Facts:
-19751: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19751: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19751: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19751: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19751: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19751: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19751: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19751: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19751: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-19751: Goal:
-19751: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19751: Order:
-19751: kbo
-19751: Leaf order:
-19751: meet 16 2 3 0,2,2
-19751: join 20 2 5 0,2
-19751: c 3 0 3 2,2,2,2
-19751: b 3 0 3 1,2,2
-19751: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19752: Facts:
-19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19752: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19752: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19752: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19752: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19752: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-19752: Goal:
-19752: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19752: Order:
-19752: lpo
-19752: Leaf order:
-19752: meet 16 2 3 0,2,2
-19752: join 20 2 5 0,2
-19752: c 3 0 3 2,2,2,2
-19752: b 3 0 3 1,2,2
-19752: a 4 0 4 1,2
-% SZS status Timeout for LAT121-1.p
-NO CLASH, using fixed ground order
-19779: Facts:
-19779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19779: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19779: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19779: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19779: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19779: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-19779: Goal:
-19779: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19779: Order:
-19779: nrkbo
-19779: Leaf order:
-19779: meet 16 2 3 0,2,2
-19779: join 20 2 5 0,2
-19779: c 3 0 3 2,2,2,2
-19779: b 3 0 3 1,2,2
-19779: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19780: Facts:
-19780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19780: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19780: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19780: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19780: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19780: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-19780: Goal:
-19780: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19780: Order:
-19780: kbo
-19780: Leaf order:
-19780: meet 16 2 3 0,2,2
-19780: join 20 2 5 0,2
-19780: c 3 0 3 2,2,2,2
-19780: b 3 0 3 1,2,2
-19780: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19781: Facts:
-19781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19781: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19781: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19781: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19781: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19781: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-19781: Goal:
-19781: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19781: Order:
-19781: lpo
-19781: Leaf order:
-19781: meet 16 2 3 0,2,2
-19781: join 20 2 5 0,2
-19781: c 3 0 3 2,2,2,2
-19781: b 3 0 3 1,2,2
-19781: a 4 0 4 1,2
-% SZS status Timeout for LAT122-1.p
-NO CLASH, using fixed ground order
-19798: Facts:
-19798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19798: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19798: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19798: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19798: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19798: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-19798: Goal:
-19798: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19798: Order:
-19798: nrkbo
-19798: Leaf order:
-19798: meet 16 2 3 0,2,2
-19798: join 20 2 5 0,2
-19798: c 3 0 3 2,2,2,2
-19798: b 3 0 3 1,2,2
-19798: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19799: Facts:
-19799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19799: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19799: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19799: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19799: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19799: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-19799: Goal:
-19799: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19799: Order:
-19799: kbo
-19799: Leaf order:
-19799: meet 16 2 3 0,2,2
-19799: join 20 2 5 0,2
-19799: c 3 0 3 2,2,2,2
-19799: b 3 0 3 1,2,2
-19799: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-19800: Facts:
-19800: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19800: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19800: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19800: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19800: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19800: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19800: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19800: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19800: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-19800: Goal:
-19800: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-19800: Order:
-19800: lpo
-19800: Leaf order:
-19800: meet 16 2 3 0,2,2
-19800: join 20 2 5 0,2
-19800: c 3 0 3 2,2,2,2
-19800: b 3 0 3 1,2,2
-19800: a 4 0 4 1,2
-% SZS status Timeout for LAT123-1.p
-NO CLASH, using fixed ground order
-19842: Facts:
-19842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19842: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19842: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19842: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19842: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19842: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-19842: Goal:
-19842: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19842: Order:
-19842: nrkbo
-19842: Leaf order:
-19842: meet 17 2 5 0,2
-19842: join 20 2 4 0,2,2
-19842: c 3 0 3 2,2,2
-19842: b 3 0 3 1,2,2
-19842: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19843: Facts:
-19843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19843: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19843: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19843: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19843: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19843: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-19843: Goal:
-19843: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19843: Order:
-19843: kbo
-19843: Leaf order:
-19843: meet 17 2 5 0,2
-19843: join 20 2 4 0,2,2
-19843: c 3 0 3 2,2,2
-19843: b 3 0 3 1,2,2
-19843: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19844: Facts:
-19844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19844: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19844: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19844: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19844: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19844: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-19844: Goal:
-19844: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19844: Order:
-19844: lpo
-19844: Leaf order:
-19844: meet 17 2 5 0,2
-19844: join 20 2 4 0,2,2
-19844: c 3 0 3 2,2,2
-19844: b 3 0 3 1,2,2
-19844: a 5 0 5 1,2
-% SZS status Timeout for LAT124-1.p
-NO CLASH, using fixed ground order
-19863: Facts:
-19863: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19863: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19863: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19863: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19863: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19863: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19863: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19863: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19863: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-19863: Goal:
-19863: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19863: Order:
-19863: nrkbo
-19863: Leaf order:
-19863: meet 18 2 5 0,2
-19863: join 18 2 4 0,2,2
-19863: c 3 0 3 2,2,2
-19863: b 3 0 3 1,2,2
-19863: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19864: Facts:
-19864: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19864: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19864: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19864: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19864: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19864: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19864: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19864: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19864: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-19864: Goal:
-19864: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19864: Order:
-19864: kbo
-19864: Leaf order:
-19864: meet 18 2 5 0,2
-19864: join 18 2 4 0,2,2
-19864: c 3 0 3 2,2,2
-19864: b 3 0 3 1,2,2
-19864: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19865: Facts:
-19865: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19865: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19865: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19865: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19865: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19865: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19865: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19865: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19865: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-19865: Goal:
-19865: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19865: Order:
-19865: lpo
-19865: Leaf order:
-19865: meet 18 2 5 0,2
-19865: join 18 2 4 0,2,2
-19865: c 3 0 3 2,2,2
-19865: b 3 0 3 1,2,2
-19865: a 5 0 5 1,2
-% SZS status Timeout for LAT125-1.p
-NO CLASH, using fixed ground order
-19895: Facts:
-19895: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19895: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19895: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19895: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19895: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19895: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19895: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19895: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19895: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-19895: Goal:
-19895: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19895: Order:
-19895: kbo
-19895: Leaf order:
-19895: meet 18 2 5 0,2
-19895: join 18 2 4 0,2,2
-19895: c 3 0 3 2,2,2
-19895: b 3 0 3 1,2,2
-19895: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19894: Facts:
-19894: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19894: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19894: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19894: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19894: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19894: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19894: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19894: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19894: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-19894: Goal:
-19894: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19894: Order:
-19894: nrkbo
-19894: Leaf order:
-19894: meet 18 2 5 0,2
-19894: join 18 2 4 0,2,2
-19894: c 3 0 3 2,2,2
-19894: b 3 0 3 1,2,2
-19894: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-19896: Facts:
-19896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19896: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19896: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19896: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19896: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19896: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-19896: Goal:
-19896: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-19896: Order:
-19896: lpo
-19896: Leaf order:
-19896: meet 18 2 5 0,2
-19896: join 18 2 4 0,2,2
-19896: c 3 0 3 2,2,2
-19896: b 3 0 3 1,2,2
-19896: a 5 0 5 1,2
-% SZS status Timeout for LAT126-1.p
-NO CLASH, using fixed ground order
-19924: Facts:
-19924: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19924: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19924: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19924: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19924: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19924: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19924: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19924: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19924: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-19924: Goal:
-19924: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-19924: Order:
-19924: nrkbo
-19924: Leaf order:
-19924: join 16 2 4 0,2,2
-19924: meet 20 2 6 0,2
-19924: c 3 0 3 2,2,2,2
-19924: b 3 0 3 1,2,2
-19924: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-19925: Facts:
-19925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19925: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19925: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19925: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19925: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19925: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-19925: Goal:
-19925: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-19925: Order:
-19925: kbo
-19925: Leaf order:
-19925: join 16 2 4 0,2,2
-19925: meet 20 2 6 0,2
-19925: c 3 0 3 2,2,2,2
-19925: b 3 0 3 1,2,2
-19925: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-19926: Facts:
-19926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19926: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19926: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19926: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19926: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19926: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-19926: Goal:
-19926: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-19926: Order:
-19926: lpo
-19926: Leaf order:
-19926: join 16 2 4 0,2,2
-19926: meet 20 2 6 0,2
-19926: c 3 0 3 2,2,2,2
-19926: b 3 0 3 1,2,2
-19926: a 6 0 6 1,2
-% SZS status Timeout for LAT127-1.p
-NO CLASH, using fixed ground order
-20053: Facts:
-20053: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20053: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20053: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20053: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20053: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20053: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20053: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20053: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20053: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20053: Goal:
-20053: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-20053: Order:
-20053: nrkbo
-20053: Leaf order:
-20053: join 17 2 4 0,2,2
-20053: meet 19 2 6 0,2
-20053: c 3 0 3 2,2,2,2
-20053: b 4 0 4 1,2,2
-20053: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-20054: Facts:
-20054: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20054: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20054: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20054: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20054: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20054: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20054: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20054: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20054: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20054: Goal:
-20054: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-20054: Order:
-20054: kbo
-20054: Leaf order:
-20054: join 17 2 4 0,2,2
-20054: meet 19 2 6 0,2
-20054: c 3 0 3 2,2,2,2
-20054: b 4 0 4 1,2,2
-20054: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-20055: Facts:
-20055: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20055: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20055: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20055: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20055: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20055: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20055: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20055: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20055: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20055: Goal:
-20055: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-20055: Order:
-20055: lpo
-20055: Leaf order:
-20055: join 17 2 4 0,2,2
-20055: meet 19 2 6 0,2
-20055: c 3 0 3 2,2,2,2
-20055: b 4 0 4 1,2,2
-20055: a 5 0 5 1,2
-% SZS status Timeout for LAT128-1.p
-NO CLASH, using fixed ground order
-20071: Facts:
-20071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20071: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20071: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20071: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20071: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20071: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20071: Goal:
-20071: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-20071: Order:
-20071: nrkbo
-20071: Leaf order:
-20071: join 16 2 3 0,2,2
-20071: meet 18 2 5 0,2
-20071: c 3 0 3 2,2,2,2
-20071: b 3 0 3 1,2,2
-20071: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20072: Facts:
-20072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20072: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20072: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20072: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20072: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20072: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20072: Goal:
-20072: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-20072: Order:
-20072: kbo
-20072: Leaf order:
-20072: join 16 2 3 0,2,2
-20072: meet 18 2 5 0,2
-20072: c 3 0 3 2,2,2,2
-20072: b 3 0 3 1,2,2
-20072: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20073: Facts:
-20073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20073: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20073: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20073: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20073: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20073: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-20073: Goal:
-20073: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-20073: Order:
-20073: lpo
-20073: Leaf order:
-20073: join 16 2 3 0,2,2
-20073: meet 18 2 5 0,2
-20073: c 3 0 3 2,2,2,2
-20073: b 3 0 3 1,2,2
-20073: a 4 0 4 1,2
-% SZS status Timeout for LAT129-1.p
-NO CLASH, using fixed ground order
-20105: Facts:
-20105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20105: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20105: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20105: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20105: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20105: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20105: Goal:
-20105: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-20105: Order:
-20105: nrkbo
-20105: Leaf order:
-20105: meet 17 2 5 0,2
-20105: join 17 2 4 0,2,2
-20105: d 2 0 2 2,2,2,2,2
-20105: c 3 0 3 1,2,2,2
-20105: b 2 0 2 1,2,2
-20105: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20106: Facts:
-20106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20106: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20106: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20106: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20106: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20106: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20106: Goal:
-20106: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-20106: Order:
-20106: kbo
-20106: Leaf order:
-20106: meet 17 2 5 0,2
-20106: join 17 2 4 0,2,2
-20106: d 2 0 2 2,2,2,2,2
-20106: c 3 0 3 1,2,2,2
-20106: b 2 0 2 1,2,2
-20106: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20107: Facts:
-20107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20107: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20107: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20107: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20107: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20107: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20107: Goal:
-20107: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-20107: Order:
-20107: lpo
-20107: Leaf order:
-20107: meet 17 2 5 0,2
-20107: join 17 2 4 0,2,2
-20107: d 2 0 2 2,2,2,2,2
-20107: c 3 0 3 1,2,2,2
-20107: b 2 0 2 1,2,2
-20107: a 4 0 4 1,2
-% SZS status Timeout for LAT130-1.p
-NO CLASH, using fixed ground order
-20123: Facts:
-20123: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20123: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20123: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20123: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20123: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20123: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20123: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20123: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20123: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20123: Goal:
-20123: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20123: Order:
-20123: nrkbo
-20123: Leaf order:
-20123: meet 17 2 5 0,2
-20123: join 18 2 5 0,2,2
-20123: d 2 0 2 2,2,2,2,2
-20123: c 3 0 3 1,2,2,2
-20123: b 3 0 3 1,2,2
-20123: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20124: Facts:
-20124: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20124: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20124: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20124: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20124: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20124: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20124: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20124: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20124: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20124: Goal:
-20124: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20124: Order:
-20124: kbo
-20124: Leaf order:
-20124: meet 17 2 5 0,2
-20124: join 18 2 5 0,2,2
-20124: d 2 0 2 2,2,2,2,2
-20124: c 3 0 3 1,2,2,2
-20124: b 3 0 3 1,2,2
-20124: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20125: Facts:
-20125: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20125: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20125: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20125: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20125: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20125: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20125: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20125: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20125: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-20125: Goal:
-20125: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20125: Order:
-20125: lpo
-20125: Leaf order:
-20125: meet 17 2 5 0,2
-20125: join 18 2 5 0,2,2
-20125: d 2 0 2 2,2,2,2,2
-20125: c 3 0 3 1,2,2,2
-20125: b 3 0 3 1,2,2
-20125: a 4 0 4 1,2
-% SZS status Timeout for LAT131-1.p
-NO CLASH, using fixed ground order
-20152: Facts:
-20152: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20152: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20152: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20152: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20152: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20152: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20152: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20152: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20152: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-20152: Goal:
-20152: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20152: Order:
-20152: nrkbo
-20152: Leaf order:
-20152: meet 18 2 5 0,2
-20152: join 19 2 5 0,2,2
-20152: d 2 0 2 2,2,2,2,2
-20152: c 3 0 3 1,2,2,2
-20152: b 3 0 3 1,2,2
-20152: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20153: Facts:
-20153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20153: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20153: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20153: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20153: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20153: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-20153: Goal:
-20153: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20153: Order:
-20153: kbo
-20153: Leaf order:
-20153: meet 18 2 5 0,2
-20153: join 19 2 5 0,2,2
-20153: d 2 0 2 2,2,2,2,2
-20153: c 3 0 3 1,2,2,2
-20153: b 3 0 3 1,2,2
-20153: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20154: Facts:
-20154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20154: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20154: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20154: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20154: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20154: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-20154: Goal:
-20154: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-20154: Order:
-20154: lpo
-20154: Leaf order:
-20154: meet 18 2 5 0,2
-20154: join 19 2 5 0,2,2
-20154: d 2 0 2 2,2,2,2,2
-20154: c 3 0 3 1,2,2,2
-20154: b 3 0 3 1,2,2
-20154: a 4 0 4 1,2
-% SZS status Timeout for LAT132-1.p
-NO CLASH, using fixed ground order
-20170: Facts:
-20170: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20170: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20170: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20170: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20170: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20170: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20170: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20170: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20170: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-20170: Goal:
-20170: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-20170: Order:
-20170: nrkbo
-20170: Leaf order:
-20170: meet 16 2 4 0,2,2
-20170: join 20 2 6 0,2
-20170: c 3 0 3 2,2,2,2
-20170: b 3 0 3 1,2,2
-20170: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-20171: Facts:
-20171: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20171: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20171: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20171: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20171: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20171: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20171: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20171: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20171: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-20171: Goal:
-20171: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-20171: Order:
-20171: kbo
-20171: Leaf order:
-20171: meet 16 2 4 0,2,2
-20171: join 20 2 6 0,2
-20171: c 3 0 3 2,2,2,2
-20171: b 3 0 3 1,2,2
-20171: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-20172: Facts:
-20172: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20172: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20172: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20172: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20172: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20172: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20172: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20172: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20172: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-20172: Goal:
-20172: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-20172: Order:
-20172: lpo
-20172: Leaf order:
-20172: meet 16 2 4 0,2,2
-20172: join 20 2 6 0,2
-20172: c 3 0 3 2,2,2,2
-20172: b 3 0 3 1,2,2
-20172: a 6 0 6 1,2
-% SZS status Timeout for LAT133-1.p
-NO CLASH, using fixed ground order
-20205: Facts:
-20205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20205: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20205: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20205: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20205: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20205: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-20205: Goal:
-20205: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-20205: Order:
-20205: kbo
-20205: Leaf order:
-20205: meet 16 2 4 0,2
-20205: c 3 0 3 2,2,2
-20205: join 20 2 6 0,1,2
-20205: b 4 0 4 2,1,2
-20205: a 5 0 5 1,1,2
-NO CLASH, using fixed ground order
-20204: Facts:
-20204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20204: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20204: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20204: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20204: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20204: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-20204: Goal:
-20204: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-20204: Order:
-20204: nrkbo
-20204: Leaf order:
-20204: meet 16 2 4 0,2
-20204: c 3 0 3 2,2,2
-20204: join 20 2 6 0,1,2
-20204: b 4 0 4 2,1,2
-20204: a 5 0 5 1,1,2
-NO CLASH, using fixed ground order
-20206: Facts:
-20206: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20206: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20206: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20206: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20206: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20206: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20206: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20206: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20206: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-20206: Goal:
-20206: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-20206: Order:
-20206: lpo
-20206: Leaf order:
-20206: meet 16 2 4 0,2
-20206: c 3 0 3 2,2,2
-20206: join 20 2 6 0,1,2
-20206: b 4 0 4 2,1,2
-20206: a 5 0 5 1,1,2
-% SZS status Timeout for LAT134-1.p
-NO CLASH, using fixed ground order
-20243: Facts:
-20243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20243: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20243: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20243: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20243: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20243: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-20243: Goal:
-20243: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20243: Order:
-20243: nrkbo
-20243: Leaf order:
-20243: join 17 2 5 0,2
-20243: meet 17 2 4 0,2,2
-20243: d 2 0 2 2,2,2,2,2
-20243: c 3 0 3 1,2,2,2
-20243: b 2 0 2 1,2,2
-20243: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20244: Facts:
-20244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20244: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20244: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20244: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20244: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20244: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-20244: Goal:
-20244: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20244: Order:
-20244: kbo
-20244: Leaf order:
-20244: join 17 2 5 0,2
-20244: meet 17 2 4 0,2,2
-20244: d 2 0 2 2,2,2,2,2
-20244: c 3 0 3 1,2,2,2
-20244: b 2 0 2 1,2,2
-20244: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20245: Facts:
-20245: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20245: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20245: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20245: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20245: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20245: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20245: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20245: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20245: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-20245: Goal:
-20245: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =>=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20245: Order:
-20245: lpo
-20245: Leaf order:
-20245: join 17 2 5 0,2
-20245: meet 17 2 4 0,2,2
-20245: d 2 0 2 2,2,2,2,2
-20245: c 3 0 3 1,2,2,2
-20245: b 2 0 2 1,2,2
-20245: a 4 0 4 1,2
-% SZS status Timeout for LAT135-1.p
-NO CLASH, using fixed ground order
-20272: Facts:
-20272: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20272: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20272: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20272: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20272: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20272: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20272: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20272: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20272: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20272: Goal:
-20272: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20272: Order:
-20272: nrkbo
-20272: Leaf order:
-20272: join 18 2 5 0,2
-20272: meet 18 2 4 0,2,2
-20272: d 2 0 2 2,2,2,2,2
-20272: c 3 0 3 1,2,2,2
-20272: b 2 0 2 1,2,2
-20272: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20273: Facts:
-20273: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20273: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20273: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20273: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20273: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20273: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20273: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20273: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20273: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20273: Goal:
-20273: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20273: Order:
-20273: kbo
-20273: Leaf order:
-20273: join 18 2 5 0,2
-20273: meet 18 2 4 0,2,2
-20273: d 2 0 2 2,2,2,2,2
-20273: c 3 0 3 1,2,2,2
-20273: b 2 0 2 1,2,2
-20273: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20274: Facts:
-20274: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20274: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20274: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20274: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20274: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20274: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20274: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20274: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20274: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20274: Goal:
-20274: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =>=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-20274: Order:
-20274: lpo
-20274: Leaf order:
-20274: join 18 2 5 0,2
-20274: meet 18 2 4 0,2,2
-20274: d 2 0 2 2,2,2,2,2
-20274: c 3 0 3 1,2,2,2
-20274: b 2 0 2 1,2,2
-20274: a 4 0 4 1,2
-% SZS status Timeout for LAT136-1.p
-NO CLASH, using fixed ground order
-20301: Facts:
-20301: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20301: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20301: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20301: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20301: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20301: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20301: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20301: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20301: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20301: Goal:
-20301: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-20301: Order:
-20301: nrkbo
-20301: Leaf order:
-20301: join 18 2 5 0,2
-20301: meet 19 2 5 0,2,2
-20301: d 2 0 2 2,2,2,2,2
-20301: c 3 0 3 1,2,2,2
-20301: b 3 0 3 1,2,2
-20301: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20302: Facts:
-20302: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20302: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20302: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20302: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20302: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20302: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20302: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20302: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20302: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20302: Goal:
-20302: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-20302: Order:
-20302: kbo
-20302: Leaf order:
-20302: join 18 2 5 0,2
-20302: meet 19 2 5 0,2,2
-20302: d 2 0 2 2,2,2,2,2
-20302: c 3 0 3 1,2,2,2
-20302: b 3 0 3 1,2,2
-20302: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-20303: Facts:
-20303: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20303: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20303: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20303: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20303: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20303: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20303: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20303: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20303: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-20303: Goal:
-20303: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-20303: Order:
-20303: lpo
-20303: Leaf order:
-20303: join 18 2 5 0,2
-20303: meet 19 2 5 0,2,2
-20303: d 2 0 2 2,2,2,2,2
-20303: c 3 0 3 1,2,2,2
-20303: b 3 0 3 1,2,2
-20303: a 4 0 4 1,2
-% SZS status Timeout for LAT137-1.p
-NO CLASH, using fixed ground order
-20331: Facts:
-20331: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20331: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20331: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20331: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20331: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20331: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20331: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20331: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20331: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-20331: Goal:
-20331: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-20331: Order:
-20331: nrkbo
-20331: Leaf order:
-20331: join 16 2 4 0,2,2
-20331: meet 20 2 6 0,2
-20331: c 3 0 3 2,2,2,2
-20331: b 3 0 3 1,2,2
-20331: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-20332: Facts:
-20332: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20332: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20332: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20332: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20332: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20332: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20332: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20332: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20332: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-20332: Goal:
-20332: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-20332: Order:
-20332: kbo
-20332: Leaf order:
-20332: join 16 2 4 0,2,2
-20332: meet 20 2 6 0,2
-20332: c 3 0 3 2,2,2,2
-20332: b 3 0 3 1,2,2
-20332: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-20333: Facts:
-20333: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-20333: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-20333: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-20333: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-20333: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-20333: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-20333: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-20333: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-20333: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-20333: Goal:
-20333: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-20333: Order:
-20333: lpo
-20333: Leaf order:
-20333: join 16 2 4 0,2,2
-20333: meet 20 2 6 0,2
-20333: c 3 0 3 2,2,2,2
-20333: b 3 0 3 1,2,2
-20333: a 6 0 6 1,2
-% SZS status Timeout for LAT171-1.p
-NO CLASH, using fixed ground order
-20686: Facts:
-20686: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20686: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20686: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20686: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20686: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-20686: Goal:
-20686: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-20686: Order:
-20686: nrkbo
-20686: Leaf order:
-20686: y 2 0 0
-20686: not 2 1 0
-20686: truth 4 0 1 3
-20686: implies 16 2 1 0,2
-20686: z 2 0 1 2,2
-20686: x 2 0 1 1,2
-NO CLASH, using fixed ground order
-20687: Facts:
-20687: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20687: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20687: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20687: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20687: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-20687: Goal:
-20687: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-20687: Order:
-20687: kbo
-20687: Leaf order:
-20687: y 2 0 0
-20687: not 2 1 0
-20687: truth 4 0 1 3
-20687: implies 16 2 1 0,2
-20687: z 2 0 1 2,2
-20687: x 2 0 1 1,2
-NO CLASH, using fixed ground order
-20688: Facts:
-20688: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20688: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20688: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20688: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20688: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-20688: Goal:
-20688: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-20688: Order:
-20688: lpo
-20688: Leaf order:
-20688: y 2 0 0
-20688: not 2 1 0
-20688: truth 4 0 1 3
-20688: implies 16 2 1 0,2
-20688: z 2 0 1 2,2
-20688: x 2 0 1 1,2
-% SZS status Timeout for LCL136-1.p
-NO CLASH, using fixed ground order
-20715: Facts:
-20715: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20715: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20715: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20715: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20715: Goal:
-20715: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-20715: Order:
-20715: nrkbo
-20715: Leaf order:
-20715: not 2 1 0
-20715: truth 4 0 1 3
-20715: z 2 0 2 2,1,2,2
-20715: implies 19 2 6 0,2
-20715: y 3 0 3 2,1,1,2
-20715: x 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-20716: Facts:
-20716: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20716: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20716: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20716: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20716: Goal:
-20716: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-20716: Order:
-20716: kbo
-20716: Leaf order:
-20716: not 2 1 0
-20716: truth 4 0 1 3
-20716: z 2 0 2 2,1,2,2
-20716: implies 19 2 6 0,2
-20716: y 3 0 3 2,1,1,2
-20716: x 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-20717: Facts:
-20717: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20717: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20717: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20717: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20717: Goal:
-20717: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-20717: Order:
-20717: lpo
-20717: Leaf order:
-20717: not 2 1 0
-20717: truth 4 0 1 3
-20717: z 2 0 2 2,1,2,2
-20717: implies 19 2 6 0,2
-20717: y 3 0 3 2,1,1,2
-20717: x 2 0 2 1,1,1,2
-% SZS status Timeout for LCL137-1.p
-NO CLASH, using fixed ground order
-20733: Facts:
-20733: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20733: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20733: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20733: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20733: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-20733: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-20733: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-20733: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-20733: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-20733: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-20733: Goal:
-20733: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-20733: Order:
-20733: nrkbo
-20733: Leaf order:
-20733: implies 14 2 0
-20733: truth 3 0 0
-20733: not 12 1 6 0,2
-20733: and 11 2 4 0,1,1,2
-20733: or 12 2 4 0,1,2
-20733: x 10 0 10 1,1,1,2
-NO CLASH, using fixed ground order
-20734: Facts:
-20734: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20734: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20734: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20734: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20734: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-20734: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-20734: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-20734: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-20734: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-20734: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-20734: Goal:
-NO CLASH, using fixed ground order
-20735: Facts:
-20735: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-20735: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-20735: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-20735: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-20735: Id : 6, {_}:
- or ?14 ?15 =>= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-20735: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-20735: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-20735: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-20735: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-20735: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-20735: Goal:
-20735: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-20735: Order:
-20735: lpo
-20735: Leaf order:
-20735: implies 14 2 0
-20735: truth 3 0 0
-20735: not 12 1 6 0,2
-20735: and 11 2 4 0,1,1,2
-20735: or 12 2 4 0,1,2
-20735: x 10 0 10 1,1,1,2
-20734: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-20734: Order:
-20734: kbo
-20734: Leaf order:
-20734: implies 14 2 0
-20734: truth 3 0 0
-20734: not 12 1 6 0,2
-20734: and 11 2 4 0,1,1,2
-20734: or 12 2 4 0,1,2
-20734: x 10 0 10 1,1,1,2
-% SZS status Timeout for LCL165-1.p
-NO CLASH, using fixed ground order
-20763: Facts:
-20763: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20763: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20763: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20763: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20763: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20763: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20763: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20763: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20763: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20763: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20763: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20763: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20763: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20763: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20763: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20763: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20763: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20763: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20763: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20763: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20763: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20763: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20763: Goal:
-20763: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-20763: Order:
-20763: kbo
-20763: Leaf order:
-20763: commutator 1 2 0
-20763: additive_inverse 22 1 0
-20763: multiply 40 2 0
-20763: additive_identity 8 0 0
-20763: associator 4 3 3 0,2
-20763: add 26 2 2 0,3,2
-20763: v 2 0 2 2,3,2
-20763: u 2 0 2 1,3,2
-20763: y 3 0 3 2,2
-20763: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-20762: Facts:
-20762: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20762: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20762: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20762: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20762: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20762: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20762: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20762: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20762: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20762: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20762: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20762: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20762: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20762: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20762: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20762: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20762: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20762: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20762: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20762: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20762: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20762: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20762: Goal:
-20762: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-20762: Order:
-20762: nrkbo
-20762: Leaf order:
-20762: commutator 1 2 0
-20762: additive_inverse 22 1 0
-20762: multiply 40 2 0
-20762: additive_identity 8 0 0
-20762: associator 4 3 3 0,2
-20762: add 26 2 2 0,3,2
-20762: v 2 0 2 2,3,2
-20762: u 2 0 2 1,3,2
-20762: y 3 0 3 2,2
-20762: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-20764: Facts:
-20764: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20764: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20764: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20764: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20764: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20764: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20764: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20764: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20764: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20764: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20764: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20764: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20764: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20764: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20764: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20764: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20764: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20764: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20764: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20764: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20764: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20764: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20764: Goal:
-20764: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-20764: Order:
-20764: lpo
-20764: Leaf order:
-20764: commutator 1 2 0
-20764: additive_inverse 22 1 0
-20764: multiply 40 2 0
-20764: additive_identity 8 0 0
-20764: associator 4 3 3 0,2
-20764: add 26 2 2 0,3,2
-20764: v 2 0 2 2,3,2
-20764: u 2 0 2 1,3,2
-20764: y 3 0 3 2,2
-20764: x 3 0 3 1,2
-% SZS status Timeout for RNG019-7.p
-NO CLASH, using fixed ground order
-20780: Facts:
-20780: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20780: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20780: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20780: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20780: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20780: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20780: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20780: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20780: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20780: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20780: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20780: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20780: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20780: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20780: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20780: Goal:
-20780: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20780: Order:
-20780: nrkbo
-20780: Leaf order:
-20780: commutator 1 2 0
-20780: additive_inverse 6 1 0
-20780: multiply 22 2 0
-20780: additive_identity 8 0 0
-20780: associator 4 3 3 0,2
-20780: y 3 0 3 3,2
-20780: add 18 2 2 0,2,2
-20780: v 2 0 2 2,2,2
-20780: u 2 0 2 1,2,2
-20780: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-20781: Facts:
-20781: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20781: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20781: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20781: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20781: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20781: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20781: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20781: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20781: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20781: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20781: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20781: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20781: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20781: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20781: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20781: Goal:
-20781: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20781: Order:
-20781: kbo
-20781: Leaf order:
-20781: commutator 1 2 0
-20781: additive_inverse 6 1 0
-20781: multiply 22 2 0
-20781: additive_identity 8 0 0
-20781: associator 4 3 3 0,2
-20781: y 3 0 3 3,2
-20781: add 18 2 2 0,2,2
-20781: v 2 0 2 2,2,2
-20781: u 2 0 2 1,2,2
-20781: x 3 0 3 1,2
-NO CLASH, using fixed ground order
-20782: Facts:
-20782: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20782: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20782: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20782: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20782: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20782: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20782: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20782: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20782: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20782: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20782: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20782: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20782: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20782: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20782: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20782: Goal:
-20782: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20782: Order:
-20782: lpo
-20782: Leaf order:
-20782: commutator 1 2 0
-20782: additive_inverse 6 1 0
-20782: multiply 22 2 0
-20782: additive_identity 8 0 0
-20782: associator 4 3 3 0,2
-20782: y 3 0 3 3,2
-20782: add 18 2 2 0,2,2
-20782: v 2 0 2 2,2,2
-20782: u 2 0 2 1,2,2
-20782: x 3 0 3 1,2
-% SZS status Timeout for RNG020-6.p
-NO CLASH, using fixed ground order
-20815: Facts:
-20815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20815: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20815: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20815: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20815: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20815: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20815: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20815: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20815: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20815: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20815: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20815: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20815: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-NO CLASH, using fixed ground order
-20816: Facts:
-20816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20816: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20816: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20816: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-NO CLASH, using fixed ground order
-20817: Facts:
-20817: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20817: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20816: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20817: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20816: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20817: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20817: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20816: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20817: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20817: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20816: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20817: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20816: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20815: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20816: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20815: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20816: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20816: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20815: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20816: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20815: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20816: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20815: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20816: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20815: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20816: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20815: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20815: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20815: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20815: Goal:
-20815: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20815: Order:
-20815: nrkbo
-20815: Leaf order:
-20815: commutator 1 2 0
-20815: additive_inverse 22 1 0
-20815: multiply 40 2 0
-20815: additive_identity 8 0 0
-20815: associator 4 3 3 0,2
-20815: y 3 0 3 3,2
-20815: add 26 2 2 0,2,2
-20815: v 2 0 2 2,2,2
-20815: u 2 0 2 1,2,2
-20815: x 3 0 3 1,2
-20817: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20816: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20816: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20816: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20816: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20816: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20816: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20816: Goal:
-20816: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20816: Order:
-20816: kbo
-20816: Leaf order:
-20816: commutator 1 2 0
-20816: additive_inverse 22 1 0
-20816: multiply 40 2 0
-20816: additive_identity 8 0 0
-20816: associator 4 3 3 0,2
-20816: y 3 0 3 3,2
-20816: add 26 2 2 0,2,2
-20816: v 2 0 2 2,2,2
-20816: u 2 0 2 1,2,2
-20816: x 3 0 3 1,2
-20817: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20817: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20817: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20817: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20817: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20817: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20817: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20817: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20817: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20817: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20817: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20817: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20817: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20817: Goal:
-20817: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-20817: Order:
-20817: lpo
-20817: Leaf order:
-20817: commutator 1 2 0
-20817: additive_inverse 22 1 0
-20817: multiply 40 2 0
-20817: additive_identity 8 0 0
-20817: associator 4 3 3 0,2
-20817: y 3 0 3 3,2
-20817: add 26 2 2 0,2,2
-20817: v 2 0 2 2,2,2
-20817: u 2 0 2 1,2,2
-20817: x 3 0 3 1,2
-% SZS status Timeout for RNG020-7.p
-NO CLASH, using fixed ground order
-20843: Facts:
-20843: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20843: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20843: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20843: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20843: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20843: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20843: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20843: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20843: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20843: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20843: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20843: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20843: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20843: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20843: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20843: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20843: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20843: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20843: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20843: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20843: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20843: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20843: Goal:
-20843: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-20843: Order:
-20843: kbo
-20843: Leaf order:
-20843: commutator 1 2 0
-20843: additive_inverse 22 1 0
-20843: multiply 40 2 0
-20843: additive_identity 8 0 0
-20843: associator 4 3 3 0,2
-20843: y 3 0 3 3,2
-20843: x 3 0 3 2,2
-20843: add 26 2 2 0,1,2
-20843: v 2 0 2 2,1,2
-20843: u 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20842: Facts:
-20842: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20842: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20842: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20842: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20842: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20842: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20842: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20842: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20842: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20842: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20842: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20842: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20842: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20842: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20842: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20842: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20842: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20842: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20842: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20842: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20842: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20842: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20842: Goal:
-20842: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-20842: Order:
-20842: nrkbo
-20842: Leaf order:
-20842: commutator 1 2 0
-20842: additive_inverse 22 1 0
-20842: multiply 40 2 0
-20842: additive_identity 8 0 0
-20842: associator 4 3 3 0,2
-20842: y 3 0 3 3,2
-20842: x 3 0 3 2,2
-20842: add 26 2 2 0,1,2
-20842: v 2 0 2 2,1,2
-20842: u 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20844: Facts:
-20844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20844: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20844: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20844: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20844: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20844: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20844: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20844: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20844: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20844: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20844: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20844: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20844: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20844: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20844: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20844: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-20844: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-20844: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-20844: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-20844: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-20844: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-20844: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-20844: Goal:
-20844: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-20844: Order:
-20844: lpo
-20844: Leaf order:
-20844: commutator 1 2 0
-20844: additive_inverse 22 1 0
-20844: multiply 40 2 0
-20844: additive_identity 8 0 0
-20844: associator 4 3 3 0,2
-20844: y 3 0 3 3,2
-20844: x 3 0 3 2,2
-20844: add 26 2 2 0,1,2
-20844: v 2 0 2 2,1,2
-20844: u 2 0 2 1,1,2
-% SZS status Timeout for RNG021-7.p
-NO CLASH, using fixed ground order
-20871: Facts:
-20871: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20871: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20871: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20871: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20871: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20871: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20871: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20871: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20871: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20871: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20871: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20871: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20871: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20871: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20871: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20871: Goal:
-20871: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-20871: Order:
-20871: nrkbo
-20871: Leaf order:
-20871: commutator 1 2 0
-20871: additive_inverse 6 1 0
-20871: multiply 22 2 0
-20871: additive_identity 9 0 1 3
-20871: add 17 2 1 0,2
-20871: associator 3 3 2 0,1,2
-20871: z 2 0 2 3,1,2
-20871: y 2 0 2 2,1,2
-20871: x 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20872: Facts:
-20872: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20872: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20872: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20872: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20872: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20872: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20872: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20872: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20872: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20872: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20872: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20872: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20872: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20872: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20872: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20872: Goal:
-20872: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-20872: Order:
-20872: kbo
-20872: Leaf order:
-20872: commutator 1 2 0
-20872: additive_inverse 6 1 0
-20872: multiply 22 2 0
-20872: additive_identity 9 0 1 3
-20872: add 17 2 1 0,2
-20872: associator 3 3 2 0,1,2
-20872: z 2 0 2 3,1,2
-20872: y 2 0 2 2,1,2
-20872: x 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20873: Facts:
-20873: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20873: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20873: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20873: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20873: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20873: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20873: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20873: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20873: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20873: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20873: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20873: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20873: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20873: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20873: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20873: Goal:
-20873: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-20873: Order:
-20873: lpo
-20873: Leaf order:
-20873: commutator 1 2 0
-20873: additive_inverse 6 1 0
-20873: multiply 22 2 0
-20873: additive_identity 9 0 1 3
-20873: add 17 2 1 0,2
-20873: associator 3 3 2 0,1,2
-20873: z 2 0 2 3,1,2
-20873: y 2 0 2 2,1,2
-20873: x 2 0 2 1,1,2
-% SZS status Timeout for RNG025-4.p
-NO CLASH, using fixed ground order
-20890: Facts:
-20890: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-20890: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-20890: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-20890: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-20890: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-20890: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-20890: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-20890: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-20890: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-20890: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-20890: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-20890: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20890: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20890: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =<=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-20890: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =<=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-20890: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =<=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-NO CLASH, using fixed ground order
-20891: Facts:
-20891: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-20891: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-20891: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-20891: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-20891: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-20891: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-20891: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-20891: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-NO CLASH, using fixed ground order
-20892: Facts:
-20892: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-20892: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-20892: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-20892: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-20892: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-20892: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-20892: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-20892: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-20892: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-20891: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-20890: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-20890: Goal:
-20892: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-20890: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20890: Order:
-20890: nrkbo
-20890: Leaf order:
-20892: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-20892: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20892: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20892: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =>=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-20892: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =>=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-20892: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =>=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-20892: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-20892: Goal:
-20892: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20892: Order:
-20892: lpo
-20892: Leaf order:
-20892: commutator 1 2 0
-20892: additive_inverse 5 1 0
-20892: multiply 18 2 0
-20892: additive_identity 9 0 1 3
-20892: add 22 2 1 0,2
-20892: associator 11 3 2 0,1,2
-20892: c 2 0 2 3,1,2
-20892: b 2 0 2 2,1,2
-20892: a 2 0 2 1,1,2
-20891: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-20890: commutator 1 2 0
-20890: additive_inverse 5 1 0
-20890: multiply 18 2 0
-20890: additive_identity 9 0 1 3
-20890: add 22 2 1 0,2
-20890: associator 11 3 2 0,1,2
-20890: c 2 0 2 3,1,2
-20890: b 2 0 2 2,1,2
-20890: a 2 0 2 1,1,2
-20891: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-20891: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20891: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20891: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =<=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-20891: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =<=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-20891: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =<=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-20891: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-20891: Goal:
-20891: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20891: Order:
-20891: kbo
-20891: Leaf order:
-20891: commutator 1 2 0
-20891: additive_inverse 5 1 0
-20891: multiply 18 2 0
-20891: additive_identity 9 0 1 3
-20891: add 22 2 1 0,2
-20891: associator 11 3 2 0,1,2
-20891: c 2 0 2 3,1,2
-20891: b 2 0 2 2,1,2
-20891: a 2 0 2 1,1,2
-% SZS status Timeout for RNG025-8.p
-NO CLASH, using fixed ground order
-20920: Facts:
-20920: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-20920: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =<=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-20920: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =<=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-20920: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-20920: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-20920: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-20920: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-20920: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-20920: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-20920: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-20920: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-20920: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-20920: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-20920: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-20920: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-20920: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-20920: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-20920: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-20920: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-20920: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-20920: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =<=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-20920: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =<=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-20920: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =<=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-20920: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-20920: Goal:
-20920: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20920: Order:
-20920: nrkbo
-20920: Leaf order:
-20920: commutator 1 2 0
-20920: multiply 36 2 0 add
-20920: additive_inverse 21 1 0
-20920: additive_identity 9 0 1 3
-20920: add 30 2 1 0,2
-20920: associator 11 3 2 0,1,2
-20920: c 2 0 2 3,1,2
-20920: b 2 0 2 2,1,2
-20920: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20921: Facts:
-20921: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-20921: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =<=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-20921: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =<=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-20921: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-20921: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-20921: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-20921: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-20921: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-20921: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-20921: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-20921: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-20921: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-20921: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-20921: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-20921: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-20921: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-20921: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-20921: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-20921: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-20921: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-20921: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =<=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-20921: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =<=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-20921: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =<=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-20921: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-20921: Goal:
-20921: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20921: Order:
-20921: kbo
-20921: Leaf order:
-20921: commutator 1 2 0
-20921: multiply 36 2 0 add
-20921: additive_inverse 21 1 0
-20921: additive_identity 9 0 1 3
-20921: add 30 2 1 0,2
-20921: associator 11 3 2 0,1,2
-20921: c 2 0 2 3,1,2
-20921: b 2 0 2 2,1,2
-20921: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-20922: Facts:
-20922: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-20922: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =<=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-20922: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =<=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-20922: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-20922: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-20922: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-20922: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-20922: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-20922: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-20922: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-20922: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-20922: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-20922: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-20922: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-20922: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-20922: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-20922: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-20922: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-20922: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-20922: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-20922: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =>=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-20922: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =>=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-20922: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =>=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-20922: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-20922: Goal:
-20922: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-20922: Order:
-20922: lpo
-20922: Leaf order:
-20922: commutator 1 2 0
-20922: multiply 36 2 0 add
-20922: additive_inverse 21 1 0
-20922: additive_identity 9 0 1 3
-20922: add 30 2 1 0,2
-20922: associator 11 3 2 0,1,2
-20922: c 2 0 2 3,1,2
-20922: b 2 0 2 2,1,2
-20922: a 2 0 2 1,1,2
-% SZS status Timeout for RNG025-9.p
-NO CLASH, using fixed ground order
-20954: Facts:
-20954: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-20954: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-20954: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-20954: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =<=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-20954: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-20954: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-20954: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-20954: Goal:
-20954: Id : 1, {_}:
- add a (multiply b c) =<= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-20954: Order:
-20954: nrkbo
-20954: Leaf order:
-20954: pixley 4 3 0
-20954: n1 1 0 0
-20954: inverse 3 1 0
-20954: add 9 2 3 0,2
-20954: multiply 9 2 2 0,2,2
-20954: c 2 0 2 2,2,2
-20954: b 2 0 2 1,2,2
-20954: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-20955: Facts:
-20955: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-20955: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-20955: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-20955: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =<=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-20955: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-20955: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-20955: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-20955: Goal:
-20955: Id : 1, {_}:
- add a (multiply b c) =<= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-20955: Order:
-20955: kbo
-20955: Leaf order:
-20955: pixley 4 3 0
-20955: n1 1 0 0
-20955: inverse 3 1 0
-20955: add 9 2 3 0,2
-20955: multiply 9 2 2 0,2,2
-20955: c 2 0 2 2,2,2
-20955: b 2 0 2 1,2,2
-20955: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-20956: Facts:
-20956: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-20956: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =?= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-20956: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-20956: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =<=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-20956: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-20956: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-20956: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-20956: Goal:
-20956: Id : 1, {_}:
- add a (multiply b c) =<= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-20956: Order:
-20956: lpo
-20956: Leaf order:
-20956: pixley 4 3 0
-20956: n1 1 0 0
-20956: inverse 3 1 0
-20956: add 9 2 3 0,2
-20956: multiply 9 2 2 0,2,2
-20956: c 2 0 2 2,2,2
-20956: b 2 0 2 1,2,2
-20956: a 3 0 3 1,2
-Statistics :
-Max weight : 22
-Found proof, 38.942991s
-% SZS status Unsatisfiable for BOO023-1.p
-% SZS output start CNFRefutation for BOO023-1.p
-Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35
-Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13
-Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3
-Id : 485, {_}: multiply (pixley ?939 ?940 ?941) (multiply ?941 (add ?939 (inverse ?940))) =>= multiply ?941 (add ?939 (inverse ?940)) [941, 940, 939] by Super 2 with 19 at 1,2
-Id : 505, {_}: multiply ?1017 (multiply ?1018 (add ?1017 (inverse ?1018))) =>= multiply ?1018 (add ?1017 (inverse ?1018)) [1018, 1017] by Super 485 with 7 at 1,2
-Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3
-Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3
-Id : 413, {_}: ?825 =<= add (multiply ?826 (inverse ?826)) (multiply ?825 n1) [826, 825] by Demod 22 with 6 at 2
-Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2
-Id : 428, {_}: ?870 =<= add (inverse n1) (multiply ?870 n1) [870] by Super 413 with 16 at 1,3
-Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3
-Id : 548, {_}: ?1062 =<= add (inverse n1) (multiply ?1062 n1) [1062] by Super 413 with 16 at 1,3
-Id : 593, {_}: add ?1120 n1 =?= add (inverse n1) n1 [1120] by Super 548 with 2 at 2,3
-Id : 553, {_}: add ?1072 n1 =?= add (inverse n1) n1 [1072] by Super 548 with 2 at 2,3
-Id : 607, {_}: add ?1148 n1 =?= add ?1149 n1 [1149, 1148] by Super 593 with 553 at 3
-Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3
-Id : 408, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2
-Id : 412, {_}: multiply (multiply ?822 n1) (add ?823 ?822) =<= add (multiply ?823 (multiply ?822 n1)) (multiply ?822 n1) [823, 822] by Super 13 with 408 at 2,2,2
-Id : 274, {_}: multiply (multiply ?502 (add ?503 ?504)) (multiply ?504 ?502) =>= multiply ?504 ?502 [504, 503, 502] by Super 2 with 3 at 1,2
-Id : 284, {_}: multiply (multiply ?542 n1) (multiply (inverse ?543) ?542) =>= multiply (inverse ?543) ?542 [543, 542] by Super 274 with 4 at 2,1,2
-Id : 173, {_}: multiply (inverse ?334) (add ?335 n1) =<= add (multiply ?335 (inverse ?334)) (inverse ?334) [335, 334] by Super 3 with 16 at 2,3
-Id : 1514, {_}: multiply ?2669 (multiply ?2670 (add ?2669 (inverse ?2670))) =>= multiply ?2670 (add ?2669 (inverse ?2670)) [2670, 2669] by Super 485 with 7 at 1,2
-Id : 672, {_}: multiply (multiply ?1271 n1) (multiply (inverse ?1272) ?1271) =>= multiply (inverse ?1272) ?1271 [1272, 1271] by Super 274 with 4 at 2,1,2
-Id : 688, {_}: multiply n1 (multiply (inverse ?1320) (add ?1321 n1)) =>= multiply (inverse ?1320) (add ?1321 n1) [1321, 1320] by Super 672 with 2 at 1,2
-Id : 199, {_}: multiply (inverse ?371) (add ?372 n1) =<= add (multiply ?372 (inverse ?371)) (inverse ?371) [372, 371] by Super 3 with 16 at 2,3
-Id : 210, {_}: multiply (inverse ?404) (add (add ?405 (inverse ?404)) n1) =>= add (inverse ?404) (inverse ?404) [405, 404] by Super 199 with 2 at 1,3
-Id : 966, {_}: add (inverse ?404) (multiply n1 (inverse ?404)) =>= add (inverse ?404) (inverse ?404) [404] by Demod 210 with 14 at 2
-Id : 174, {_}: multiply (inverse ?337) (add n1 ?338) =<= add (inverse ?337) (multiply ?338 (inverse ?337)) [338, 337] by Super 3 with 16 at 1,3
-Id : 967, {_}: multiply (inverse ?404) (add n1 n1) =?= add (inverse ?404) (inverse ?404) [404] by Demod 966 with 174 at 2
-Id : 982, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) (add n1 n1) [1904] by Super 688 with 967 at 2,2
-Id : 1530, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 1514 with 982 at 2,2
-Id : 1554, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 1530 with 967 at 2,2
-Id : 1555, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 1554 with 982 at 3
-Id : 1556, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 1555 with 967 at 3
-Id : 1568, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 1556 at 2,3
-Id : 1597, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1568 with 8 at 2
-Id : 1814, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 1597 at 2,2
-Id : 1906, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 1814 with 173 at 3
-Id : 1990, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3163 n1) [3163] by Super 1906 with 607 at 2,3
-Id : 2009, {_}: multiply (inverse n1) (inverse n1) =>= add (inverse n1) (inverse n1) [] by Super 1990 with 967 at 3
-Id : 2048, {_}: multiply (inverse n1) (add (inverse n1) n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Super 173 with 2009 at 1,3
-Id : 1928, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Super 1906 with 607 at 2,3
-Id : 2040, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 1928 with 2009 at 2
-Id : 2082, {_}: add (inverse n1) (inverse n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Demod 2048 with 2040 at 2
-Id : 2135, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Super 14 with 2082 at 2,2
-Id : 2186, {_}: add (inverse n1) (inverse n1) =<= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 2135 with 1556 at 2
-Id : 2187, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add n1 (inverse n1)) [] by Demod 2186 with 174 at 3
-Id : 2188, {_}: add (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2187 with 4 at 2,3
-Id : 2041, {_}: inverse n1 =<= add (add (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1597 with 2009 at 1,3
-Id : 2225, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (add (inverse n1) (inverse n1)) [] by Demod 2041 with 2188 at 1,3
-Id : 2226, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (multiply (inverse n1) n1) [] by Demod 2225 with 2188 at 2,3
-Id : 2235, {_}: inverse n1 =<= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 2226 with 3 at 3
-Id : 2236, {_}: inverse n1 =<= multiply (inverse n1) (add n1 n1) [] by Demod 2235 with 982 at 3
-Id : 2237, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 2236 with 967 at 3
-Id : 2238, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 2237 with 2188 at 3
-Id : 2244, {_}: add (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2188 with 2238 at 3
-Id : 2259, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= add (multiply ?3306 (inverse n1)) (inverse n1) [3306] by Super 13 with 2244 at 2,2,2
-Id : 2294, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= multiply (inverse n1) (add ?3306 n1) [3306] by Demod 2259 with 173 at 3
-Id : 2232, {_}: multiply (inverse n1) n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2040 with 2188 at 2
-Id : 2243, {_}: inverse n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2232 with 2238 at 2
-Id : 2295, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= inverse n1 [3306] by Demod 2294 with 2243 at 3
-Id : 2419, {_}: multiply (multiply (add ?3405 (inverse n1)) n1) (inverse n1) =>= multiply (inverse n1) (add ?3405 (inverse n1)) [3405] by Super 284 with 2295 at 2,2
-Id : 3205, {_}: multiply (multiply (add ?4259 (inverse n1)) n1) (inverse n1) =>= inverse n1 [4259] by Demod 2419 with 2295 at 3
-Id : 3222, {_}: multiply (multiply n1 n1) (inverse n1) =>= inverse n1 [] by Super 3205 with 4 at 1,1,2
-Id : 3294, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= add (inverse n1) (multiply ?4332 (inverse n1)) [4332] by Super 3 with 3222 at 1,3
-Id : 3323, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= multiply (inverse n1) (add n1 ?4332) [4332] by Demod 3294 with 174 at 3
-Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3
-Id : 2249, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Super 24 with 2244 at 1,2,2,3
-Id : 2310, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Demod 2249 with 2244 at 1,2
-Id : 2311, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (inverse n1)) [3289] by Demod 2310 with 2244 at 2,2,3
-Id : 2312, {_}: pixley (inverse n1) n1 ?3289 =<= multiply (inverse n1) (add n1 ?3289) [3289] by Demod 2311 with 174 at 3
-Id : 3528, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4508) =>= pixley (inverse n1) n1 ?4508 [4508] by Demod 3323 with 2312 at 3
-Id : 3542, {_}: multiply (inverse n1) (multiply n1 (add n1 ?4535)) =>= pixley (inverse n1) n1 (multiply ?4535 n1) [4535] by Super 3528 with 3 at 2,2
-Id : 2258, {_}: pixley (inverse n1) n1 ?3304 =<= add (multiply (inverse n1) (inverse n1)) (multiply ?3304 (inverse n1)) [3304] by Super 19 with 2244 at 2,2,3
-Id : 2766, {_}: pixley (inverse n1) n1 ?3924 =<= multiply (inverse n1) (add (inverse n1) ?3924) [3924] by Demod 2258 with 3 at 3
-Id : 2784, {_}: pixley (inverse n1) n1 (multiply ?3959 n1) =>= multiply (inverse n1) ?3959 [3959] by Super 2766 with 428 at 2,3
-Id : 4047, {_}: multiply (inverse n1) (multiply n1 (add n1 ?5164)) =>= multiply (inverse n1) ?5164 [5164] by Demod 3542 with 2784 at 3
-Id : 4052, {_}: multiply (inverse n1) (multiply n1 n1) =>= multiply (inverse n1) (inverse n1) [] by Super 4047 with 4 at 2,2,2
-Id : 2233, {_}: multiply (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2009 with 2188 at 3
-Id : 2242, {_}: multiply (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2233 with 2238 at 3
-Id : 4088, {_}: multiply (inverse n1) (multiply n1 n1) =>= inverse n1 [] by Demod 4052 with 2242 at 3
-Id : 4118, {_}: multiply (multiply n1 n1) (add (inverse n1) n1) =>= add (inverse n1) (multiply n1 n1) [] by Super 412 with 4088 at 1,3
-Id : 1137, {_}: multiply (multiply ?2152 n1) (add ?2152 ?2153) =<= add (multiply ?2152 n1) (multiply ?2153 (multiply ?2152 n1)) [2153, 2152] by Super 14 with 408 at 1,2,2
-Id : 411, {_}: multiply ?820 (multiply ?820 n1) =>= multiply ?820 n1 [820] by Super 2 with 408 at 1,2
-Id : 1151, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= add (multiply ?2193 n1) (multiply ?2193 n1) [2193] by Super 1137 with 411 at 2,3
-Id : 1282, {_}: multiply (multiply ?2412 n1) (add ?2412 ?2412) =>= multiply n1 (add ?2412 ?2412) [2412] by Demod 1151 with 3 at 3
-Id : 1286, {_}: multiply (multiply n1 n1) (add ?2420 n1) =>= multiply n1 (add n1 n1) [2420] by Super 1282 with 607 at 2,2
-Id : 4147, {_}: multiply n1 (add n1 n1) =<= add (inverse n1) (multiply n1 n1) [] by Demod 4118 with 1286 at 2
-Id : 4148, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
-Id : 4590, {_}: multiply (add n1 n1) (add n1 ?5598) =>= add n1 (multiply ?5598 (add n1 n1)) [5598] by Super 3 with 4148 at 1,3
-Id : 4186, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
-Id : 4194, {_}: multiply n1 (add ?5284 n1) =>= n1 [5284] by Super 4186 with 607 at 2,2
-Id : 4313, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 4194 at 2
-Id : 4601, {_}: multiply (add n1 n1) n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Super 4590 with 4313 at 2,2
-Id : 4648, {_}: n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Demod 4601 with 2 at 2
-Id : 1187, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= multiply n1 (add ?2193 ?2193) [2193] by Demod 1151 with 3 at 3
-Id : 4649, {_}: n1 =<= add n1 (multiply n1 (add n1 n1)) [] by Demod 4648 with 1187 at 2,3
-Id : 4650, {_}: n1 =<= add n1 n1 [] by Demod 4649 with 4194 at 2,3
-Id : 4692, {_}: add ?5677 n1 =>= n1 [5677] by Super 607 with 4650 at 3
-Id : 5124, {_}: multiply ?6342 n1 =<= add ?6342 (multiply n1 ?6342) [6342] by Super 14 with 4692 at 2,2
-Id : 4670, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) n1 [1904] by Demod 982 with 4650 at 2,3
-Id : 4669, {_}: multiply (inverse ?404) n1 =<= add (inverse ?404) (inverse ?404) [404] by Demod 967 with 4650 at 2,2
-Id : 4674, {_}: multiply n1 (multiply (inverse ?1904) n1) =>= multiply (inverse ?1904) n1 [1904] by Demod 4670 with 4669 at 2,2
-Id : 5136, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= add (multiply (inverse ?6367) n1) (multiply (inverse ?6367) n1) [6367] by Super 5124 with 4674 at 2,3
-Id : 5182, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= multiply n1 (add (inverse ?6367) (inverse ?6367)) [6367] by Demod 5136 with 3 at 3
-Id : 5183, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply n1 (multiply (inverse ?6367) n1) [6367] by Demod 5182 with 4669 at 2,3
-Id : 5184, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply (inverse ?6367) n1 [6367] by Demod 5183 with 4674 at 3
-Id : 5206, {_}: multiply (inverse ?6424) n1 =<= add (inverse n1) (multiply (inverse ?6424) n1) [6424] by Super 428 with 5184 at 2,3
-Id : 5244, {_}: multiply (inverse ?6424) n1 =>= inverse ?6424 [6424] by Demod 5206 with 428 at 3
-Id : 5308, {_}: inverse ?6512 =<= add (inverse n1) (inverse ?6512) [6512] by Super 428 with 5244 at 2,3
-Id : 5370, {_}: pixley (inverse n1) ?6557 ?6558 =<= add (multiply (inverse n1) (inverse ?6557)) (multiply ?6558 (inverse ?6557)) [6558, 6557] by Super 19 with 5308 at 2,2,3
-Id : 7459, {_}: pixley (inverse n1) ?8766 ?8767 =<= multiply (inverse ?8766) (add (inverse n1) ?8767) [8767, 8766] by Demod 5370 with 3 at 3
-Id : 5371, {_}: inverse (inverse n1) =>= n1 [] by Super 4 with 5308 at 2
-Id : 7482, {_}: pixley (inverse n1) (inverse n1) ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Super 7459 with 5371 at 1,3
-Id : 7542, {_}: ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Demod 7482 with 6 at 2
-Id : 5466, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 (inverse (inverse n1))) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Super 19 with 5371 at 2,2,2,3
-Id : 5516, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Demod 5466 with 5371 at 2,1,3
-Id : 5517, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 n1) [6673, 6672] by Demod 5516 with 4692 at 2,2,3
-Id : 5854, {_}: pixley ?6987 (inverse n1) ?6988 =<= multiply n1 (add ?6987 ?6988) [6988, 6987] by Demod 5517 with 3 at 3
-Id : 5871, {_}: pixley (inverse n1) (inverse n1) (multiply ?7040 n1) =>= multiply n1 ?7040 [7040] by Super 5854 with 428 at 2,3
-Id : 5916, {_}: multiply ?7040 n1 =?= multiply n1 ?7040 [7040] by Demod 5871 with 6 at 2
-Id : 5518, {_}: pixley ?6672 (inverse n1) ?6673 =<= multiply n1 (add ?6672 ?6673) [6673, 6672] by Demod 5517 with 3 at 3
-Id : 5837, {_}: multiply ?6926 (pixley ?6926 (inverse n1) (inverse n1)) =>= multiply n1 (add ?6926 (inverse n1)) [6926] by Super 505 with 5518 at 2,2
-Id : 5906, {_}: multiply ?6926 ?6926 =?= multiply n1 (add ?6926 (inverse n1)) [6926] by Demod 5837 with 7 at 2,2
-Id : 5907, {_}: multiply ?6926 ?6926 =?= pixley ?6926 (inverse n1) (inverse n1) [6926] by Demod 5906 with 5518 at 3
-Id : 5908, {_}: multiply ?6926 ?6926 =>= ?6926 [6926] by Demod 5907 with 7 at 3
-Id : 7131, {_}: multiply ?8481 (add ?8482 ?8481) =>= add (multiply ?8482 ?8481) ?8481 [8482, 8481] by Super 3 with 5908 at 2,3
-Id : 5066, {_}: multiply ?6275 n1 =<= add ?6275 (multiply n1 ?6275) [6275] by Super 14 with 4692 at 2,2
-Id : 6609, {_}: multiply ?7988 n1 =<= add ?7988 (multiply ?7988 n1) [7988] by Super 5066 with 5916 at 2,3
-Id : 7156, {_}: multiply (multiply ?8553 n1) (multiply ?8553 n1) =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Super 7131 with 6609 at 2,2
-Id : 7254, {_}: multiply ?8553 n1 =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Demod 7156 with 5908 at 2
-Id : 7255, {_}: multiply ?8553 n1 =<= multiply (multiply ?8553 n1) (add ?8553 ?8553) [8553] by Demod 7254 with 412 at 3
-Id : 5833, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= pixley ?2193 (inverse n1) ?2193 [2193] by Demod 1187 with 5518 at 3
-Id : 5835, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5833 with 8 at 3
-Id : 7256, {_}: multiply ?8553 n1 =>= ?8553 [8553] by Demod 7255 with 5835 at 3
-Id : 7273, {_}: ?7040 =<= multiply n1 ?7040 [7040] by Demod 5916 with 7256 at 2
-Id : 7543, {_}: ?8832 =<= add (inverse n1) ?8832 [8832] by Demod 7542 with 7273 at 3
-Id : 7582, {_}: multiply (inverse n1) (multiply ?8919 (inverse ?8919)) =?= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Super 505 with 7543 at 2,2,2
-Id : 5473, {_}: multiply ?6687 (multiply (inverse n1) (add ?6687 n1)) =?= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Super 505 with 5371 at 2,2,2,2
-Id : 5499, {_}: multiply ?6687 (multiply (inverse n1) n1) =<= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Demod 5473 with 4692 at 2,2,2
-Id : 5500, {_}: multiply ?6687 (multiply (inverse n1) n1) =?= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5499 with 5371 at 2,2,3
-Id : 5501, {_}: multiply ?6687 (inverse n1) =<= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5500 with 5244 at 2,2
-Id : 5502, {_}: multiply ?6687 (inverse n1) =?= multiply (inverse n1) n1 [6687] by Demod 5501 with 4692 at 2,3
-Id : 5503, {_}: multiply ?6687 (inverse n1) =>= inverse n1 [6687] by Demod 5502 with 5244 at 3
-Id : 5615, {_}: multiply (inverse n1) (add n1 ?6752) =>= add (inverse n1) (inverse n1) [6752] by Super 174 with 5503 at 2,3
-Id : 5636, {_}: pixley (inverse n1) n1 ?6752 =?= add (inverse n1) (inverse n1) [6752] by Demod 5615 with 2312 at 2
-Id : 5285, {_}: inverse ?404 =<= add (inverse ?404) (inverse ?404) [404] by Demod 4669 with 5244 at 2
-Id : 5637, {_}: pixley (inverse n1) n1 ?6752 =>= inverse n1 [6752] by Demod 5636 with 5285 at 3
-Id : 5782, {_}: inverse n1 =<= multiply (inverse n1) ?3959 [3959] by Demod 2784 with 5637 at 2
-Id : 7613, {_}: inverse n1 =<= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Demod 7582 with 5782 at 2
-Id : 7614, {_}: inverse n1 =<= multiply ?8919 (inverse ?8919) [8919] by Demod 7613 with 7543 at 2,3
-Id : 7674, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =?= add (inverse n1) (multiply ?8985 (inverse ?8984)) [8985, 8984] by Super 3 with 7614 at 1,3
-Id : 7731, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =>= multiply ?8985 (inverse ?8984) [8985, 8984] by Demod 7674 with 7543 at 3
-Id : 289, {_}: multiply (multiply ?563 (multiply (inverse ?564) (add ?565 n1))) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [565, 564, 563] by Super 274 with 173 at 2,1,2
-Id : 8394, {_}: multiply (multiply ?563 (multiply (inverse ?564) n1)) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [564, 563] by Demod 289 with 4692 at 2,2,1,2
-Id : 8406, {_}: multiply (multiply ?9773 (inverse ?9774)) (multiply (inverse ?9774) ?9773) =>= multiply (inverse ?9774) ?9773 [9774, 9773] by Demod 8394 with 7256 at 2,1,2
-Id : 8444, {_}: multiply (inverse n1) (multiply (inverse ?9877) ?9877) =>= multiply (inverse ?9877) ?9877 [9877] by Super 8406 with 7614 at 1,2
-Id : 8534, {_}: inverse n1 =<= multiply (inverse ?9877) ?9877 [9877] by Demod 8444 with 5782 at 2
-Id : 8551, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= add (multiply ?9926 ?9925) (inverse n1) [9926, 9925] by Super 3 with 8534 at 2,3
-Id : 367, {_}: multiply ?731 (add (add ?732 ?731) ?733) =>= add ?731 (multiply ?733 ?731) [733, 732, 731] by Super 12 with 2 at 1,3
-Id : 379, {_}: multiply ?780 n1 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Super 367 with 4 at 2,2
-Id : 7285, {_}: ?780 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Demod 379 with 7256 at 2
-Id : 7585, {_}: ?8927 =<= add ?8927 (multiply (inverse ?8927) ?8927) [8927] by Super 7285 with 7543 at 1,1,2,3
-Id : 8670, {_}: ?8927 =<= add ?8927 (inverse n1) [8927] by Demod 7585 with 8534 at 2,3
-Id : 9041, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= multiply ?9926 ?9925 [9926, 9925] by Demod 8551 with 8670 at 3
-Id : 172, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 (add n1 (inverse ?331))) [332, 331] by Super 19 with 16 at 1,3
-Id : 9053, {_}: pixley n1 ?10412 ?10412 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Super 172 with 9041 at 2,3
-Id : 9135, {_}: n1 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Demod 9053 with 7 at 2
-Id : 9136, {_}: n1 =<= add (inverse ?10412) ?10412 [10412] by Demod 9135 with 7273 at 2,3
-Id : 9201, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =<= add (multiply (inverse (inverse ?10589)) (inverse ?10589)) (multiply ?10590 n1) [10590, 10589] by Super 19 with 9136 at 2,2,3
-Id : 9238, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =?= add (inverse n1) (multiply ?10590 n1) [10590, 10589] by Demod 9201 with 8534 at 1,3
-Id : 9239, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= add (inverse n1) ?10590 [10590, 10589] by Demod 9238 with 7256 at 2,3
-Id : 9240, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= ?10590 [10590, 10589] by Demod 9239 with 7543 at 3
-Id : 10446, {_}: ?12102 =<= inverse (inverse ?12102) [12102] by Super 7 with 9240 at 2
-Id : 10555, {_}: multiply (inverse ?12273) (add ?12274 ?12273) =>= multiply ?12274 (inverse ?12273) [12274, 12273] by Super 9041 with 10446 at 2,2,2
-Id : 11456, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 (inverse (inverse ?13532)) =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Super 24 with 10555 at 2,3
-Id : 11548, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Demod 11456 with 10446 at 3,2
-Id : 8892, {_}: multiply (inverse ?10244) (add ?10244 ?10245) =>= multiply ?10245 (inverse ?10244) [10245, 10244] by Demod 7674 with 7543 at 3
-Id : 7580, {_}: multiply ?8914 (add ?8915 ?8914) =?= add (multiply (inverse n1) ?8914) ?8914 [8915, 8914] by Super 13 with 7543 at 2,2
-Id : 5958, {_}: multiply ?7147 (add ?7148 ?7147) =>= add (multiply ?7148 ?7147) ?7147 [7148, 7147] by Super 3 with 5908 at 2,3
-Id : 7619, {_}: add (multiply ?8915 ?8914) ?8914 =?= add (multiply (inverse n1) ?8914) ?8914 [8914, 8915] by Demod 7580 with 5958 at 2
-Id : 7620, {_}: add (multiply ?8915 ?8914) ?8914 =>= add (inverse n1) ?8914 [8914, 8915] by Demod 7619 with 5782 at 1,3
-Id : 7775, {_}: add (multiply ?9114 ?9115) ?9115 =>= ?9115 [9115, 9114] by Demod 7620 with 7543 at 3
-Id : 7621, {_}: add (multiply ?8915 ?8914) ?8914 =>= ?8914 [8914, 8915] by Demod 7620 with 7543 at 3
-Id : 7749, {_}: multiply ?7147 (add ?7148 ?7147) =>= ?7147 [7148, 7147] by Demod 5958 with 7621 at 3
-Id : 7792, {_}: add ?9167 (add ?9168 ?9167) =>= add ?9168 ?9167 [9168, 9167] by Super 7775 with 7749 at 1,2
-Id : 8900, {_}: multiply (inverse ?10265) (add ?10266 ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10266, 10265] by Super 8892 with 7792 at 2,2
-Id : 11444, {_}: multiply ?10266 (inverse ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10265, 10266] by Demod 8900 with 10555 at 2
-Id : 11549, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =?= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11548 with 11444 at 2,3
-Id : 11550, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11549 with 7 at 2
-Id : 11551, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 ?13532) [13532, 13531] by Demod 11550 with 10446 at 2,2,3
-Id : 11841, {_}: multiply (inverse (inverse ?13951)) (add ?13952 (inverse ?13951)) =>= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13952, 13951] by Super 7731 with 11551 at 2,2
-Id : 11918, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13951, 13952] by Demod 11841 with 10555 at 2
-Id : 11919, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11918 with 10446 at 2,3
-Id : 11920, {_}: multiply ?13952 ?13951 =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11919 with 10446 at 2,2
-Id : 12244, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= add (multiply ?14435 ?14434) (multiply ?14436 ?14434) [14436, 14435, 14434] by Super 3 with 11920 at 2,3
-Id : 29011, {_}: multiply ?35505 (add ?35506 (multiply ?35507 ?35505)) =>= multiply ?35505 (add ?35506 ?35507) [35507, 35506, 35505] by Demod 12244 with 3 at 3
-Id : 29060, {_}: multiply ?35715 (add ?35716 (inverse n1)) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Super 29011 with 8534 at 2,2,2
-Id : 11860, {_}: add ?14021 (inverse ?14022) =<= add (inverse ?14022) (multiply ?14021 ?14022) [14022, 14021] by Demod 11550 with 10446 at 2,2,3
-Id : 11890, {_}: add n1 (inverse ?14122) =<= add (inverse ?14122) ?14122 [14122] by Super 11860 with 7273 at 2,3
-Id : 11943, {_}: add n1 (inverse ?14122) =>= n1 [14122] by Demod 11890 with 9136 at 3
-Id : 11977, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 n1) [332, 331] by Demod 172 with 11943 at 2,2,3
-Id : 11984, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) ?332 [332, 331] by Demod 11977 with 7256 at 2,3
-Id : 11991, {_}: add ?13531 (inverse ?13532) =<= pixley n1 ?13532 (multiply ?13531 ?13532) [13532, 13531] by Demod 11551 with 11984 at 3
-Id : 12023, {_}: add n1 (inverse ?14257) =>= n1 [14257] by Demod 11890 with 9136 at 3
-Id : 12028, {_}: add n1 ?14267 =>= n1 [14267] by Super 12023 with 10446 at 2,2
-Id : 12137, {_}: multiply ?14331 (add n1 ?14332) =?= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Super 14 with 12028 at 1,2,2
-Id : 12188, {_}: multiply ?14331 n1 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12137 with 12028 at 2,2
-Id : 12598, {_}: ?14940 =<= add ?14940 (multiply ?14941 ?14940) [14941, 14940] by Demod 12188 with 7256 at 2
-Id : 409, {_}: multiply (multiply ?814 n1) (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Super 14 with 408 at 1,2,2
-Id : 7278, {_}: multiply ?814 (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 409 with 7256 at 1,2
-Id : 7279, {_}: multiply ?814 (add ?814 ?815) =<= add ?814 (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 7278 with 7256 at 1,3
-Id : 7280, {_}: multiply ?814 (add ?814 ?815) =>= add ?814 (multiply ?815 ?814) [815, 814] by Demod 7279 with 7256 at 2,2,3
-Id : 12189, {_}: ?14331 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12188 with 7256 at 2
-Id : 12573, {_}: multiply ?814 (add ?814 ?815) =>= ?814 [815, 814] by Demod 7280 with 12189 at 3
-Id : 12624, {_}: add ?15025 ?15026 =<= add (add ?15025 ?15026) ?15025 [15026, 15025] by Super 12598 with 12573 at 2,3
-Id : 12720, {_}: multiply ?15175 (add (inverse ?15175) ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Super 9041 with 12624 at 2,2
-Id : 12767, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Demod 12720 with 11984 at 2,2
-Id : 12768, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15176, 15175] by Demod 12767 with 11984 at 1,3
-Id : 8552, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= add (inverse n1) (multiply ?9929 ?9928) [9929, 9928] by Super 3 with 8534 at 1,3
-Id : 8614, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8552 with 7543 at 3
-Id : 11985, {_}: multiply ?9928 (pixley n1 ?9928 ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8614 with 11984 at 2,2
-Id : 12769, {_}: multiply ?15176 ?15175 =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15175, 15176] by Demod 12768 with 11985 at 2
-Id : 15132, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= pixley n1 ?18424 (multiply ?18425 ?18424) [18425, 18424] by Super 11991 with 12769 at 3,3
-Id : 15170, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15132 with 11991 at 3
-Id : 12729, {_}: add ?15203 ?15204 =<= add (add ?15203 ?15204) ?15203 [15204, 15203] by Super 12598 with 12573 at 2,3
-Id : 12745, {_}: add (inverse ?15249) ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Super 12729 with 11984 at 1,3
-Id : 12826, {_}: pixley n1 ?15249 ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Demod 12745 with 11984 at 2
-Id : 23185, {_}: pixley n1 ?18424 ?18425 =<= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15170 with 12826 at 2
-Id : 29209, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Demod 29060 with 23185 at 2,2
-Id : 29210, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29209 with 23185 at 2,3
-Id : 29211, {_}: multiply ?35715 ?35716 =<= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29210 with 6 at 2,2
-Id : 29212, {_}: multiply ?35715 ?35716 =?= multiply ?35716 ?35715 [35716, 35715] by Demod 29211 with 11985 at 3
-Id : 11904, {_}: add ?14161 (inverse (inverse ?14162)) =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Super 11860 with 10446 at 1,3
-Id : 11970, {_}: add ?14161 ?14162 =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Demod 11904 with 10446 at 2,2
-Id : 15099, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18302 (multiply ?18303 (inverse ?18302)) [18303, 18302] by Super 11970 with 12769 at 2,3
-Id : 15201, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15099 with 11970 at 3
-Id : 10547, {_}: pixley n1 (inverse ?12250) ?12251 =<= add (inverse (inverse ?12250)) (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Super 172 with 10446 at 2,2,2,3
-Id : 10574, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Demod 10547 with 10446 at 1,3
-Id : 17614, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 n1) [12251, 12250] by Demod 10574 with 12028 at 2,2,3
-Id : 17615, {_}: pixley n1 (inverse ?12250) ?12251 =>= add ?12250 ?12251 [12251, 12250] by Demod 17614 with 7256 at 2,3
-Id : 23377, {_}: add (add ?18302 ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15201 with 17615 at 1,2
-Id : 23378, {_}: add ?18302 ?18303 =?= add ?18303 ?18302 [18303, 18302] by Demod 23377 with 12624 at 2
-Id : 363, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =<= add (multiply ?716 (add (add ?713 ?714) ?715)) (add ?714 (multiply ?715 ?714)) [716, 715, 714, 713] by Super 3 with 14 at 2,3
-Id : 33202, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =>= add (multiply ?716 (add (add ?713 ?714) ?715)) ?714 [716, 715, 714, 713] by Demod 363 with 12189 at 2,3
-Id : 33249, {_}: multiply (add (add ?41120 ?41121) ?41122) (add ?41123 ?41121) =>= add ?41121 (multiply ?41123 (add (add ?41120 ?41121) ?41122)) [41123, 41122, 41121, 41120] by Demod 33202 with 23378 at 3
-Id : 7276, {_}: multiply ?2193 (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5835 with 7256 at 1,2
-Id : 7300, {_}: add (multiply ?2193 ?2193) ?2193 =>= ?2193 [2193] by Demod 7276 with 5958 at 2
-Id : 7301, {_}: add ?2193 ?2193 =>= ?2193 [2193] by Demod 7300 with 5908 at 1,2
-Id : 33300, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =<= add ?41375 (multiply ?41376 (add (add ?41374 ?41375) (add ?41374 ?41375))) [41376, 41375, 41374] by Super 33249 with 7301 at 1,2
-Id : 33433, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =>= add ?41375 (multiply ?41376 (add ?41374 ?41375)) [41376, 41375, 41374] by Demod 33300 with 7301 at 2,2,3
-Id : 42671, {_}: multiply ?52830 (add ?52831 ?52832) =<= add (multiply ?52830 ?52831) (multiply ?52832 ?52830) [52832, 52831, 52830] by Super 3 with 29212 at 1,3
-Id : 42679, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add (multiply (add ?52859 ?52860) ?52861) ?52860 [52861, 52860, 52859] by Super 42671 with 7749 at 2,3
-Id : 42859, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52861, 52860, 52859] by Demod 42679 with 23378 at 3
-Id : 58778, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =?= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52859, 52861, 52860] by Demod 42859 with 33433 at 2
-Id : 42225, {_}: multiply ?51978 (add ?51979 ?51980) =<= add (multiply ?51979 ?51978) (multiply ?51978 ?51980) [51980, 51979, 51978] by Super 3 with 29212 at 2,3
-Id : 56980, {_}: multiply (add ?78761 ?78762) (add ?78762 ?78763) =>= add ?78762 (multiply (add ?78761 ?78762) ?78763) [78763, 78762, 78761] by Super 42225 with 7749 at 1,3
-Id : 57032, {_}: multiply (add ?78985 ?78986) (add ?78985 ?78987) =>= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Super 56980 with 23378 at 1,2
-Id : 42307, {_}: multiply (add ?52335 ?52336) (add ?52335 ?52337) =>= add ?52335 (multiply (add ?52335 ?52336) ?52337) [52337, 52336, 52335] by Super 42225 with 12573 at 1,3
-Id : 69246, {_}: add ?78985 (multiply (add ?78985 ?78986) ?78987) =?= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 57032 with 42307 at 2
-Id : 42691, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add (multiply (add ?52915 ?52916) ?52917) ?52915 [52917, 52916, 52915] by Super 42671 with 12573 at 2,3
-Id : 42878, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 42691 with 23378 at 3
-Id : 33277, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =<= add ?41259 (multiply ?41261 (add (add ?41259 ?41259) ?41260)) [41261, 41260, 41259] by Super 33249 with 7301 at 1,1,2
-Id : 33397, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =>= add ?41259 (multiply ?41261 (add ?41259 ?41260)) [41261, 41260, 41259] by Demod 33277 with 7301 at 1,2,2,3
-Id : 59822, {_}: add ?52915 (multiply ?52917 (add ?52915 ?52916)) =?= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52916, 52917, 52915] by Demod 42878 with 33397 at 2
-Id : 49363, {_}: multiply (add ?63432 ?63433) (add ?63433 ?63434) =>= add ?63433 (multiply ?63432 (add ?63433 ?63434)) [63434, 63433, 63432] by Super 29212 with 33397 at 3
-Id : 42295, {_}: multiply (add ?52279 ?52280) (add ?52280 ?52281) =>= add ?52280 (multiply (add ?52279 ?52280) ?52281) [52281, 52280, 52279] by Super 42225 with 7749 at 1,3
-Id : 65944, {_}: add ?95703 (multiply (add ?95704 ?95703) ?95705) =?= add ?95703 (multiply ?95704 (add ?95703 ?95705)) [95705, 95704, 95703] by Demod 49363 with 42295 at 2
-Id : 12345, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= multiply ?14434 (add ?14435 ?14436) [14436, 14435, 14434] by Demod 12244 with 3 at 3
-Id : 66007, {_}: add ?95981 (multiply (add ?95982 ?95981) (multiply ?95983 ?95982)) =>= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95983, 95982, 95981] by Super 65944 with 12345 at 2,3
-Id : 12571, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= ?41 [43, 42, 41] by Demod 14 with 12189 at 3
-Id : 12574, {_}: multiply (multiply ?14855 ?14856) (add ?14856 ?14857) =>= multiply ?14855 ?14856 [14857, 14856, 14855] by Super 12571 with 12189 at 1,2,2
-Id : 32599, {_}: multiply (add ?39770 ?39771) (multiply ?39772 ?39770) =>= multiply ?39772 ?39770 [39772, 39771, 39770] by Super 29212 with 12574 at 3
-Id : 66421, {_}: add ?95981 (multiply ?95983 ?95982) =<= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95982, 95983, 95981] by Demod 66007 with 32599 at 2,2
-Id : 74546, {_}: add ?52915 (multiply ?52916 ?52917) =<= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 59822 with 66421 at 2
-Id : 74547, {_}: add ?78985 (multiply ?78986 ?78987) =<= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 69246 with 74546 at 2
-Id : 74549, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =>= add ?52860 (multiply ?52859 ?52861) [52859, 52861, 52860] by Demod 58778 with 74547 at 3
-Id : 75087, {_}: add a (multiply c b) =?= add a (multiply c b) [] by Demod 57307 with 74549 at 3
-Id : 57307, {_}: add a (multiply c b) =<= add a (multiply b (add c a)) [] by Demod 57306 with 33433 at 3
-Id : 57306, {_}: add a (multiply c b) =<= multiply (add c a) (add b a) [] by Demod 57305 with 29212 at 3
-Id : 57305, {_}: add a (multiply c b) =<= multiply (add b a) (add c a) [] by Demod 57304 with 23378 at 2,3
-Id : 57304, {_}: add a (multiply c b) =<= multiply (add b a) (add a c) [] by Demod 57303 with 23378 at 1,3
-Id : 57303, {_}: add a (multiply c b) =<= multiply (add a b) (add a c) [] by Demod 1 with 29212 at 2,2
-Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property
-% SZS output end CNFRefutation for BOO023-1.p
-20955: solved BOO023-1.p in 19.273203 using kbo
-20955: status Unsatisfiable for BOO023-1.p
-NO CLASH, using fixed ground order
-21165: Facts:
-NO CLASH, using fixed ground order
-21166: Facts:
-21166: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-21166: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-21166: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-21166: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-21166: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-21166: Goal:
-21166: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-21166: Order:
-21166: kbo
-21166: Leaf order:
-21166: g 2 0 2 3,3,1,2,2
-21166: f 2 0 2 2,1,2,2
-21166: e 2 0 2 3,1,1,2,2
-21166: d 3 0 3 2,1,1,2,2
-21166: c 3 0 3 1,1,1,2,2
-21166: multiply 16 3 7 0,2
-21166: b 2 0 2 3,1,2
-21166: inverse 4 1 2 0,2,1,2
-21166: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21167: Facts:
-21167: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-21167: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-21167: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-21167: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-21167: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-21167: Goal:
-21167: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-21167: Order:
-21167: lpo
-21167: Leaf order:
-21167: g 2 0 2 3,3,1,2,2
-21167: f 2 0 2 2,1,2,2
-21167: e 2 0 2 3,1,1,2,2
-21167: d 3 0 3 2,1,1,2,2
-21167: c 3 0 3 1,1,1,2,2
-21167: multiply 16 3 7 0,2
-21167: b 2 0 2 3,1,2
-21167: inverse 4 1 2 0,2,1,2
-21167: a 2 0 2 1,1,2
-21165: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-21165: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-21165: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-21165: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-21165: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-21165: Goal:
-21165: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-21165: Order:
-21165: nrkbo
-21165: Leaf order:
-21165: g 2 0 2 3,3,1,2,2
-21165: f 2 0 2 2,1,2,2
-21165: e 2 0 2 3,1,1,2,2
-21165: d 3 0 3 2,1,1,2,2
-21165: c 3 0 3 1,1,1,2,2
-21165: multiply 16 3 7 0,2
-21165: b 2 0 2 3,1,2
-21165: inverse 4 1 2 0,2,1,2
-21165: a 2 0 2 1,1,2
-Statistics :
-Max weight : 24
-Found proof, 10.936664s
-% SZS status Unsatisfiable for BOO034-1.p
-% SZS output start CNFRefutation for BOO034-1.p
-Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
-Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
-Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
-Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2
-Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2
-Id : 920, {_}: multiply (multiply ?2937 ?2938 ?2939) ?2937 ?2938 =?= multiply ?2939 ?2937 (multiply ?2937 ?2938 ?2938) [2939, 2938, 2937] by Super 12 with 13 at 3
-Id : 1359, {_}: multiply (multiply ?4051 ?4052 ?4053) ?4051 ?4052 =>= multiply ?4053 ?4051 ?4052 [4053, 4052, 4051] by Demod 920 with 3 at 3,3
-Id : 1364, {_}: multiply ?4070 ?4070 ?4071 =?= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Super 1359 with 6 at 1,2
-Id : 1413, {_}: ?4070 =<= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Demod 1364 with 4 at 2
-Id : 1453, {_}: multiply (multiply ?4288 ?4289 (inverse ?4289)) ?4290 ?4289 =>= multiply ?4288 ?4289 ?4290 [4290, 4289, 4288] by Super 12 with 1413 at 3,3
-Id : 1476, {_}: multiply ?4288 ?4290 ?4289 =?= multiply ?4288 ?4289 ?4290 [4289, 4290, 4288] by Demod 1453 with 6 at 1,2
-Id : 519, {_}: multiply (multiply ?1786 ?1787 ?1788) ?1789 ?1787 =?= multiply ?1786 ?1787 (multiply ?1788 ?1789 ?1787) [1789, 1788, 1787, 1786] by Super 2 with 3 at 3,2
-Id : 659, {_}: multiply (multiply ?2172 ?2173 ?2174) ?2174 ?2173 =>= multiply ?2172 ?2173 ?2174 [2174, 2173, 2172] by Super 519 with 4 at 3,3
-Id : 664, {_}: multiply ?2191 (inverse ?2192) ?2192 =?= multiply ?2191 ?2192 (inverse ?2192) [2192, 2191] by Super 659 with 6 at 1,2
-Id : 701, {_}: multiply ?2191 (inverse ?2192) ?2192 =>= ?2191 [2192, 2191] by Demod 664 with 6 at 3
-Id : 1371, {_}: multiply ?4106 ?4106 (inverse ?4107) =?= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Super 1359 with 701 at 1,2
-Id : 1415, {_}: ?4106 =<= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Demod 1371 with 4 at 2
-Id : 1522, {_}: multiply ?4441 ?4442 (multiply ?4443 ?4441 (inverse ?4441)) =>= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Super 13 with 1415 at 3,3
-Id : 1536, {_}: multiply ?4441 ?4442 ?4443 =?= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Demod 1522 with 6 at 3,2
-Id : 727, {_}: inverse (inverse ?2329) =>= ?2329 [2329] by Super 5 with 701 at 2
-Id : 761, {_}: multiply ?2420 (inverse ?2420) ?2421 =>= ?2421 [2421, 2420] by Super 5 with 727 at 1,2
-Id : 40424, {_}: b === b [] by Demod 40423 with 6 at 2
-Id : 40423, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 40422 with 1476 at 3,1,3,2
-Id : 40422, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 40421 with 1536 at 3,1,3,2
-Id : 40421, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f g e))) =>= b [] by Demod 40420 with 1476 at 3,1,3,2
-Id : 40420, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f e g))) =>= b [] by Demod 40419 with 1536 at 3,1,3,2
-Id : 40419, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e g f))) =>= b [] by Demod 40418 with 1476 at 3,1,3,2
-Id : 40418, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e f g))) =>= b [] by Demod 40417 with 1476 at 1,3,2
-Id : 40417, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40416 with 1476 at 2
-Id : 40416, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d c (multiply g f e)) =>= b [] by Demod 40415 with 1536 at 2
-Id : 40415, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40414 with 1536 at 1,3,2
-Id : 40414, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40413 with 761 at 2,2
-Id : 40413, {_}: multiply (multiply d c (multiply g f e)) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40412 with 1476 at 1,2
-Id : 40412, {_}: multiply (multiply d (multiply g f e) c) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40411 with 1476 at 2
-Id : 40411, {_}: multiply (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) =>= b [] by Demod 40410 with 1536 at 2
-Id : 40410, {_}: multiply (multiply a (inverse a) b) (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 11 with 1476 at 2
-Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2
-Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
-% SZS output end CNFRefutation for BOO034-1.p
-21165: solved BOO034-1.p in 10.220638 using nrkbo
-21165: status Unsatisfiable for BOO034-1.p
-CLASH, statistics insufficient
-21378: Facts:
-21378: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21378: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-21378: Goal:
-21378: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-21378: Order:
-21378: nrkbo
-21378: Leaf order:
-21378: k 1 0 0
-21378: s 1 0 0
-21378: g 3 1 3 0,2,2
-21378: apply 13 2 5 0,2
-21378: f 3 1 3 0,2,1,2
-CLASH, statistics insufficient
-21379: Facts:
-21379: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21379: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-21379: Goal:
-21379: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-21379: Order:
-21379: kbo
-21379: Leaf order:
-21379: k 1 0 0
-21379: s 1 0 0
-21379: g 3 1 3 0,2,2
-21379: apply 13 2 5 0,2
-21379: f 3 1 3 0,2,1,2
-CLASH, statistics insufficient
-21380: Facts:
-21380: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21380: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-21380: Goal:
-21380: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-21380: Order:
-21380: lpo
-21380: Leaf order:
-21380: k 1 0 0
-21380: s 1 0 0
-21380: g 3 1 3 0,2,2
-21380: apply 13 2 5 0,2
-21380: f 3 1 3 0,2,1,2
-% SZS status Timeout for COL004-1.p
-NO CLASH, using fixed ground order
-21607: Facts:
-21607: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-21607: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-21607: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-21607: Goal:
-21607: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-21607: Order:
-21607: nrkbo
-21607: Leaf order:
-21607: k 13 0 0
-21607: s 11 0 0
-21607: apply 32 2 3 0,2
-21607: fixed_pt 3 0 3 2,2
-21607: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-21608: Facts:
-21608: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-21608: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-21608: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-21608: Goal:
-21608: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-21608: Order:
-21608: kbo
-21608: Leaf order:
-21608: k 13 0 0
-21608: s 11 0 0
-21608: apply 32 2 3 0,2
-21608: fixed_pt 3 0 3 2,2
-21608: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-21609: Facts:
-21609: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-21609: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-21609: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-21609: Goal:
-21609: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-21609: Order:
-21609: lpo
-21609: Leaf order:
-21609: k 13 0 0
-21609: s 11 0 0
-21609: apply 32 2 3 0,2
-21609: fixed_pt 3 0 3 2,2
-21609: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL006-6.p
-CLASH, statistics insufficient
-21625: Facts:
-21625: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21625: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-21625: Id : 4, {_}:
- apply (apply t ?11) ?12 =>= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-21625: Goal:
-21625: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-21625: Order:
-21625: nrkbo
-21625: Leaf order:
-21625: t 1 0 0
-21625: b 1 0 0
-21625: s 1 0 0
-21625: apply 17 2 3 0,2
-21625: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-21626: Facts:
-21626: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21626: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-21626: Id : 4, {_}:
- apply (apply t ?11) ?12 =>= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-21626: Goal:
-21626: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-21626: Order:
-21626: kbo
-21626: Leaf order:
-21626: t 1 0 0
-21626: b 1 0 0
-21626: s 1 0 0
-21626: apply 17 2 3 0,2
-21626: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-21627: Facts:
-21627: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-21627: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-21627: Id : 4, {_}:
- apply (apply t ?11) ?12 =?= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-21627: Goal:
-21627: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-21627: Order:
-21627: lpo
-21627: Leaf order:
-21627: t 1 0 0
-21627: b 1 0 0
-21627: s 1 0 0
-21627: apply 17 2 3 0,2
-21627: f 3 1 3 0,2,2
-% SZS status Timeout for COL036-1.p
-CLASH, statistics insufficient
-21654: Facts:
-21654: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-CLASH, statistics insufficient
-21655: Facts:
-21655: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-21655: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-21655: Goal:
-21655: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-21655: Order:
-21655: kbo
-21655: Leaf order:
-21655: t 1 0 0
-21655: b 1 0 0
-21655: h 2 1 2 0,2,2
-21655: g 2 1 2 0,2,1,2
-21655: apply 13 2 5 0,2
-21655: f 2 1 2 0,2,1,1,2
-21654: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-21654: Goal:
-21654: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-21654: Order:
-21654: nrkbo
-21654: Leaf order:
-21654: t 1 0 0
-21654: b 1 0 0
-21654: h 2 1 2 0,2,2
-21654: g 2 1 2 0,2,1,2
-21654: apply 13 2 5 0,2
-21654: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-21656: Facts:
-21656: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-21656: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-21656: Goal:
-21656: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-21656: Order:
-21656: lpo
-21656: Leaf order:
-21656: t 1 0 0
-21656: b 1 0 0
-21656: h 2 1 2 0,2,2
-21656: g 2 1 2 0,2,1,2
-21656: apply 13 2 5 0,2
-21656: f 2 1 2 0,2,1,1,2
-Goal subsumed
-Statistics :
-Max weight : 100
-Found proof, 5.123186s
-% SZS status Unsatisfiable for COL063-1.p
-% SZS output start CNFRefutation for COL063-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2
-Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2
-Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
-Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
-% SZS output end CNFRefutation for COL063-1.p
-21654: solved COL063-1.p in 5.12832 using nrkbo
-21654: status Unsatisfiable for COL063-1.p
-NO CLASH, using fixed ground order
-21661: Facts:
-21661: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21661: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21661: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21661: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21661: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21661: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21661: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21661: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21661: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21661: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21661: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21661: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21661: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21661: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21661: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21661: Goal:
-21661: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-21661: Order:
-21661: nrkbo
-21661: Leaf order:
-21661: inverse 1 1 0
-21661: multiply 19 2 1 0,3
-21661: greatest_lower_bound 14 2 1 0,2,3
-21661: least_upper_bound 14 2 1 0,1,3
-21661: identity 4 0 2 2,1,3
-21661: a 3 0 3 2
-NO CLASH, using fixed ground order
-21662: Facts:
-21662: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21662: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21662: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21662: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21662: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21662: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21662: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21662: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21662: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21662: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21662: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21662: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21662: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21662: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21662: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21662: Goal:
-21662: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-21662: Order:
-21662: kbo
-21662: Leaf order:
-21662: inverse 1 1 0
-21662: multiply 19 2 1 0,3
-21662: greatest_lower_bound 14 2 1 0,2,3
-21662: least_upper_bound 14 2 1 0,1,3
-21662: identity 4 0 2 2,1,3
-21662: a 3 0 3 2
-NO CLASH, using fixed ground order
-21663: Facts:
-21663: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21663: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21663: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21663: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21663: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21663: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21663: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21663: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21663: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21663: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21663: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21663: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21663: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21663: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21663: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21663: Goal:
-21663: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-21663: Order:
-21663: lpo
-21663: Leaf order:
-21663: inverse 1 1 0
-21663: multiply 19 2 1 0,3
-21663: greatest_lower_bound 14 2 1 0,2,3
-21663: least_upper_bound 14 2 1 0,1,3
-21663: identity 4 0 2 2,1,3
-21663: a 3 0 3 2
-% SZS status Timeout for GRP167-3.p
-NO CLASH, using fixed ground order
-21683: Facts:
-21683: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21683: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21683: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21683: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21683: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21683: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21683: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21683: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21683: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21683: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21683: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21683: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21683: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21683: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21683: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21683: Goal:
-21683: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =<=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-21683: Order:
-21683: nrkbo
-21683: Leaf order:
-21683: multiply 18 2 0
-21683: identity 2 0 0
-21683: greatest_lower_bound 14 2 1 0,3
-21683: inverse 4 1 3 0,2
-21683: least_upper_bound 14 2 1 0,1,2
-21683: b 2 0 2 2,1,2
-21683: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21684: Facts:
-21684: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21684: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21684: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21684: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21684: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21684: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21684: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21684: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21684: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21684: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21684: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21684: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-NO CLASH, using fixed ground order
-21685: Facts:
-21685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21685: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21685: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21685: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21685: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21685: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21685: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21685: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21685: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21685: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21685: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21685: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21685: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21685: Goal:
-21685: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =>=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-21685: Order:
-21685: lpo
-21685: Leaf order:
-21685: multiply 18 2 0
-21685: identity 2 0 0
-21685: greatest_lower_bound 14 2 1 0,3
-21685: inverse 4 1 3 0,2
-21685: least_upper_bound 14 2 1 0,1,2
-21685: b 2 0 2 2,1,2
-21685: a 2 0 2 1,1,2
-21684: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21684: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21684: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21684: Goal:
-21684: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =<=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-21684: Order:
-21684: kbo
-21684: Leaf order:
-21684: multiply 18 2 0
-21684: identity 2 0 0
-21684: greatest_lower_bound 14 2 1 0,3
-21684: inverse 4 1 3 0,2
-21684: least_upper_bound 14 2 1 0,1,2
-21684: b 2 0 2 2,1,2
-21684: a 2 0 2 1,1,2
-% SZS status Timeout for GRP179-1.p
-NO CLASH, using fixed ground order
-21733: Facts:
-21733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21733: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21733: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21733: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21733: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21733: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21733: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21733: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21733: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21733: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21733: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21733: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21733: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21733: Goal:
-21733: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-21733: Order:
-21733: kbo
-21733: Leaf order:
-21733: multiply 18 2 0
-21733: greatest_lower_bound 14 2 1 0,1,3
-21733: least_upper_bound 14 2 1 0,2
-21733: identity 4 0 2 2,2
-21733: inverse 3 1 2 0,1,2
-21733: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21732: Facts:
-21732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21732: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21732: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21732: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21732: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21732: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21732: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21732: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21732: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21732: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21732: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21732: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21732: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21732: Goal:
-21732: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-21732: Order:
-21732: nrkbo
-21732: Leaf order:
-21732: multiply 18 2 0
-21732: greatest_lower_bound 14 2 1 0,1,3
-21732: least_upper_bound 14 2 1 0,2
-21732: identity 4 0 2 2,2
-21732: inverse 3 1 2 0,1,2
-21732: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21734: Facts:
-21734: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21734: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21734: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21734: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21734: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21734: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21734: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21734: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21734: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21734: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21734: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21734: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21734: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21734: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21734: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21734: Goal:
-21734: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =<=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-21734: Order:
-21734: lpo
-21734: Leaf order:
-21734: multiply 18 2 0
-21734: greatest_lower_bound 14 2 1 0,1,3
-21734: least_upper_bound 14 2 1 0,2
-21734: identity 4 0 2 2,2
-21734: inverse 3 1 2 0,1,2
-21734: a 2 0 2 1,1,2
-% SZS status Timeout for GRP179-2.p
-NO CLASH, using fixed ground order
-21751: Facts:
-21751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21751: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21751: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21751: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21751: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21751: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21751: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21751: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21751: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21751: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21751: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21751: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21751: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21751: Goal:
-21751: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-21751: Order:
-21751: nrkbo
-21751: Leaf order:
-21751: identity 2 0 0
-21751: least_upper_bound 14 2 1 0,3
-21751: multiply 20 2 2 0,2
-21751: inverse 2 1 1 0,1,2,2
-21751: greatest_lower_bound 14 2 1 0,1,1,2,2
-21751: b 3 0 3 2,1,1,2,2
-21751: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-21752: Facts:
-21752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21752: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21752: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21752: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21752: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21752: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21752: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21752: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21752: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21752: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21752: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21752: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21752: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21752: Goal:
-21752: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-21752: Order:
-21752: kbo
-21752: Leaf order:
-21752: identity 2 0 0
-21752: least_upper_bound 14 2 1 0,3
-21752: multiply 20 2 2 0,2
-21752: inverse 2 1 1 0,1,2,2
-21752: greatest_lower_bound 14 2 1 0,1,1,2,2
-21752: b 3 0 3 2,1,1,2,2
-21752: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-21753: Facts:
-21753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21753: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21753: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21753: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21753: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21753: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21753: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21753: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21753: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21753: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21753: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21753: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21753: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21753: Goal:
-21753: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-21753: Order:
-21753: lpo
-21753: Leaf order:
-21753: identity 2 0 0
-21753: least_upper_bound 14 2 1 0,3
-21753: multiply 20 2 2 0,2
-21753: inverse 2 1 1 0,1,2,2
-21753: greatest_lower_bound 14 2 1 0,1,1,2,2
-21753: b 3 0 3 2,1,1,2,2
-21753: a 3 0 3 1,2
-% SZS status Timeout for GRP180-1.p
-NO CLASH, using fixed ground order
-21783: Facts:
-21783: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21783: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21783: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21783: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21783: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21783: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21783: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21783: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21783: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21783: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21783: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21783: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21783: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21783: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21783: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21783: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-21783: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-21783: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-21783: Goal:
-21783: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-21783: Order:
-21783: nrkbo
-21783: Leaf order:
-21783: multiply 20 2 0
-21783: inverse 8 1 1 0,2,2
-21783: greatest_lower_bound 15 2 2 0,2
-21783: least_upper_bound 14 2 1 0,1,2
-21783: identity 7 0 3 2,1,2
-21783: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21785: Facts:
-21785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21785: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21785: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21785: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21785: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21785: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21785: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21785: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21785: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21785: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21785: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21785: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21785: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21785: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-21785: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-21785: Id : 19, {_}:
- inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-21785: Goal:
-21785: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-21785: Order:
-21785: lpo
-21785: Leaf order:
-21785: multiply 20 2 0
-21785: inverse 8 1 1 0,2,2
-21785: greatest_lower_bound 15 2 2 0,2
-21785: least_upper_bound 14 2 1 0,1,2
-21785: identity 7 0 3 2,1,2
-21785: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21784: Facts:
-21784: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21784: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21784: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21784: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21784: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21784: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21784: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21784: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21784: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21784: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21784: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21784: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21784: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21784: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21784: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21784: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-21784: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-21784: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-21784: Goal:
-21784: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-21784: Order:
-21784: kbo
-21784: Leaf order:
-21784: multiply 20 2 0
-21784: inverse 8 1 1 0,2,2
-21784: greatest_lower_bound 15 2 2 0,2
-21784: least_upper_bound 14 2 1 0,1,2
-21784: identity 7 0 3 2,1,2
-21784: a 2 0 2 1,1,2
-% SZS status Timeout for GRP183-2.p
-NO CLASH, using fixed ground order
-21802: Facts:
-21802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21802: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21802: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21802: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21802: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21802: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21802: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21802: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21802: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21802: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21802: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21802: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21802: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21802: Goal:
-21802: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-21802: Order:
-21802: nrkbo
-21802: Leaf order:
-21802: greatest_lower_bound 14 2 1 0,1,2,3
-21802: inverse 3 1 2 0,2,3
-21802: least_upper_bound 14 2 1 0,2
-21802: identity 3 0 1 2,2
-21802: multiply 20 2 2 0,1,2
-21802: b 2 0 2 2,1,2
-21802: a 3 0 3 1,1,2
-NO CLASH, using fixed ground order
-21803: Facts:
-21803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21803: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21803: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21803: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21803: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21803: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21803: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21803: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21803: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21803: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21803: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21803: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21803: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21803: Goal:
-21803: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-21803: Order:
-21803: kbo
-21803: Leaf order:
-21803: greatest_lower_bound 14 2 1 0,1,2,3
-21803: inverse 3 1 2 0,2,3
-21803: least_upper_bound 14 2 1 0,2
-21803: identity 3 0 1 2,2
-21803: multiply 20 2 2 0,1,2
-21803: b 2 0 2 2,1,2
-21803: a 3 0 3 1,1,2
-NO CLASH, using fixed ground order
-21804: Facts:
-21804: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-21804: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-21804: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-21804: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-21804: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-21804: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-21804: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-21804: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-21804: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-21804: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-21804: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-21804: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-21804: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-21804: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-21804: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-21804: Goal:
-21804: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-21804: Order:
-21804: lpo
-21804: Leaf order:
-21804: greatest_lower_bound 14 2 1 0,1,2,3
-21804: inverse 3 1 2 0,2,3
-21804: least_upper_bound 14 2 1 0,2
-21804: identity 3 0 1 2,2
-21804: multiply 20 2 2 0,1,2
-21804: b 2 0 2 2,1,2
-21804: a 3 0 3 1,1,2
-% SZS status Timeout for GRP186-1.p
-NO CLASH, using fixed ground order
-21831: Facts:
-21831: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-21831: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-21831: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-21831: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-21831: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-21831: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-21831: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-21831: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-21831: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-21831: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-21831: Goal:
-21831: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-21831: Order:
-21831: nrkbo
-21831: Leaf order:
-21831: n0 1 0 0
-21831: n1 2 0 1 3
-21831: meet 14 2 5 0,1,2,2
-21831: join 17 2 5 0,2
-21831: b 4 0 4 1,2,1,2,1,2,2
-21831: complement 15 1 6 0,1,1,2,2
-21831: a 7 0 7 1,2
-NO CLASH, using fixed ground order
-21832: Facts:
-21832: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-21832: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-21832: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-21832: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-21832: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-21832: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-21832: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-21832: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-21832: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-21832: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-21832: Goal:
-21832: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-21832: Order:
-21832: kbo
-21832: Leaf order:
-21832: n0 1 0 0
-21832: n1 2 0 1 3
-21832: meet 14 2 5 0,1,2,2
-21832: join 17 2 5 0,2
-21832: b 4 0 4 1,2,1,2,1,2,2
-21832: complement 15 1 6 0,1,1,2,2
-21832: a 7 0 7 1,2
-NO CLASH, using fixed ground order
-21833: Facts:
-21833: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-21833: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-21833: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-21833: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-21833: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-21833: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-21833: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-21833: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-21833: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-21833: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-21833: Goal:
-21833: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-21833: Order:
-21833: lpo
-21833: Leaf order:
-21833: n0 1 0 0
-21833: n1 2 0 1 3
-21833: meet 14 2 5 0,1,2,2
-21833: join 17 2 5 0,2
-21833: b 4 0 4 1,2,1,2,1,2,2
-21833: complement 15 1 6 0,1,1,2,2
-21833: a 7 0 7 1,2
-% SZS status Timeout for LAT017-1.p
-NO CLASH, using fixed ground order
-21853: Facts:
-21853: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21853: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21853: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-21853: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-21853: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-21853: Id : 7, {_}:
- join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-21853: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-21853: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-21853: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =>=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-21853: Goal:
-21853: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-21853: Order:
-21853: nrkbo
-21853: Leaf order:
-21853: meet 21 2 3 0,2
-21853: join 20 2 2 0,2,2
-21853: c 2 0 2 2,2,2
-21853: b 2 0 2 1,2,2
-21853: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-21854: Facts:
-21854: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21854: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21854: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-21854: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-21854: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-21854: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-21854: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-21854: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-21854: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =>=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-21854: Goal:
-21854: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-21854: Order:
-21854: kbo
-21854: Leaf order:
-21854: meet 21 2 3 0,2
-21854: join 20 2 2 0,2,2
-21854: c 2 0 2 2,2,2
-21854: b 2 0 2 1,2,2
-21854: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-21855: Facts:
-21855: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21855: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21855: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-21855: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-21855: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-21855: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-21855: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-21855: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-21855: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =>=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-21855: Goal:
-21855: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-21855: Order:
-21855: lpo
-21855: Leaf order:
-21855: meet 21 2 3 0,2
-21855: join 20 2 2 0,2,2
-21855: c 2 0 2 2,2,2
-21855: b 2 0 2 1,2,2
-21855: a 3 0 3 1,2
-% SZS status Timeout for LAT020-1.p
-NO CLASH, using fixed ground order
-21955: Facts:
-21955: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21955: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21955: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21955: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21955: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21955: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21955: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21955: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21955: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21955: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21955: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21955: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21955: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21955: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21955: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21955: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21955: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21955: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21955: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21955: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21955: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21955: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21955: Goal:
-21955: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-21955: Order:
-21955: nrkbo
-21955: Leaf order:
-21955: commutator 1 2 0
-21955: additive_inverse 22 1 0
-21955: multiply 40 2 0
-21955: additive_identity 9 0 1 3
-21955: add 25 2 1 0,2
-21955: associator 3 3 2 0,1,2
-21955: z 2 0 2 3,1,2
-21955: y 2 0 2 2,1,2
-21955: x 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21956: Facts:
-21956: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21956: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21956: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21956: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21956: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21956: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21956: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21956: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21956: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21956: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21956: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21956: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21956: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21956: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21956: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21956: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21956: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21956: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21956: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21956: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21956: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21956: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21956: Goal:
-21956: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-21956: Order:
-21956: kbo
-21956: Leaf order:
-21956: commutator 1 2 0
-21956: additive_inverse 22 1 0
-21956: multiply 40 2 0
-21956: additive_identity 9 0 1 3
-21956: add 25 2 1 0,2
-21956: associator 3 3 2 0,1,2
-21956: z 2 0 2 3,1,2
-21956: y 2 0 2 2,1,2
-21956: x 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-21957: Facts:
-21957: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21957: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21957: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21957: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21957: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21957: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21957: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21957: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21957: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21957: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21957: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21957: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21957: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21957: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21957: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21957: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21957: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21957: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21957: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21957: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21957: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21957: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21957: Goal:
-21957: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-21957: Order:
-21957: lpo
-21957: Leaf order:
-21957: commutator 1 2 0
-21957: additive_inverse 22 1 0
-21957: multiply 40 2 0
-21957: additive_identity 9 0 1 3
-21957: add 25 2 1 0,2
-21957: associator 3 3 2 0,1,2
-21957: z 2 0 2 3,1,2
-21957: y 2 0 2 2,1,2
-21957: x 2 0 2 1,1,2
-% SZS status Timeout for RNG025-5.p
-NO CLASH, using fixed ground order
-21975: Facts:
-21975: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21975: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21975: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21975: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21975: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21975: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21975: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21975: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21975: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21975: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21975: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21975: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21975: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21975: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21975: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21975: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21975: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21975: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21975: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21975: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21975: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21975: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21975: Goal:
-21975: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-21975: Order:
-21975: nrkbo
-21975: Leaf order:
-21975: commutator 1 2 0
-21975: additive_inverse 22 1 0
-21975: multiply 40 2 0
-21975: add 24 2 0
-21975: additive_identity 9 0 1 3
-21975: associator 2 3 1 0,2
-21975: y 1 0 1 2,2
-21975: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-21976: Facts:
-21976: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21976: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21976: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21976: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21976: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21976: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21976: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21976: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21976: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21976: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21976: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21976: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21976: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21976: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21976: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21976: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21976: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21976: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21976: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21976: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21976: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21976: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21976: Goal:
-21976: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-21976: Order:
-21976: kbo
-21976: Leaf order:
-21976: commutator 1 2 0
-21976: additive_inverse 22 1 0
-21976: multiply 40 2 0
-21976: add 24 2 0
-21976: additive_identity 9 0 1 3
-21976: associator 2 3 1 0,2
-21976: y 1 0 1 2,2
-21976: x 2 0 2 1,2
-NO CLASH, using fixed ground order
-21977: Facts:
-21977: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-21977: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-21977: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-21977: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-21977: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-21977: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-21977: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-21977: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-21977: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-21977: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-21977: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-21977: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-21977: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-21977: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-21977: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-21977: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-21977: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-21977: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-21977: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-21977: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-21977: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-21977: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-21977: Goal:
-21977: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-21977: Order:
-21977: lpo
-21977: Leaf order:
-21977: commutator 1 2 0
-21977: additive_inverse 22 1 0
-21977: multiply 40 2 0
-21977: add 24 2 0
-21977: additive_identity 9 0 1 3
-21977: associator 2 3 1 0,2
-21977: y 1 0 1 2,2
-21977: x 2 0 2 1,2
-% SZS status Timeout for RNG025-7.p
-CLASH, statistics insufficient
-22004: Facts:
-22004: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-CLASH, statistics insufficient
-22005: Facts:
-22005: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22005: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-22005: Goal:
-22005: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22005: Order:
-22005: kbo
-22005: Leaf order:
-22005: k 1 0 0
-22005: s 1 0 0
-22005: apply 11 2 3 0,2
-22005: f 3 1 3 0,2,2
-22004: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-22004: Goal:
-22004: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22004: Order:
-22004: nrkbo
-22004: Leaf order:
-22004: k 1 0 0
-22004: s 1 0 0
-22004: apply 11 2 3 0,2
-22004: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-22006: Facts:
-22006: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22006: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-22006: Goal:
-22006: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22006: Order:
-22006: lpo
-22006: Leaf order:
-22006: k 1 0 0
-22006: s 1 0 0
-22006: apply 11 2 3 0,2
-22006: f 3 1 3 0,2,2
-% SZS status Timeout for COL006-1.p
-NO CLASH, using fixed ground order
-22027: Facts:
-22027: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22027: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-NO CLASH, using fixed ground order
-22028: Facts:
-22028: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22028: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-22028: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-22028: Goal:
-22028: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22028: Order:
-22028: kbo
-22028: Leaf order:
-22028: k 10 0 0
-22028: s 11 0 0
-22028: apply 29 2 3 0,2
-22028: fixed_pt 3 0 3 2,2
-22028: strong_fixed_point 3 0 2 1,2
-22027: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-22027: Goal:
-22027: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22027: Order:
-22027: nrkbo
-22027: Leaf order:
-22027: k 10 0 0
-22027: s 11 0 0
-22027: apply 29 2 3 0,2
-22027: fixed_pt 3 0 3 2,2
-22027: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22029: Facts:
-22029: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22029: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-22029: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-22029: Goal:
-22029: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22029: Order:
-22029: lpo
-22029: Leaf order:
-22029: k 10 0 0
-22029: s 11 0 0
-22029: apply 29 2 3 0,2
-22029: fixed_pt 3 0 3 2,2
-22029: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL006-5.p
-NO CLASH, using fixed ground order
-22056: Facts:
-22056: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22056: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-22056: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-22056: Goal:
-22056: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22056: Order:
-22056: nrkbo
-22056: Leaf order:
-22056: k 7 0 0
-22056: s 10 0 0
-22056: apply 25 2 3 0,2
-22056: fixed_pt 3 0 3 2,2
-22056: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22057: Facts:
-22057: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22057: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-22057: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-22057: Goal:
-22057: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22057: Order:
-22057: kbo
-22057: Leaf order:
-22057: k 7 0 0
-22057: s 10 0 0
-22057: apply 25 2 3 0,2
-22057: fixed_pt 3 0 3 2,2
-22057: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22058: Facts:
-22058: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-22058: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-22058: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-22058: Goal:
-22058: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22058: Order:
-22058: lpo
-22058: Leaf order:
-22058: k 7 0 0
-22058: s 10 0 0
-22058: apply 25 2 3 0,2
-22058: fixed_pt 3 0 3 2,2
-22058: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL006-7.p
-NO CLASH, using fixed ground order
-22074: Facts:
-22074: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22074: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22074: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-22074: Goal:
-22074: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22074: Order:
-22074: nrkbo
-22074: Leaf order:
-22074: n 6 0 0
-22074: b 9 0 0
-22074: apply 26 2 3 0,2
-22074: fixed_pt 3 0 3 2,2
-22074: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22075: Facts:
-22075: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22075: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22075: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-22075: Goal:
-22075: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22075: Order:
-22075: kbo
-22075: Leaf order:
-22075: n 6 0 0
-22075: b 9 0 0
-22075: apply 26 2 3 0,2
-22075: fixed_pt 3 0 3 2,2
-22075: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22076: Facts:
-22076: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22076: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22076: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-22076: Goal:
-22076: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22076: Order:
-22076: lpo
-22076: Leaf order:
-22076: n 6 0 0
-22076: b 9 0 0
-22076: apply 26 2 3 0,2
-22076: fixed_pt 3 0 3 2,2
-22076: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL044-6.p
-NO CLASH, using fixed ground order
-22116: Facts:
-22116: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22116: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22116: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-22116: Goal:
-22116: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22116: Order:
-22116: nrkbo
-22116: Leaf order:
-22116: n 6 0 0
-22116: b 9 0 0
-22116: apply 26 2 3 0,2
-22116: fixed_pt 3 0 3 2,2
-22116: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22117: Facts:
-22117: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22117: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22117: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-22117: Goal:
-22117: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22117: Order:
-22117: kbo
-22117: Leaf order:
-22117: n 6 0 0
-22117: b 9 0 0
-22117: apply 26 2 3 0,2
-22117: fixed_pt 3 0 3 2,2
-22117: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-22118: Facts:
-22118: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22118: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-22118: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-22118: Goal:
-22118: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22118: Order:
-22118: lpo
-22118: Leaf order:
-22118: n 6 0 0
-22118: b 9 0 0
-22118: apply 26 2 3 0,2
-22118: fixed_pt 3 0 3 2,2
-22118: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL044-7.p
-CLASH, statistics insufficient
-22135: Facts:
-22135: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22135: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22135: Goal:
-22135: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-22135: Order:
-22135: nrkbo
-22135: Leaf order:
-22135: t 1 0 0
-22135: b 1 0 0
-22135: h 2 1 2 0,2,2
-22135: g 2 1 2 0,2,1,2
-22135: apply 13 2 5 0,2
-22135: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-22136: Facts:
-22136: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22136: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22136: Goal:
-22136: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-22136: Order:
-22136: kbo
-22136: Leaf order:
-22136: t 1 0 0
-22136: b 1 0 0
-22136: h 2 1 2 0,2,2
-22136: g 2 1 2 0,2,1,2
-22136: apply 13 2 5 0,2
-22136: f 2 1 2 0,2,1,1,2
-CLASH, statistics insufficient
-22137: Facts:
-22137: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22137: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22137: Goal:
-22137: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-22137: Order:
-22137: lpo
-22137: Leaf order:
-22137: t 1 0 0
-22137: b 1 0 0
-22137: h 2 1 2 0,2,2
-22137: g 2 1 2 0,2,1,2
-22137: apply 13 2 5 0,2
-22137: f 2 1 2 0,2,1,1,2
-Goal subsumed
-Statistics :
-Max weight : 124
-Found proof, 35.273110s
-% SZS status Unsatisfiable for COL064-1.p
-% SZS output start CNFRefutation for COL064-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2
-Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2
-Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2
-Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2
-Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
-Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
-% SZS output end CNFRefutation for COL064-1.p
-22135: solved COL064-1.p in 35.146196 using nrkbo
-22135: status Unsatisfiable for COL064-1.p
-CLASH, statistics insufficient
-22153: Facts:
-22153: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22153: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22153: Goal:
-22153: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-22153: Order:
-22153: nrkbo
-22153: Leaf order:
-22153: t 1 0 0
-22153: b 1 0 0
-22153: i 2 1 2 0,2,2
-22153: h 2 1 2 0,2,1,2
-22153: g 2 1 2 0,2,1,1,2
-22153: apply 15 2 7 0,2
-22153: f 2 1 2 0,2,1,1,1,2
-CLASH, statistics insufficient
-22154: Facts:
-22154: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22154: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22154: Goal:
-22154: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-22154: Order:
-22154: kbo
-22154: Leaf order:
-22154: t 1 0 0
-22154: b 1 0 0
-22154: i 2 1 2 0,2,2
-22154: h 2 1 2 0,2,1,2
-22154: g 2 1 2 0,2,1,1,2
-22154: apply 15 2 7 0,2
-22154: f 2 1 2 0,2,1,1,1,2
-CLASH, statistics insufficient
-22155: Facts:
-22155: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22155: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-22155: Goal:
-22155: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-22155: Order:
-22155: lpo
-22155: Leaf order:
-22155: t 1 0 0
-22155: b 1 0 0
-22155: i 2 1 2 0,2,2
-22155: h 2 1 2 0,2,1,2
-22155: g 2 1 2 0,2,1,1,2
-22155: apply 15 2 7 0,2
-22155: f 2 1 2 0,2,1,1,1,2
-% SZS status Timeout for COL065-1.p
-CLASH, statistics insufficient
-22171: Facts:
-22171: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22171: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22171: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22171: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22171: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22171: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22171: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22171: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22171: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22171: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22171: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22171: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22171: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22171: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22171: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22171: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-22171: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-22171: Goal:
-22171: Id : 1, {_}: a =>= b [] by prove_p12
-22171: Order:
-22171: nrkbo
-22171: Leaf order:
-22171: c 4 0 0
-22171: least_upper_bound 15 2 0
-22171: greatest_lower_bound 15 2 0
-22171: inverse 1 1 0
-22171: multiply 18 2 0
-22171: identity 2 0 0
-22171: b 3 0 1 3
-22171: a 3 0 1 2
-CLASH, statistics insufficient
-22172: Facts:
-22172: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22172: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22172: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22172: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22172: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22172: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22172: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22172: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22172: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22172: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22172: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22172: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22172: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22172: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22172: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22172: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-22172: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-22172: Goal:
-22172: Id : 1, {_}: a =>= b [] by prove_p12
-22172: Order:
-22172: kbo
-22172: Leaf order:
-22172: c 4 0 0
-22172: least_upper_bound 15 2 0
-22172: greatest_lower_bound 15 2 0
-22172: inverse 1 1 0
-22172: multiply 18 2 0
-22172: identity 2 0 0
-22172: b 3 0 1 3
-22172: a 3 0 1 2
-CLASH, statistics insufficient
-22173: Facts:
-22173: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22173: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22173: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22173: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22173: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22173: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22173: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22173: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22173: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22173: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22173: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22173: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22173: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22173: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22173: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22173: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-22173: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-22173: Goal:
-22173: Id : 1, {_}: a =>= b [] by prove_p12
-22173: Order:
-22173: lpo
-22173: Leaf order:
-22173: c 4 0 0
-22173: least_upper_bound 15 2 0
-22173: greatest_lower_bound 15 2 0
-22173: inverse 1 1 0
-22173: multiply 18 2 0
-22173: identity 2 0 0
-22173: b 3 0 1 3
-22173: a 3 0 1 2
-% SZS status Timeout for GRP181-1.p
-CLASH, statistics insufficient
-22201: Facts:
-22201: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22201: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22201: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22201: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22201: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22201: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22201: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22201: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22201: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22201: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22201: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22201: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22201: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22201: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22201: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22201: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-22201: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-22201: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-22201: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-22201: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-22201: Goal:
-22201: Id : 1, {_}: a =>= b [] by prove_p12
-22201: Order:
-22201: kbo
-22201: Leaf order:
-22201: c 4 0 0
-22201: least_upper_bound 15 2 0
-22201: greatest_lower_bound 15 2 0
-22201: inverse 7 1 0
-22201: multiply 20 2 0
-22201: identity 4 0 0
-22201: b 3 0 1 3
-22201: a 3 0 1 2
-CLASH, statistics insufficient
-22202: Facts:
-22202: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22202: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22202: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22202: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22202: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22202: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22202: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22202: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22202: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22202: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22202: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22202: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22202: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22202: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22202: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22202: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-22202: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-22202: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-22202: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-22202: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-22202: Goal:
-22202: Id : 1, {_}: a =>= b [] by prove_p12
-22202: Order:
-22202: lpo
-22202: Leaf order:
-22202: c 4 0 0
-22202: least_upper_bound 15 2 0
-22202: greatest_lower_bound 15 2 0
-22202: inverse 7 1 0
-22202: multiply 20 2 0
-22202: identity 4 0 0
-22202: b 3 0 1 3
-22202: a 3 0 1 2
-CLASH, statistics insufficient
-22200: Facts:
-22200: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22200: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22200: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22200: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22200: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22200: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22200: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22200: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22200: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22200: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22200: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22200: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22200: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22200: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22200: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22200: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-22200: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-22200: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-22200: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-22200: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-22200: Goal:
-22200: Id : 1, {_}: a =>= b [] by prove_p12
-22200: Order:
-22200: nrkbo
-22200: Leaf order:
-22200: c 4 0 0
-22200: least_upper_bound 15 2 0
-22200: greatest_lower_bound 15 2 0
-22200: inverse 7 1 0
-22200: multiply 20 2 0
-22200: identity 4 0 0
-22200: b 3 0 1 3
-22200: a 3 0 1 2
-% SZS status Timeout for GRP181-2.p
-NO CLASH, using fixed ground order
-22218: Facts:
-22218: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22218: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22218: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22218: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22218: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22218: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22218: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22218: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22218: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22218: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22218: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22218: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22218: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22218: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22218: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22218: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-22218: Goal:
-22218: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
-22218: Order:
-22218: nrkbo
-22218: Leaf order:
-22218: least_upper_bound 15 2 0
-22218: greatest_lower_bound 14 2 0
-22218: inverse 3 1 0
-22218: identity 3 0 0
-22218: multiply 20 2 2 0,2
-22218: b 4 0 2 2,2
-22218: a 4 0 2 1,2
-NO CLASH, using fixed ground order
-22219: Facts:
-22219: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22219: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22219: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22219: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22219: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22219: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22219: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22219: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22219: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22219: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22219: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22219: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22219: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22219: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22219: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22219: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-22219: Goal:
-22219: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
-22219: Order:
-22219: kbo
-22219: Leaf order:
-22219: least_upper_bound 15 2 0
-22219: greatest_lower_bound 14 2 0
-22219: inverse 3 1 0
-22219: identity 3 0 0
-22219: multiply 20 2 2 0,2
-22219: b 4 0 2 2,2
-22219: a 4 0 2 1,2
-NO CLASH, using fixed ground order
-22220: Facts:
-22220: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22220: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22220: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22220: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22220: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22220: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22220: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22220: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22220: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22220: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22220: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22220: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22220: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22220: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22220: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22220: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-22220: Goal:
-22220: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
-22220: Order:
-22220: lpo
-22220: Leaf order:
-22220: least_upper_bound 15 2 0
-22220: greatest_lower_bound 14 2 0
-22220: inverse 3 1 0
-22220: identity 3 0 0
-22220: multiply 20 2 2 0,2
-22220: b 4 0 2 2,2
-22220: a 4 0 2 1,2
-% SZS status Timeout for GRP187-1.p
-NO CLASH, using fixed ground order
-22280: Facts:
-22280: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22280: Goal:
-22280: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-22280: Order:
-22280: nrkbo
-22280: Leaf order:
-22280: b1 2 0 2 1,1,3
-22280: multiply 12 2 2 0,2
-22280: inverse 9 1 2 0,1,2
-22280: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-22281: Facts:
-22281: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22281: Goal:
-22281: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-22281: Order:
-22281: kbo
-22281: Leaf order:
-22281: b1 2 0 2 1,1,3
-22281: multiply 12 2 2 0,2
-22281: inverse 9 1 2 0,1,2
-22281: a1 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-22282: Facts:
-22282: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22282: Goal:
-22282: Id : 1, {_}:
- multiply (inverse a1) a1 =>= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-22282: Order:
-22282: lpo
-22282: Leaf order:
-22282: b1 2 0 2 1,1,3
-22282: multiply 12 2 2 0,2
-22282: inverse 9 1 2 0,1,2
-22282: a1 2 0 2 1,1,2
-% SZS status Timeout for GRP505-1.p
-NO CLASH, using fixed ground order
-22298: Facts:
-22298: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22298: Goal:
-22298: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-22298: Order:
-22298: nrkbo
-22298: Leaf order:
-22298: inverse 7 1 0
-22298: c3 2 0 2 2,2
-22298: multiply 14 2 4 0,2
-22298: b3 2 0 2 2,1,2
-22298: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-22299: Facts:
-22299: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22299: Goal:
-22299: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-22299: Order:
-22299: kbo
-22299: Leaf order:
-22299: inverse 7 1 0
-22299: c3 2 0 2 2,2
-22299: multiply 14 2 4 0,2
-22299: b3 2 0 2 2,1,2
-22299: a3 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-22300: Facts:
-22300: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22300: Goal:
-22300: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-22300: Order:
-22300: lpo
-22300: Leaf order:
-22300: inverse 7 1 0
-22300: c3 2 0 2 2,2
-22300: multiply 14 2 4 0,2
-22300: b3 2 0 2 2,1,2
-22300: a3 2 0 2 1,1,2
-% SZS status Timeout for GRP507-1.p
-NO CLASH, using fixed ground order
-22343: Facts:
-22343: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22343: Goal:
-22343: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-22343: Order:
-22343: nrkbo
-22343: Leaf order:
-22343: inverse 7 1 0
-22343: multiply 12 2 2 0,2
-22343: b 2 0 2 2,2
-22343: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-22344: Facts:
-22344: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22344: Goal:
-22344: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-22344: Order:
-22344: kbo
-22344: Leaf order:
-22344: inverse 7 1 0
-22344: multiply 12 2 2 0,2
-22344: b 2 0 2 2,2
-22344: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-22345: Facts:
-22345: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22345: Goal:
-22345: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
-22345: Order:
-22345: lpo
-22345: Leaf order:
-22345: inverse 7 1 0
-22345: multiply 12 2 2 0,2
-22345: b 2 0 2 2,2
-22345: a 2 0 2 1,2
-% SZS status Timeout for GRP508-1.p
-NO CLASH, using fixed ground order
-22381: Facts:
-22381: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22381: Goal:
-22381: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-22381: Order:
-22381: nrkbo
-22381: Leaf order:
-22381: join 20 2 0
-22381: meet 19 2 1 0,2
-22381: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22382: Facts:
-22382: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22382: Goal:
-22382: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-22382: Order:
-22382: kbo
-22382: Leaf order:
-22382: join 20 2 0
-22382: meet 19 2 1 0,2
-22382: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22383: Facts:
-22383: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22383: Goal:
-22383: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-22383: Order:
-22383: lpo
-22383: Leaf order:
-22383: join 20 2 0
-22383: meet 19 2 1 0,2
-22383: a 3 0 3 1,2
-% SZS status Timeout for LAT080-1.p
-NO CLASH, using fixed ground order
-22413: Facts:
-22413: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22413: Goal:
-22413: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-22413: Order:
-22413: nrkbo
-22413: Leaf order:
-22413: meet 18 2 0
-22413: join 21 2 1 0,2
-22413: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22414: Facts:
-22414: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22414: Goal:
-22414: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-22414: Order:
-22414: kbo
-22414: Leaf order:
-22414: meet 18 2 0
-22414: join 21 2 1 0,2
-22414: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22415: Facts:
-22415: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-22415: Goal:
-22415: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-22415: Order:
-22415: lpo
-22415: Leaf order:
-22415: meet 18 2 0
-22415: join 21 2 1 0,2
-22415: a 3 0 3 1,2
-% SZS status Timeout for LAT083-1.p
-NO CLASH, using fixed ground order
-22432: Facts:
-22432: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22432: Goal:
-22432: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-22432: Order:
-22432: nrkbo
-22432: Leaf order:
-22432: join 18 2 0
-22432: meet 19 2 1 0,2
-22432: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22434: Facts:
-22434: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22434: Goal:
-22434: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-22434: Order:
-22434: lpo
-22434: Leaf order:
-22434: join 18 2 0
-22434: meet 19 2 1 0,2
-22434: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22433: Facts:
-22433: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22433: Goal:
-22433: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-22433: Order:
-22433: kbo
-22433: Leaf order:
-22433: join 18 2 0
-22433: meet 19 2 1 0,2
-22433: a 3 0 3 1,2
-% SZS status Timeout for LAT092-1.p
-NO CLASH, using fixed ground order
-22466: Facts:
-22466: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22466: Goal:
-22466: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-22466: Order:
-22466: nrkbo
-22466: Leaf order:
-22466: join 18 2 0
-22466: meet 20 2 2 0,2
-22466: a 2 0 2 2,2
-22466: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-22467: Facts:
-22467: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22467: Goal:
-22467: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-22467: Order:
-22467: kbo
-22467: Leaf order:
-22467: join 18 2 0
-22467: meet 20 2 2 0,2
-22467: a 2 0 2 2,2
-22467: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-22468: Facts:
-22468: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22468: Goal:
-22468: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
-22468: Order:
-22468: lpo
-22468: Leaf order:
-22468: join 18 2 0
-22468: meet 20 2 2 0,2
-22468: a 2 0 2 2,2
-22468: b 2 0 2 1,2
-% SZS status Timeout for LAT093-1.p
-NO CLASH, using fixed ground order
-22493: Facts:
-22493: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22493: Goal:
-22493: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-22493: Order:
-22493: nrkbo
-22493: Leaf order:
-22493: meet 18 2 0
-22493: join 19 2 1 0,2
-22493: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22494: Facts:
-22494: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22494: Goal:
-22494: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-22494: Order:
-22494: kbo
-22494: Leaf order:
-22494: meet 18 2 0
-22494: join 19 2 1 0,2
-22494: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22495: Facts:
-22495: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22495: Goal:
-22495: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-22495: Order:
-22495: lpo
-22495: Leaf order:
-22495: meet 18 2 0
-22495: join 19 2 1 0,2
-22495: a 3 0 3 1,2
-% SZS status Timeout for LAT094-1.p
-NO CLASH, using fixed ground order
-22522: Facts:
-22522: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22522: Goal:
-22522: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
-22522: Order:
-22522: nrkbo
-22522: Leaf order:
-22522: meet 18 2 0
-22522: join 20 2 2 0,2
-22522: a 2 0 2 2,2
-22522: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-22523: Facts:
-22523: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22523: Goal:
-22523: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
-22523: Order:
-22523: kbo
-22523: Leaf order:
-22523: meet 18 2 0
-22523: join 20 2 2 0,2
-22523: a 2 0 2 2,2
-22523: b 2 0 2 1,2
-NO CLASH, using fixed ground order
-22524: Facts:
-22524: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22524: Goal:
-22524: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
-22524: Order:
-22524: lpo
-22524: Leaf order:
-22524: meet 18 2 0
-22524: join 20 2 2 0,2
-22524: a 2 0 2 2,2
-22524: b 2 0 2 1,2
-% SZS status Timeout for LAT095-1.p
-NO CLASH, using fixed ground order
-22540: Facts:
-22540: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22540: Goal:
-22540: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-22540: Order:
-22540: nrkbo
-22540: Leaf order:
-22540: meet 20 2 2 0,2
-22540: c 1 0 1 1,2,1,2
-22540: join 20 2 2 0,1,1,2
-22540: b 4 0 4 2,1,1,2
-22540: a 1 0 1 1,1,1,2
-NO CLASH, using fixed ground order
-22541: Facts:
-22541: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22541: Goal:
-22541: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-22541: Order:
-22541: kbo
-22541: Leaf order:
-22541: meet 20 2 2 0,2
-22541: c 1 0 1 1,2,1,2
-22541: join 20 2 2 0,1,1,2
-22541: b 4 0 4 2,1,1,2
-22541: a 1 0 1 1,1,1,2
-NO CLASH, using fixed ground order
-22542: Facts:
-22542: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22542: Goal:
-22542: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-22542: Order:
-22542: lpo
-22542: Leaf order:
-22542: meet 20 2 2 0,2
-22542: c 1 0 1 1,2,1,2
-22542: join 20 2 2 0,1,1,2
-22542: b 4 0 4 2,1,1,2
-22542: a 1 0 1 1,1,1,2
-% SZS status Timeout for LAT096-1.p
-NO CLASH, using fixed ground order
-22569: Facts:
-22569: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22569: Goal:
-22569: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-22569: Order:
-22569: nrkbo
-22569: Leaf order:
-22569: join 20 2 2 0,2
-22569: c 1 0 1 1,2,1,2
-22569: meet 20 2 2 0,1,1,2
-22569: b 4 0 4 2,1,1,2
-22569: a 1 0 1 1,1,1,2
-NO CLASH, using fixed ground order
-22570: Facts:
-22570: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22570: Goal:
-22570: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-22570: Order:
-22570: kbo
-22570: Leaf order:
-22570: join 20 2 2 0,2
-22570: c 1 0 1 1,2,1,2
-22570: meet 20 2 2 0,1,1,2
-22570: b 4 0 4 2,1,1,2
-22570: a 1 0 1 1,1,1,2
-NO CLASH, using fixed ground order
-22571: Facts:
-22571: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-22571: Goal:
-22571: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-22571: Order:
-22571: lpo
-22571: Leaf order:
-22571: join 20 2 2 0,2
-22571: c 1 0 1 1,2,1,2
-22571: meet 20 2 2 0,1,1,2
-22571: b 4 0 4 2,1,1,2
-22571: a 1 0 1 1,1,1,2
-% SZS status Timeout for LAT097-1.p
-NO CLASH, using fixed ground order
-22740: Facts:
-22740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22740: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22740: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22740: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22740: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22740: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22740: Goal:
-22740: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-22740: Order:
-22740: nrkbo
-22740: Leaf order:
-22740: join 16 2 3 0,2,2
-22740: meet 21 2 7 0,2
-22740: d 3 0 3 2,2,2,2,2
-22740: c 2 0 2 1,2,2,2,2
-22740: b 3 0 3 1,2,2
-22740: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-22742: Facts:
-22742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22742: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22742: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22742: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22742: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22742: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22742: Goal:
-22742: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-22742: Order:
-22742: lpo
-22742: Leaf order:
-22742: join 16 2 3 0,2,2
-22742: meet 21 2 7 0,2
-22742: d 3 0 3 2,2,2,2,2
-22742: c 2 0 2 1,2,2,2,2
-22742: b 3 0 3 1,2,2
-22742: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-22741: Facts:
-22741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22741: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22741: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22741: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22741: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22741: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22741: Goal:
-22741: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-22741: Order:
-22741: kbo
-22741: Leaf order:
-22741: join 16 2 3 0,2,2
-22741: meet 21 2 7 0,2
-22741: d 3 0 3 2,2,2,2,2
-22741: c 2 0 2 1,2,2,2,2
-22741: b 3 0 3 1,2,2
-22741: a 4 0 4 1,2
-% SZS status Timeout for LAT146-1.p
-NO CLASH, using fixed ground order
-22773: Facts:
-22773: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22773: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22773: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22773: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22773: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22773: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22773: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22773: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22773: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22773: Goal:
-22773: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-22773: Order:
-22773: nrkbo
-22773: Leaf order:
-22773: join 17 2 4 0,2,2
-22773: meet 20 2 6 0,2
-22773: c 2 0 2 2,2,2,2
-22773: b 4 0 4 1,2,2
-22773: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-22774: Facts:
-22774: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22774: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22774: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22774: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22774: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22774: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22774: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22774: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22774: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22774: Goal:
-22774: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-22774: Order:
-22774: kbo
-22774: Leaf order:
-22774: join 17 2 4 0,2,2
-22774: meet 20 2 6 0,2
-22774: c 2 0 2 2,2,2,2
-22774: b 4 0 4 1,2,2
-22774: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-22775: Facts:
-22775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22775: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22775: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22775: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22775: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22775: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-22775: Goal:
-22775: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-22775: Order:
-22775: lpo
-22775: Leaf order:
-22775: join 17 2 4 0,2,2
-22775: meet 20 2 6 0,2
-22775: c 2 0 2 2,2,2,2
-22775: b 4 0 4 1,2,2
-22775: a 6 0 6 1,2
-% SZS status Timeout for LAT148-1.p
-NO CLASH, using fixed ground order
-22791: Facts:
-22791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22791: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22791: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22791: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22791: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22791: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-22791: Goal:
-22791: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-22791: Order:
-22791: nrkbo
-22791: Leaf order:
-22791: join 18 2 4 0,2,2
-22791: meet 20 2 6 0,2
-22791: c 3 0 3 2,2,2,2
-22791: b 3 0 3 1,2,2
-22791: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-22792: Facts:
-22792: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22792: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22792: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22792: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22792: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22792: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22792: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22792: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22792: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-22792: Goal:
-22792: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-22792: Order:
-22792: kbo
-22792: Leaf order:
-22792: join 18 2 4 0,2,2
-22792: meet 20 2 6 0,2
-22792: c 3 0 3 2,2,2,2
-22792: b 3 0 3 1,2,2
-22792: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-22793: Facts:
-22793: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22793: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22793: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22793: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22793: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22793: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22793: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22793: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22793: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-22793: Goal:
-22793: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-22793: Order:
-22793: lpo
-22793: Leaf order:
-22793: join 18 2 4 0,2,2
-22793: meet 20 2 6 0,2
-22793: c 3 0 3 2,2,2,2
-22793: b 3 0 3 1,2,2
-22793: a 6 0 6 1,2
-% SZS status Timeout for LAT156-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-22830: Facts:
-22830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22830: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22830: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22830: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22830: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22830: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-22830: Goal:
-22830: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-22830: Order:
-22830: kbo
-22830: Leaf order:
-22830: meet 19 2 5 0,2
-22830: join 18 2 4 0,2,2
-22830: d 2 0 2 2,2,2,2,2
-22830: c 3 0 3 1,2,2,2
-22830: b 2 0 2 1,2,2
-22830: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-22831: Facts:
-22831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22831: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22831: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22831: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22831: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22831: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-22831: Goal:
-22831: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-22831: Order:
-22831: lpo
-22831: Leaf order:
-22831: meet 19 2 5 0,2
-22831: join 18 2 4 0,2,2
-22831: d 2 0 2 2,2,2,2,2
-22831: c 3 0 3 1,2,2,2
-22831: b 2 0 2 1,2,2
-22831: a 4 0 4 1,2
-22829: Facts:
-22829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-22829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-22829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-22829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-22829: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-22829: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-22829: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-22829: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-22829: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-22829: Goal:
-22829: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-22829: Order:
-22829: nrkbo
-22829: Leaf order:
-22829: meet 19 2 5 0,2
-22829: join 18 2 4 0,2,2
-22829: d 2 0 2 2,2,2,2,2
-22829: c 3 0 3 1,2,2,2
-22829: b 2 0 2 1,2,2
-22829: a 4 0 4 1,2
-% SZS status Timeout for LAT160-1.p
-NO CLASH, using fixed ground order
-22849: Facts:
-22849: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-22849: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-22849: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-22849: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-22849: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-22849: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-22849: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-22849: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-22849: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-22849: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-22849: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-22849: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-22849: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-22849: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-22849: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-22849: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-22849: Goal:
-22849: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =>=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-22849: Order:
-22849: nrkbo
-22849: Leaf order:
-22849: falsehood 1 0 0
-22849: and 9 2 0
-22849: or 10 2 0
-22849: not 12 1 0
-22849: implies 14 2 0
-22849: and_star 11 2 4 0,2
-22849: y 3 0 3 2,1,1,2
-22849: xor 7 2 4 0,1,2
-22849: x 3 0 3 2,1,1,1,2
-22849: truth 8 0 4 1,1,1,1,2
-NO CLASH, using fixed ground order
-22850: Facts:
-22850: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-22850: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-22850: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-22850: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-22850: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-22850: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-22850: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-22850: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-22850: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-22850: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-22850: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-22850: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-22850: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-22850: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-22850: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-22850: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-22850: Goal:
-22850: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =?=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-22850: Order:
-22850: kbo
-22850: Leaf order:
-22850: falsehood 1 0 0
-22850: and 9 2 0
-22850: or 10 2 0
-22850: not 12 1 0
-22850: implies 14 2 0
-22850: and_star 11 2 4 0,2
-22850: y 3 0 3 2,1,1,2
-22850: xor 7 2 4 0,1,2
-22850: x 3 0 3 2,1,1,1,2
-22850: truth 8 0 4 1,1,1,1,2
-NO CLASH, using fixed ground order
-22851: Facts:
-22851: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-22851: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-22851: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-22851: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-22851: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-22851: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-22851: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-22851: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-22851: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-22851: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-22851: Id : 12, {_}:
- xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-22851: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-22851: Id : 14, {_}:
- and_star ?40 ?41 =>= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-22851: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-22851: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-22851: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-22851: Goal:
-22851: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =>=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-22851: Order:
-22851: lpo
-22851: Leaf order:
-22851: falsehood 1 0 0
-22851: and 9 2 0
-22851: or 10 2 0
-22851: not 12 1 0
-22851: implies 14 2 0
-22851: and_star 11 2 4 0,2
-22851: y 3 0 3 2,1,1,2
-22851: xor 7 2 4 0,1,2
-22851: x 3 0 3 2,1,1,1,2
-22851: truth 8 0 4 1,1,1,1,2
-% SZS status Timeout for LCL160-1.p
-NO CLASH, using fixed ground order
-22879: Facts:
-22879: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-22879: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-22879: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-22879: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =<=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-22879: Id : 6, {_}:
- add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-22879: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-22879: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-22879: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-22879: Goal:
-22879: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
-22879: Order:
-22879: nrkbo
-22879: Leaf order:
-22879: additive_inverse 1 1 0
-22879: add 12 2 0
-22879: additive_identity 2 0 0
-22879: multiply 14 2 2 0,2
-22879: b 2 0 2 2,2
-22879: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-22880: Facts:
-22880: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-22880: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-22880: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-22880: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =<=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-22880: Id : 6, {_}:
- add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-22880: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-22880: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-22880: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-22880: Goal:
-22880: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
-22880: Order:
-22880: kbo
-22880: Leaf order:
-22880: additive_inverse 1 1 0
-22880: add 12 2 0
-22880: additive_identity 2 0 0
-22880: multiply 14 2 2 0,2
-22880: b 2 0 2 2,2
-22880: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-22881: Facts:
-22881: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-22881: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-22881: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-22881: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =>=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-22881: Id : 6, {_}:
- add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-22881: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-22881: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-22881: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-22881: Goal:
-22881: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
-22881: Order:
-22881: lpo
-22881: Leaf order:
-22881: additive_inverse 1 1 0
-22881: add 12 2 0
-22881: additive_identity 2 0 0
-22881: multiply 14 2 2 0,2
-22881: b 2 0 2 2,2
-22881: a 2 0 2 1,2
-% SZS status Timeout for RNG009-5.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-22919: Facts:
-22919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22919: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22919: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-22919: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-22919: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-22919: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-22919: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-22919: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-22919: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-22919: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-22919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-22919: Goal:
-22919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-22919: Order:
-22919: kbo
-22919: Leaf order:
-22919: additive_inverse 2 1 0
-22919: add 14 2 0
-22919: additive_identity 4 0 0
-22919: c 2 0 1 3
-22919: multiply 14 2 1 0,2
-22919: a 2 0 1 2,2
-22919: b 2 0 1 1,2
-22918: Facts:
-22918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22918: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22918: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-22918: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-22918: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-22918: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-22918: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-22918: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-22918: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-22918: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-22918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-22918: Goal:
-22918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-22918: Order:
-22918: nrkbo
-22918: Leaf order:
-22918: additive_inverse 2 1 0
-22918: add 14 2 0
-22918: additive_identity 4 0 0
-22918: c 2 0 1 3
-22918: multiply 14 2 1 0,2
-22918: a 2 0 1 2,2
-22918: b 2 0 1 1,2
-NO CLASH, using fixed ground order
-22920: Facts:
-22920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22920: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22920: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-22920: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-22920: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-22920: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-22920: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-22920: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-22920: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-22920: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-22920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-22920: Goal:
-22920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-22920: Order:
-22920: lpo
-22920: Leaf order:
-22920: additive_inverse 2 1 0
-22920: add 14 2 0
-22920: additive_identity 4 0 0
-22920: c 2 0 1 3
-22920: multiply 14 2 1 0,2
-22920: a 2 0 1 2,2
-22920: b 2 0 1 1,2
-% SZS status Timeout for RNG009-7.p
-NO CLASH, using fixed ground order
-22947: Facts:
-22947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22947: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22947: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22947: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22947: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22947: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22947: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22947: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22947: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22947: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22947: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22947: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22947: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22947: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22947: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22947: Goal:
-22947: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22947: Order:
-22947: nrkbo
-22947: Leaf order:
-22947: commutator 1 2 0
-22947: additive_identity 9 0 1 3
-22947: additive_inverse 7 1 1 0,2,2
-22947: add 20 2 4 0,2
-22947: associator 6 3 5 0,1,1,2
-22947: d 5 0 5 3,1,1,2
-22947: c 5 0 5 2,1,1,2
-22947: multiply 27 2 5 0,1,1,1,2
-22947: b 5 0 5 2,1,1,1,2
-22947: a 5 0 5 1,1,1,1,2
-NO CLASH, using fixed ground order
-22948: Facts:
-22948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22948: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22948: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22948: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22948: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22948: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22948: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22948: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22948: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22948: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22948: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22948: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22948: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22948: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22948: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22948: Goal:
-22948: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22948: Order:
-22948: kbo
-22948: Leaf order:
-22948: commutator 1 2 0
-22948: additive_identity 9 0 1 3
-22948: additive_inverse 7 1 1 0,2,2
-22948: add 20 2 4 0,2
-22948: associator 6 3 5 0,1,1,2
-22948: d 5 0 5 3,1,1,2
-22948: c 5 0 5 2,1,1,2
-22948: multiply 27 2 5 0,1,1,1,2
-22948: b 5 0 5 2,1,1,1,2
-22948: a 5 0 5 1,1,1,1,2
-NO CLASH, using fixed ground order
-22949: Facts:
-22949: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22949: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22949: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22949: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22949: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22949: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22949: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22949: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22949: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22949: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22949: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22949: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22949: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22949: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22949: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22949: Goal:
-22949: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22949: Order:
-22949: lpo
-22949: Leaf order:
-22949: commutator 1 2 0
-22949: additive_identity 9 0 1 3
-22949: additive_inverse 7 1 1 0,2,2
-22949: add 20 2 4 0,2
-22949: associator 6 3 5 0,1,1,2
-22949: d 5 0 5 3,1,1,2
-22949: c 5 0 5 2,1,1,2
-22949: multiply 27 2 5 0,1,1,1,2
-22949: b 5 0 5 2,1,1,1,2
-22949: a 5 0 5 1,1,1,1,2
-% SZS status Timeout for RNG026-6.p
-NO CLASH, using fixed ground order
-22966: Facts:
-NO CLASH, using fixed ground order
-22967: Facts:
-22967: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22967: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22967: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-NO CLASH, using fixed ground order
-22966: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22966: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22966: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22966: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22966: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22966: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22966: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22965: Facts:
-22966: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22966: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22966: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22965: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22965: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22965: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22965: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22965: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22965: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22965: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22965: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22965: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22965: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22965: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22965: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22965: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22965: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22965: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22965: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22965: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22965: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22965: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22965: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22965: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22965: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22965: Goal:
-22965: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22965: Order:
-22965: nrkbo
-22965: Leaf order:
-22965: commutator 1 2 0
-22965: additive_identity 9 0 1 3
-22965: additive_inverse 23 1 1 0,2,2
-22965: add 28 2 4 0,2
-22965: associator 6 3 5 0,1,1,2
-22965: d 5 0 5 3,1,1,2
-22965: c 5 0 5 2,1,1,2
-22965: multiply 45 2 5 0,1,1,1,2
-22965: b 5 0 5 2,1,1,1,2
-22965: a 5 0 5 1,1,1,1,2
-22967: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22966: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22966: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22966: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22966: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22966: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22966: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22966: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22966: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22966: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22966: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22966: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22966: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22966: Goal:
-22966: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22966: Order:
-22966: kbo
-22966: Leaf order:
-22966: commutator 1 2 0
-22966: additive_identity 9 0 1 3
-22966: additive_inverse 23 1 1 0,2,2
-22966: add 28 2 4 0,2
-22966: associator 6 3 5 0,1,1,2
-22966: d 5 0 5 3,1,1,2
-22966: c 5 0 5 2,1,1,2
-22966: multiply 45 2 5 0,1,1,1,2
-22966: b 5 0 5 2,1,1,1,2
-22966: a 5 0 5 1,1,1,1,2
-22967: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22967: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22967: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22967: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22967: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22967: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22967: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22967: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22967: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22967: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22967: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22967: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22967: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22967: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22967: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22967: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22967: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22967: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22967: Goal:
-22967: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-22967: Order:
-22967: lpo
-22967: Leaf order:
-22967: commutator 1 2 0
-22967: additive_identity 9 0 1 3
-22967: additive_inverse 23 1 1 0,2,2
-22967: add 28 2 4 0,2
-22967: associator 6 3 5 0,1,1,2
-22967: d 5 0 5 3,1,1,2
-22967: c 5 0 5 2,1,1,2
-22967: multiply 45 2 5 0,1,1,1,2
-22967: b 5 0 5 2,1,1,1,2
-22967: a 5 0 5 1,1,1,1,2
-% SZS status Timeout for RNG026-7.p
-NO CLASH, using fixed ground order
-22994: Facts:
-22994: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-22994: Goal:
-22994: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-22994: Order:
-22994: nrkbo
-22994: Leaf order:
-22994: nand 12 2 6 0,2
-22994: c 2 0 2 2,2,2,2
-22994: b 3 0 3 1,2,2
-22994: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22995: Facts:
-22995: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-22995: Goal:
-22995: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-22995: Order:
-22995: kbo
-22995: Leaf order:
-22995: nand 12 2 6 0,2
-22995: c 2 0 2 2,2,2,2
-22995: b 3 0 3 1,2,2
-22995: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-22996: Facts:
-22996: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-22996: Goal:
-22996: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-22996: Order:
-22996: lpo
-22996: Leaf order:
-22996: nand 12 2 6 0,2
-22996: c 2 0 2 2,2,2,2
-22996: b 3 0 3 1,2,2
-22996: a 3 0 3 1,2
-% SZS status Timeout for BOO076-1.p
-CLASH, statistics insufficient
-23012: Facts:
-23012: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23012: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-23012: Goal:
-23012: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-23012: Order:
-23012: nrkbo
-23012: Leaf order:
-23012: w 1 0 0
-23012: b 1 0 0
-23012: apply 12 2 3 0,2
-23012: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-23013: Facts:
-23013: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23013: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-23013: Goal:
-23013: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-23013: Order:
-23013: kbo
-23013: Leaf order:
-23013: w 1 0 0
-23013: b 1 0 0
-23013: apply 12 2 3 0,2
-23013: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-23014: Facts:
-23014: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23014: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-23014: Goal:
-23014: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-23014: Order:
-23014: lpo
-23014: Leaf order:
-23014: w 1 0 0
-23014: b 1 0 0
-23014: apply 12 2 3 0,2
-23014: f 3 1 3 0,2,2
-% SZS status Timeout for COL003-1.p
-CLASH, statistics insufficient
-23460: Facts:
-23460: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23460: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-23460: Goal:
-23460: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-23460: Order:
-23460: nrkbo
-23460: Leaf order:
-23460: w1 1 0 0
-23460: b 1 0 0
-23460: apply 12 2 3 0,2
-23460: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-23462: Facts:
-23462: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23462: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-23462: Goal:
-23462: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-23462: Order:
-23462: lpo
-23462: Leaf order:
-23462: w1 1 0 0
-23462: b 1 0 0
-23462: apply 12 2 3 0,2
-23462: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-23461: Facts:
-23461: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-23461: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-23461: Goal:
-23461: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-23461: Order:
-23461: kbo
-23461: Leaf order:
-23461: w1 1 0 0
-23461: b 1 0 0
-23461: apply 12 2 3 0,2
-23461: f 3 1 3 0,2,2
-% SZS status Timeout for COL042-1.p
-NO CLASH, using fixed ground order
-23502: Facts:
-23502: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23502: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-23502: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-23502: Goal:
-23502: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23502: Order:
-23502: nrkbo
-23502: Leaf order:
-23502: h 6 0 0
-23502: b 12 0 0
-23502: apply 29 2 3 0,2
-23502: fixed_pt 3 0 3 2,2
-23502: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-23503: Facts:
-23503: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23503: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-23503: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-23503: Goal:
-23503: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23503: Order:
-23503: kbo
-23503: Leaf order:
-23503: h 6 0 0
-23503: b 12 0 0
-23503: apply 29 2 3 0,2
-23503: fixed_pt 3 0 3 2,2
-23503: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-23504: Facts:
-23504: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23504: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-23504: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-23504: Goal:
-23504: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23504: Order:
-23504: lpo
-23504: Leaf order:
-23504: h 6 0 0
-23504: b 12 0 0
-23504: apply 29 2 3 0,2
-23504: fixed_pt 3 0 3 2,2
-23504: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL043-3.p
-NO CLASH, using fixed ground order
-23537: Facts:
-23537: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23537: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23537: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-23537: Goal:
-23537: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23537: Order:
-23537: nrkbo
-23537: Leaf order:
-23537: n 6 0 0
-23537: b 10 0 0
-23537: apply 27 2 3 0,2
-23537: fixed_pt 3 0 3 2,2
-23537: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-23538: Facts:
-23538: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23538: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23538: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-23538: Goal:
-23538: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23538: Order:
-23538: kbo
-23538: Leaf order:
-23538: n 6 0 0
-23538: b 10 0 0
-23538: apply 27 2 3 0,2
-23538: fixed_pt 3 0 3 2,2
-23538: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-23539: Facts:
-23539: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23539: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23539: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-23539: Goal:
-23539: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23539: Order:
-23539: lpo
-23539: Leaf order:
-23539: n 6 0 0
-23539: b 10 0 0
-23539: apply 27 2 3 0,2
-23539: fixed_pt 3 0 3 2,2
-23539: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL044-8.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-23557: Facts:
-23557: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23557: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23557: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-23557: Goal:
-23557: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23557: Order:
-23557: kbo
-23557: Leaf order:
-23557: n 6 0 0
-23557: b 10 0 0
-23557: apply 27 2 3 0,2
-23557: fixed_pt 3 0 3 2,2
-23557: strong_fixed_point 3 0 2 1,2
-NO CLASH, using fixed ground order
-23558: Facts:
-23558: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23558: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23558: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-23558: Goal:
-23558: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23558: Order:
-23558: lpo
-23558: Leaf order:
-23558: n 6 0 0
-23558: b 10 0 0
-23558: apply 27 2 3 0,2
-23558: fixed_pt 3 0 3 2,2
-23558: strong_fixed_point 3 0 2 1,2
-23556: Facts:
-23556: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-23556: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-23556: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-23556: Goal:
-23556: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-23556: Order:
-23556: nrkbo
-23556: Leaf order:
-23556: n 6 0 0
-23556: b 10 0 0
-23556: apply 27 2 3 0,2
-23556: fixed_pt 3 0 3 2,2
-23556: strong_fixed_point 3 0 2 1,2
-% SZS status Timeout for COL044-9.p
-NO CLASH, using fixed ground order
-23710: Facts:
-23710: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-23710: Goal:
-23710: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23710: Order:
-23710: nrkbo
-23710: Leaf order:
-23710: a2 2 0 2 2,2
-23710: multiply 12 2 2 0,2
-23710: inverse 8 1 1 0,1,1,2
-23710: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-23711: Facts:
-23711: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-23711: Goal:
-23711: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23711: Order:
-23711: kbo
-23711: Leaf order:
-23711: a2 2 0 2 2,2
-23711: multiply 12 2 2 0,2
-23711: inverse 8 1 1 0,1,1,2
-23711: b2 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-23712: Facts:
-23712: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-23712: Goal:
-23712: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23712: Order:
-23712: lpo
-23712: Leaf order:
-23712: a2 2 0 2 2,2
-23712: multiply 12 2 2 0,2
-23712: inverse 8 1 1 0,1,1,2
-23712: b2 2 0 2 1,1,1,2
-% SZS status Timeout for GRP506-1.p
-NO CLASH, using fixed ground order
-23731: Facts:
-23731: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23731: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23731: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23731: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23731: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23731: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23731: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23731: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23731: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-23731: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-23731: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-23731: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-23731: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-23731: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-23731: Goal:
-23731: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-23731: Order:
-23731: nrkbo
-23731: Leaf order:
-23731: n0 1 0 0
-23731: n1 2 0 0
-23731: join 18 2 3 0,2,2
-23731: meet 19 2 5 0,2
-23731: complement 14 1 2 0,1,2,2,2,2
-23731: b 3 0 3 1,2,2
-23731: a 7 0 7 1,2
-NO CLASH, using fixed ground order
-23732: Facts:
-23732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23732: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23732: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23732: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23732: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23732: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-23732: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-23732: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-23732: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-23732: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-23732: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-23732: Goal:
-23732: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-23732: Order:
-23732: kbo
-23732: Leaf order:
-23732: n0 1 0 0
-23732: n1 2 0 0
-23732: join 18 2 3 0,2,2
-23732: meet 19 2 5 0,2
-23732: complement 14 1 2 0,1,2,2,2,2
-23732: b 3 0 3 1,2,2
-23732: a 7 0 7 1,2
-NO CLASH, using fixed ground order
-23733: Facts:
-23733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23733: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23733: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23733: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23733: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23733: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-23733: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-23733: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-23733: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-23733: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-23733: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-23733: Goal:
-23733: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-23733: Order:
-23733: lpo
-23733: Leaf order:
-23733: n0 1 0 0
-23733: n1 2 0 0
-23733: join 18 2 3 0,2,2
-23733: meet 19 2 5 0,2
-23733: complement 14 1 2 0,1,2,2,2,2
-23733: b 3 0 3 1,2,2
-23733: a 7 0 7 1,2
-% SZS status Timeout for LAT053-1.p
-NO CLASH, using fixed ground order
-23764: Facts:
-NO CLASH, using fixed ground order
-23765: Facts:
-23764: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23764: Goal:
-23764: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
-23764: Order:
-23764: nrkbo
-23764: Leaf order:
-23764: join 20 2 0
-23764: meet 20 2 2 0,2
-23764: b 2 0 2 2,2
-23764: a 2 0 2 1,2
-23765: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23765: Goal:
-23765: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
-23765: Order:
-23765: kbo
-23765: Leaf order:
-23765: join 20 2 0
-23765: meet 20 2 2 0,2
-23765: b 2 0 2 2,2
-23765: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-23766: Facts:
-23766: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23766: Goal:
-23766: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
-23766: Order:
-23766: lpo
-23766: Leaf order:
-23766: join 20 2 0
-23766: meet 20 2 2 0,2
-23766: b 2 0 2 2,2
-23766: a 2 0 2 1,2
-% SZS status Timeout for LAT081-1.p
-NO CLASH, using fixed ground order
-23787: Facts:
-23787: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23787: Goal:
-23787: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
-23787: Order:
-23787: nrkbo
-23787: Leaf order:
-23787: meet 18 2 0
-23787: join 22 2 2 0,2
-23787: b 2 0 2 2,2
-23787: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-23788: Facts:
-23788: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23788: Goal:
-23788: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
-23788: Order:
-23788: kbo
-23788: Leaf order:
-23788: meet 18 2 0
-23788: join 22 2 2 0,2
-23788: b 2 0 2 2,2
-23788: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-23789: Facts:
-23789: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23789: Goal:
-23789: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
-23789: Order:
-23789: lpo
-23789: Leaf order:
-23789: meet 18 2 0
-23789: join 22 2 2 0,2
-23789: b 2 0 2 2,2
-23789: a 2 0 2 1,2
-% SZS status Timeout for LAT084-1.p
-NO CLASH, using fixed ground order
-23816: Facts:
-23816: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23816: Goal:
-23816: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-23816: Order:
-23816: nrkbo
-23816: Leaf order:
-23816: meet 19 2 1 0,2
-23816: join 21 2 1 0,2,2
-23816: b 1 0 1 2,2,2
-23816: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-23817: Facts:
-23817: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23817: Goal:
-23817: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-23817: Order:
-23817: kbo
-23817: Leaf order:
-23817: meet 19 2 1 0,2
-23817: join 21 2 1 0,2,2
-23817: b 1 0 1 2,2,2
-23817: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-23818: Facts:
-23818: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23818: Goal:
-23818: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-23818: Order:
-23818: lpo
-23818: Leaf order:
-23818: meet 19 2 1 0,2
-23818: join 21 2 1 0,2,2
-23818: b 1 0 1 2,2,2
-23818: a 3 0 3 1,2
-% SZS status Timeout for LAT086-1.p
-NO CLASH, using fixed ground order
-23840: Facts:
-23840: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23840: Goal:
-23840: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-23840: Order:
-23840: nrkbo
-23840: Leaf order:
-23840: join 21 2 1 0,2
-23840: meet 19 2 1 0,2,2
-23840: b 1 0 1 2,2,2
-23840: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-23842: Facts:
-23842: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23842: Goal:
-23842: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-23842: Order:
-23842: lpo
-23842: Leaf order:
-23842: join 21 2 1 0,2
-23842: meet 19 2 1 0,2,2
-23842: b 1 0 1 2,2,2
-23842: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-23841: Facts:
-23841: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-23841: Goal:
-23841: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-23841: Order:
-23841: kbo
-23841: Leaf order:
-23841: join 21 2 1 0,2
-23841: meet 19 2 1 0,2,2
-23841: b 1 0 1 2,2,2
-23841: a 3 0 3 1,2
-% SZS status Timeout for LAT087-1.p
-NO CLASH, using fixed ground order
-23873: Facts:
-23873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23873: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23873: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23873: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23873: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23873: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-23873: Goal:
-23873: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-23873: Order:
-23873: nrkbo
-23873: Leaf order:
-23873: join 17 2 4 0,2,2
-23873: meet 21 2 6 0,2
-23873: c 4 0 4 2,2,2,2
-23873: b 4 0 4 1,2,2
-23873: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-23874: Facts:
-23874: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23874: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23874: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23874: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23874: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23874: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23874: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23874: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23874: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-23874: Goal:
-23874: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-23874: Order:
-23874: kbo
-23874: Leaf order:
-23874: join 17 2 4 0,2,2
-23874: meet 21 2 6 0,2
-23874: c 4 0 4 2,2,2,2
-23874: b 4 0 4 1,2,2
-23874: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-23875: Facts:
-23875: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-23875: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-23875: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-23875: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-23875: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-23875: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-23875: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-23875: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-23875: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-23875: Goal:
-23875: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-23875: Order:
-23875: lpo
-23875: Leaf order:
-23875: join 17 2 4 0,2,2
-23875: meet 21 2 6 0,2
-23875: c 4 0 4 2,2,2,2
-23875: b 4 0 4 1,2,2
-23875: a 4 0 4 1,2
-% SZS status Timeout for LAT099-1.p
-NO CLASH, using fixed ground order
-24259: Facts:
-24259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24259: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24259: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24259: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24259: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24259: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-24259: Goal:
-24259: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24259: Order:
-24259: nrkbo
-24259: Leaf order:
-24259: meet 19 2 5 0,2
-24259: join 19 2 5 0,2,2
-24259: d 2 0 2 2,2,2,2,2
-24259: c 3 0 3 1,2,2,2
-24259: b 3 0 3 1,2,2
-24259: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24260: Facts:
-24260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24260: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24260: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24260: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24260: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24260: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-24260: Goal:
-24260: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24260: Order:
-24260: kbo
-24260: Leaf order:
-24260: meet 19 2 5 0,2
-24260: join 19 2 5 0,2,2
-24260: d 2 0 2 2,2,2,2,2
-24260: c 3 0 3 1,2,2,2
-24260: b 3 0 3 1,2,2
-24260: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24261: Facts:
-24261: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24261: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24261: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24261: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24261: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24261: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24261: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24261: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24261: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-24261: Goal:
-24261: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24261: Order:
-24261: lpo
-24261: Leaf order:
-24261: meet 19 2 5 0,2
-24261: join 19 2 5 0,2,2
-24261: d 2 0 2 2,2,2,2,2
-24261: c 3 0 3 1,2,2,2
-24261: b 3 0 3 1,2,2
-24261: a 4 0 4 1,2
-% SZS status Timeout for LAT110-1.p
-NO CLASH, using fixed ground order
-24393: Facts:
-24393: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24393: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24393: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24393: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24393: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24393: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24393: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24393: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24393: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-24393: Goal:
-24393: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-24393: Order:
-24393: nrkbo
-24393: Leaf order:
-24393: meet 20 2 5 0,2
-24393: join 17 2 4 0,2,2
-24393: c 3 0 3 2,2,2
-24393: b 3 0 3 1,2,2
-24393: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-24394: Facts:
-24394: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24394: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24394: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24394: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24394: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24394: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24394: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24394: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24394: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-24394: Goal:
-24394: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-24394: Order:
-24394: kbo
-24394: Leaf order:
-24394: meet 20 2 5 0,2
-24394: join 17 2 4 0,2,2
-24394: c 3 0 3 2,2,2
-24394: b 3 0 3 1,2,2
-24394: a 5 0 5 1,2
-NO CLASH, using fixed ground order
-24395: Facts:
-24395: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24395: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24395: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24395: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24395: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24395: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24395: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24395: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24395: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-24395: Goal:
-24395: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-24395: Order:
-24395: lpo
-24395: Leaf order:
-24395: meet 20 2 5 0,2
-24395: join 17 2 4 0,2,2
-24395: c 3 0 3 2,2,2
-24395: b 3 0 3 1,2,2
-24395: a 5 0 5 1,2
-% SZS status Timeout for LAT118-1.p
-NO CLASH, using fixed ground order
-24412: Facts:
-24412: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24412: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24412: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24412: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24412: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24412: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24412: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24412: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24412: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-24412: Goal:
-24412: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24412: Order:
-24412: nrkbo
-24412: Leaf order:
-24412: join 17 2 4 0,2,2
-24412: meet 21 2 6 0,2
-24412: c 3 0 3 2,2,2,2
-24412: b 3 0 3 1,2,2
-24412: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24413: Facts:
-24413: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24413: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24413: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24413: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24413: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24413: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24413: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24413: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24413: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-24413: Goal:
-24413: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24413: Order:
-24413: kbo
-24413: Leaf order:
-24413: join 17 2 4 0,2,2
-24413: meet 21 2 6 0,2
-24413: c 3 0 3 2,2,2,2
-24413: b 3 0 3 1,2,2
-24413: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24414: Facts:
-24414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24414: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24414: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24414: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24414: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24414: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-24414: Goal:
-24414: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24414: Order:
-24414: lpo
-24414: Leaf order:
-24414: join 17 2 4 0,2,2
-24414: meet 21 2 6 0,2
-24414: c 3 0 3 2,2,2,2
-24414: b 3 0 3 1,2,2
-24414: a 6 0 6 1,2
-% SZS status Timeout for LAT142-1.p
-NO CLASH, using fixed ground order
-24444: Facts:
-24444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24444: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24444: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24444: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24444: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24444: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-24444: Goal:
-24444: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =<=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-24444: Order:
-24444: nrkbo
-24444: Leaf order:
-24444: join 16 2 3 0,2,2,2
-24444: meet 21 2 7 0,2
-24444: d 2 0 2 2,2,2,2,2
-24444: c 3 0 3 1,2,2,2
-24444: b 3 0 3 1,2,2
-24444: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24445: Facts:
-24445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24445: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24445: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24445: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24445: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24445: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-24445: Goal:
-24445: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =<=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-24445: Order:
-24445: kbo
-24445: Leaf order:
-24445: join 16 2 3 0,2,2,2
-24445: meet 21 2 7 0,2
-24445: d 2 0 2 2,2,2,2,2
-24445: c 3 0 3 1,2,2,2
-24445: b 3 0 3 1,2,2
-24445: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24446: Facts:
-24446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24446: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24446: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24446: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24446: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24446: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-24446: Goal:
-24446: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =>=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-24446: Order:
-24446: lpo
-24446: Leaf order:
-24446: join 16 2 3 0,2,2,2
-24446: meet 21 2 7 0,2
-24446: d 2 0 2 2,2,2,2,2
-24446: c 3 0 3 1,2,2,2
-24446: b 3 0 3 1,2,2
-24446: a 4 0 4 1,2
-% SZS status Timeout for LAT147-1.p
-NO CLASH, using fixed ground order
-24463: Facts:
-24463: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24463: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24463: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24463: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24463: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24463: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24463: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24463: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24463: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-24463: Goal:
-24463: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24463: Order:
-24463: kbo
-24463: Leaf order:
-24463: join 18 2 4 0,2,2
-24463: meet 20 2 6 0,2
-24463: c 3 0 3 2,2,2,2
-24463: b 3 0 3 1,2,2
-24463: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24464: Facts:
-24464: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24464: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24464: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24464: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24464: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24464: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24464: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24464: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24464: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-24464: Goal:
-24464: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24464: Order:
-24464: lpo
-24464: Leaf order:
-24464: join 18 2 4 0,2,2
-24464: meet 20 2 6 0,2
-24464: c 3 0 3 2,2,2,2
-24464: b 3 0 3 1,2,2
-24464: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24462: Facts:
-24462: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24462: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24462: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24462: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24462: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24462: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24462: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24462: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24462: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-24462: Goal:
-24462: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24462: Order:
-24462: nrkbo
-24462: Leaf order:
-24462: join 18 2 4 0,2,2
-24462: meet 20 2 6 0,2
-24462: c 3 0 3 2,2,2,2
-24462: b 3 0 3 1,2,2
-24462: a 6 0 6 1,2
-% SZS status Timeout for LAT154-1.p
-NO CLASH, using fixed ground order
-24500: Facts:
-24500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24500: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24500: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24500: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24500: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24500: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-24500: Goal:
-24500: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24500: Order:
-24500: nrkbo
-24500: Leaf order:
-24500: join 18 2 4 0,2,2
-24500: meet 20 2 6 0,2
-24500: c 4 0 4 2,2,2,2
-24500: b 4 0 4 1,2,2
-24500: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24501: Facts:
-24501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24501: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24501: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24501: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24501: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24501: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-24501: Goal:
-24501: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24501: Order:
-24501: kbo
-24501: Leaf order:
-24501: join 18 2 4 0,2,2
-24501: meet 20 2 6 0,2
-24501: c 4 0 4 2,2,2,2
-24501: b 4 0 4 1,2,2
-24501: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24502: Facts:
-24502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24502: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24502: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24502: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24502: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24502: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-24502: Goal:
-24502: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24502: Order:
-24502: lpo
-24502: Leaf order:
-24502: join 18 2 4 0,2,2
-24502: meet 20 2 6 0,2
-24502: c 4 0 4 2,2,2,2
-24502: b 4 0 4 1,2,2
-24502: a 4 0 4 1,2
-% SZS status Timeout for LAT155-1.p
-NO CLASH, using fixed ground order
-24518: Facts:
-24518: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24518: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24518: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24518: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24518: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24518: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24518: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24518: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24518: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-24518: Goal:
-24518: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24518: Order:
-24518: nrkbo
-24518: Leaf order:
-24518: meet 18 2 4 0,2
-24518: join 18 2 4 0,2,2
-24518: c 2 0 2 2,2,2
-24518: b 4 0 4 1,2,2
-24518: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24519: Facts:
-24519: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24519: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24519: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24519: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24519: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24519: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24519: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24519: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24519: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-24519: Goal:
-24519: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24519: Order:
-24519: kbo
-24519: Leaf order:
-24519: meet 18 2 4 0,2
-24519: join 18 2 4 0,2,2
-24519: c 2 0 2 2,2,2
-24519: b 4 0 4 1,2,2
-24519: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24520: Facts:
-24520: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24520: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24520: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24520: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24520: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24520: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24520: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24520: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24520: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-24520: Goal:
-24520: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24520: Order:
-24520: lpo
-24520: Leaf order:
-24520: meet 18 2 4 0,2
-24520: join 18 2 4 0,2,2
-24520: c 2 0 2 2,2,2
-24520: b 4 0 4 1,2,2
-24520: a 4 0 4 1,2
-% SZS status Timeout for LAT170-1.p
-NO CLASH, using fixed ground order
-24547: Facts:
-24547: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-24547: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-24547: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-24547: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-24547: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-24547: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-24547: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-24547: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-24547: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-24547: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-24547: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-24547: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24547: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-24547: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-24547: Goal:
-24547: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24547: Order:
-24547: nrkbo
-24547: Leaf order:
-24547: commutator 1 2 0
-24547: additive_inverse 6 1 0
-24547: add 16 2 0
-24547: additive_identity 9 0 1 3
-24547: multiply 22 2 4 0,2
-24547: associator 5 3 4 0,1,1,1,2
-24547: y 4 0 4 3,1,1,1,2
-24547: x 9 0 9 1,1,1,1,2
-NO CLASH, using fixed ground order
-24548: Facts:
-24548: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-24548: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-24548: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-24548: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-24548: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-24548: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-24548: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-24548: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-24548: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-24548: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-24548: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-24548: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24548: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-24548: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-24548: Goal:
-24548: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24548: Order:
-24548: kbo
-24548: Leaf order:
-24548: commutator 1 2 0
-24548: additive_inverse 6 1 0
-24548: add 16 2 0
-24548: additive_identity 9 0 1 3
-24548: multiply 22 2 4 0,2
-24548: associator 5 3 4 0,1,1,1,2
-24548: y 4 0 4 3,1,1,1,2
-24548: x 9 0 9 1,1,1,1,2
-NO CLASH, using fixed ground order
-24549: Facts:
-24549: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-24549: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-24549: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-24549: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-24549: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-24549: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-24549: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-24549: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-24549: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-24549: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-24549: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-24549: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24549: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-24549: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-24549: Goal:
-24549: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24549: Order:
-24549: lpo
-24549: Leaf order:
-24549: commutator 1 2 0
-24549: additive_inverse 6 1 0
-24549: add 16 2 0
-24549: additive_identity 9 0 1 3
-24549: multiply 22 2 4 0,2
-24549: associator 5 3 4 0,1,1,1,2
-24549: y 4 0 4 3,1,1,1,2
-24549: x 9 0 9 1,1,1,1,2
-% SZS status Timeout for RNG031-6.p
-NO CLASH, using fixed ground order
-24576: Facts:
-24576: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-24576: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-24576: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-24576: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-24576: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-24576: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-24576: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-24576: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-24576: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-24576: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-24576: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-24576: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-24576: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-24576: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-24576: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-24576: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-24576: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-24576: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-24576: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-24576: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-24576: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-24576: Goal:
-24576: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24576: Order:
-24576: nrkbo
-24576: Leaf order:
-24576: commutator 1 2 0
-24576: add 24 2 0
-24576: additive_inverse 22 1 0
-24576: additive_identity 9 0 1 3
-24576: multiply 40 2 4 0,2add
-24576: associator 5 3 4 0,1,1,1,2
-24576: y 4 0 4 3,1,1,1,2
-24576: x 9 0 9 1,1,1,1,2
-NO CLASH, using fixed ground order
-24577: Facts:
-24577: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-NO CLASH, using fixed ground order
-24578: Facts:
-24578: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-24578: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-24578: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-24578: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-24578: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-24578: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-24578: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-24578: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-24578: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-24578: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-24578: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-24578: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-24578: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-24578: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-24578: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-24578: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-24578: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-24578: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-24578: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-24578: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-24578: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-24578: Goal:
-24578: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24578: Order:
-24578: lpo
-24578: Leaf order:
-24578: commutator 1 2 0
-24578: add 24 2 0
-24578: additive_inverse 22 1 0
-24578: additive_identity 9 0 1 3
-24578: multiply 40 2 4 0,2add
-24578: associator 5 3 4 0,1,1,1,2
-24578: y 4 0 4 3,1,1,1,2
-24578: x 9 0 9 1,1,1,1,2
-24577: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-24577: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-24577: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-24577: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-24577: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-24577: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-24577: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-24577: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-24577: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-24577: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-24577: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-24577: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-24577: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-24577: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-24577: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-24577: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-24577: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-24577: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-24577: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-24577: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-24577: Goal:
-24577: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-24577: Order:
-24577: kbo
-24577: Leaf order:
-24577: commutator 1 2 0
-24577: add 24 2 0
-24577: additive_inverse 22 1 0
-24577: additive_identity 9 0 1 3
-24577: multiply 40 2 4 0,2add
-24577: associator 5 3 4 0,1,1,1,2
-24577: y 4 0 4 3,1,1,1,2
-24577: x 9 0 9 1,1,1,1,2
-% SZS status Timeout for RNG031-7.p
-NO CLASH, using fixed ground order
-24609: Facts:
-24609: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-24609: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-24609: Goal:
-24609: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
-24609: Order:
-24609: nrkbo
-24609: Leaf order:
-24609: f 2 1 0
-24609: g2 2 1 1 0,3
-24609: g1 2 1 1 0,2
-NO CLASH, using fixed ground order
-24610: Facts:
-24610: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-24610: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-24610: Goal:
-24610: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
-24610: Order:
-24610: kbo
-24610: Leaf order:
-24610: f 2 1 0
-24610: g2 2 1 1 0,3
-24610: g1 2 1 1 0,2
-NO CLASH, using fixed ground order
-24611: Facts:
-24611: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-24611: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-24611: Goal:
-24611: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
-24611: Order:
-24611: lpo
-24611: Leaf order:
-24611: f 2 1 0
-24611: g2 2 1 1 0,3
-24611: g1 2 1 1 0,2
-24609: status GaveUp for SYN305-1.p
-24610: status GaveUp for SYN305-1.p
-24611: status GaveUp for SYN305-1.p
-% SZS status Timeout for SYN305-1.p
-CLASH, statistics insufficient
-24616: Facts:
-24616: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24616: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-24616: Goal:
-24616: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-24616: Order:
-24616: nrkbo
-24616: Leaf order:
-24616: h 1 0 0
-24616: b 1 0 0
-24616: apply 14 2 3 0,2
-24616: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-24617: Facts:
-24617: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24617: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-24617: Goal:
-24617: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-24617: Order:
-24617: kbo
-24617: Leaf order:
-24617: h 1 0 0
-24617: b 1 0 0
-24617: apply 14 2 3 0,2
-24617: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-24618: Facts:
-24618: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24618: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-24618: Goal:
-24618: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-24618: Order:
-24618: lpo
-24618: Leaf order:
-24618: h 1 0 0
-24618: b 1 0 0
-24618: apply 14 2 3 0,2
-24618: f 3 1 3 0,2,2
-% SZS status Timeout for COL043-1.p
-CLASH, statistics insufficient
-24654: Facts:
-CLASH, statistics insufficient
-24655: Facts:
-24655: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24655: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-24655: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-24655: Goal:
-24655: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =<=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-24655: Order:
-24655: kbo
-24655: Leaf order:
-24655: w 1 0 0
-24655: q 1 0 0
-24655: b 1 0 0
-24655: h 2 1 2 0,2,2
-24655: g 4 1 4 0,2,1,1,2
-24655: apply 22 2 8 0,2
-24655: f 3 1 3 0,2,1,1,1,2
-CLASH, statistics insufficient
-24656: Facts:
-24656: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24656: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-24656: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-24656: Goal:
-24656: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-24656: Order:
-24656: lpo
-24656: Leaf order:
-24656: w 1 0 0
-24656: q 1 0 0
-24656: b 1 0 0
-24656: h 2 1 2 0,2,2
-24656: g 4 1 4 0,2,1,1,2
-24656: apply 22 2 8 0,2
-24656: f 3 1 3 0,2,1,1,1,2
-24654: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-24654: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-24654: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-24654: Goal:
-24654: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =<=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-24654: Order:
-24654: nrkbo
-24654: Leaf order:
-24654: w 1 0 0
-24654: q 1 0 0
-24654: b 1 0 0
-24654: h 2 1 2 0,2,2
-24654: g 4 1 4 0,2,1,1,2
-24654: apply 22 2 8 0,2
-24654: f 3 1 3 0,2,1,1,1,2
-% SZS status Timeout for COL066-1.p
-NO CLASH, using fixed ground order
-24759: Facts:
-24759: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-24759: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-24759: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-24759: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-24759: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-24759: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-24759: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-24759: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-24759: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-24759: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-24759: Goal:
-24759: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-24759: Order:
-24759: nrkbo
-24759: Leaf order:
-24759: n0 1 0 0
-24759: n1 2 0 1 3
-24759: join 17 2 5 0,2
-24759: meet 12 2 3 0,1,1,1,1,2
-24759: b 4 0 4 2,1,1,1,1,2
-24759: complement 15 1 6 0,1,2
-24759: a 5 0 5 1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-24760: Facts:
-24760: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-24760: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-24760: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-24760: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-24760: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-24760: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-24760: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-24760: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-24760: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-24760: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-24760: Goal:
-24760: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-24760: Order:
-24760: kbo
-24760: Leaf order:
-24760: n0 1 0 0
-24760: n1 2 0 1 3
-24760: join 17 2 5 0,2
-24760: meet 12 2 3 0,1,1,1,1,2
-24760: b 4 0 4 2,1,1,1,1,2
-24760: complement 15 1 6 0,1,2
-24760: a 5 0 5 1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-24761: Facts:
-24761: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-24761: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-24761: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-24761: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-24761: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-24761: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-24761: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-24761: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-24761: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-24761: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-24761: Goal:
-24761: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-24761: Order:
-24761: lpo
-24761: Leaf order:
-24761: n0 1 0 0
-24761: n1 2 0 1 3
-24761: join 17 2 5 0,2
-24761: meet 12 2 3 0,1,1,1,1,2
-24761: b 4 0 4 2,1,1,1,1,2
-24761: complement 15 1 6 0,1,2
-24761: a 5 0 5 1,1,1,1,1,1,2
-% SZS status Timeout for LAT018-1.p
-NO CLASH, using fixed ground order
-24778: Facts:
-24778: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24778: Goal:
-24778: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-24778: Order:
-24778: nrkbo
-24778: Leaf order:
-24778: join 20 2 0
-24778: c 2 0 2 2,2
-24778: meet 22 2 4 0,2
-24778: b 2 0 2 2,1,2
-24778: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-24779: Facts:
-24779: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24779: Goal:
-24779: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-24779: Order:
-24779: kbo
-24779: Leaf order:
-24779: join 20 2 0
-24779: c 2 0 2 2,2
-24779: meet 22 2 4 0,2
-24779: b 2 0 2 2,1,2
-24779: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-24780: Facts:
-24780: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24780: Goal:
-24780: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-24780: Order:
-24780: lpo
-24780: Leaf order:
-24780: join 20 2 0
-24780: c 2 0 2 2,2
-24780: meet 22 2 4 0,2
-24780: b 2 0 2 2,1,2
-24780: a 2 0 2 1,1,2
-% SZS status Timeout for LAT082-1.p
-NO CLASH, using fixed ground order
-24809: Facts:
-24809: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24809: Goal:
-24809: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-24809: Order:
-24809: kbo
-24809: Leaf order:
-24809: meet 18 2 0
-24809: c 2 0 2 2,2
-24809: join 24 2 4 0,2
-24809: b 2 0 2 2,1,2
-24809: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-24810: Facts:
-24810: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24810: Goal:
-24810: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-24810: Order:
-24810: lpo
-24810: Leaf order:
-24810: meet 18 2 0
-24810: c 2 0 2 2,2
-24810: join 24 2 4 0,2
-24810: b 2 0 2 2,1,2
-24810: a 2 0 2 1,1,2
-NO CLASH, using fixed ground order
-24808: Facts:
-24808: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-24808: Goal:
-24808: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-24808: Order:
-24808: nrkbo
-24808: Leaf order:
-24808: meet 18 2 0
-24808: c 2 0 2 2,2
-24808: join 24 2 4 0,2
-24808: b 2 0 2 2,1,2
-24808: a 2 0 2 1,1,2
-% SZS status Timeout for LAT085-1.p
-NO CLASH, using fixed ground order
-24831: Facts:
-24831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24831: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24831: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24831: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24831: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24831: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-24831: Goal:
-24831: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24831: Order:
-24831: nrkbo
-24831: Leaf order:
-24831: join 16 2 4 0,2,2
-24831: meet 22 2 6 0,2
-24831: c 4 0 4 2,2,2,2
-24831: b 4 0 4 1,2,2
-24831: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24832: Facts:
-24832: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24832: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24832: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24832: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24832: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24832: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24832: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24832: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24832: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-24832: Goal:
-24832: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24832: Order:
-24832: kbo
-24832: Leaf order:
-24832: join 16 2 4 0,2,2
-24832: meet 22 2 6 0,2
-24832: c 4 0 4 2,2,2,2
-24832: b 4 0 4 1,2,2
-24832: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24833: Facts:
-24833: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24833: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24833: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24833: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24833: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24833: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24833: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24833: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24833: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-24833: Goal:
-24833: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-24833: Order:
-24833: lpo
-24833: Leaf order:
-24833: join 16 2 4 0,2,2
-24833: meet 22 2 6 0,2
-24833: c 4 0 4 2,2,2,2
-24833: b 4 0 4 1,2,2
-24833: a 4 0 4 1,2
-% SZS status Timeout for LAT144-1.p
-NO CLASH, using fixed ground order
-24860: Facts:
-24860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24860: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24860: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24860: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24860: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24860: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24860: Goal:
-24860: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-24860: Order:
-24860: nrkbo
-24860: Leaf order:
-24860: meet 19 2 5 0,2
-24860: join 18 2 5 0,2,2
-24860: d 2 0 2 2,2,2,2,2
-24860: c 3 0 3 1,2,2,2
-24860: b 3 0 3 1,2,2
-24860: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24861: Facts:
-24861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24861: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24861: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24861: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24861: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24861: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24861: Goal:
-24861: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-24861: Order:
-24861: kbo
-24861: Leaf order:
-24861: meet 19 2 5 0,2
-24861: join 18 2 5 0,2,2
-24861: d 2 0 2 2,2,2,2,2
-24861: c 3 0 3 1,2,2,2
-24861: b 3 0 3 1,2,2
-24861: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24862: Facts:
-24862: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24862: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24862: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24862: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24862: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24862: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24862: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24862: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24862: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24862: Goal:
-24862: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-24862: Order:
-24862: lpo
-24862: Leaf order:
-24862: meet 19 2 5 0,2
-24862: join 18 2 5 0,2,2
-24862: d 2 0 2 2,2,2,2,2
-24862: c 3 0 3 1,2,2,2
-24862: b 3 0 3 1,2,2
-24862: a 4 0 4 1,2
-% SZS status Timeout for LAT150-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-24889: Facts:
-24889: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24889: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24889: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24889: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24889: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24889: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24889: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24889: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24889: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24889: Goal:
-24889: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24889: Order:
-24889: kbo
-24889: Leaf order:
-24889: meet 19 2 5 0,2
-24889: join 18 2 5 0,2,2
-24889: d 2 0 2 2,2,2,2,2
-24889: c 3 0 3 1,2,2,2
-24889: b 3 0 3 1,2,2
-24889: a 4 0 4 1,2
-24888: Facts:
-24888: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24888: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24888: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24888: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24888: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24888: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24888: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24888: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24888: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24888: Goal:
-24888: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24888: Order:
-24888: nrkbo
-24888: Leaf order:
-24888: meet 19 2 5 0,2
-24888: join 18 2 5 0,2,2
-24888: d 2 0 2 2,2,2,2,2
-24888: c 3 0 3 1,2,2,2
-24888: b 3 0 3 1,2,2
-24888: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-24890: Facts:
-24890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24890: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24890: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24890: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24890: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24890: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-24890: Goal:
-24890: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-24890: Order:
-24890: lpo
-24890: Leaf order:
-24890: meet 19 2 5 0,2
-24890: join 18 2 5 0,2,2
-24890: d 2 0 2 2,2,2,2,2
-24890: c 3 0 3 1,2,2,2
-24890: b 3 0 3 1,2,2
-24890: a 4 0 4 1,2
-% SZS status Timeout for LAT151-1.p
-NO CLASH, using fixed ground order
-24921: Facts:
-24921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24921: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24921: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24921: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24921: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24921: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-24921: Goal:
-24921: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24921: Order:
-24921: nrkbo
-24921: Leaf order:
-24921: join 18 2 4 0,2,2
-24921: meet 20 2 6 0,2
-24921: c 3 0 3 2,2,2,2
-24921: b 3 0 3 1,2,2
-24921: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24922: Facts:
-24922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24922: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24922: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24922: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24922: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24922: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-24922: Goal:
-24922: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24922: Order:
-24922: kbo
-24922: Leaf order:
-24922: join 18 2 4 0,2,2
-24922: meet 20 2 6 0,2
-24922: c 3 0 3 2,2,2,2
-24922: b 3 0 3 1,2,2
-24922: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24923: Facts:
-24923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24923: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24923: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24923: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24923: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24923: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-24923: Goal:
-24923: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24923: Order:
-24923: lpo
-24923: Leaf order:
-24923: join 18 2 4 0,2,2
-24923: meet 20 2 6 0,2
-24923: c 3 0 3 2,2,2,2
-24923: b 3 0 3 1,2,2
-24923: a 6 0 6 1,2
-% SZS status Timeout for LAT152-1.p
-NO CLASH, using fixed ground order
-24939: Facts:
-24939: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24939: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24939: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24939: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24939: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24939: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24939: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24939: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24939: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-24939: Goal:
-24939: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-24939: Order:
-24939: nrkbo
-24939: Leaf order:
-24939: join 18 2 4 0,2,2
-24939: meet 20 2 6 0,2
-24939: c 2 0 2 2,2,2,2
-24939: b 4 0 4 1,2,2
-24939: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24940: Facts:
-24940: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24940: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24940: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24940: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24940: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24940: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24940: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24940: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24940: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-24940: Goal:
-24940: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-24940: Order:
-24940: kbo
-24940: Leaf order:
-24940: join 18 2 4 0,2,2
-24940: meet 20 2 6 0,2
-24940: c 2 0 2 2,2,2,2
-24940: b 4 0 4 1,2,2
-24940: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24941: Facts:
-24941: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24941: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24941: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24941: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24941: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24941: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24941: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24941: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24941: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-24941: Goal:
-24941: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-24941: Order:
-24941: lpo
-24941: Leaf order:
-24941: join 18 2 4 0,2,2
-24941: meet 20 2 6 0,2
-24941: c 2 0 2 2,2,2,2
-24941: b 4 0 4 1,2,2
-24941: a 6 0 6 1,2
-% SZS status Timeout for LAT159-1.p
-NO CLASH, using fixed ground order
-24972: Facts:
-24972: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24972: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24972: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-NO CLASH, using fixed ground order
-24972: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24972: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24972: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24972: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24972: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24972: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-24972: Goal:
-24972: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-24972: Order:
-24972: nrkbo
-24972: Leaf order:
-24972: meet 19 2 6 0,2
-24972: join 15 2 3 0,2,2,2
-24972: d 2 0 2 2,2,2,2
-24972: c 3 0 3 1,2,2,2
-24972: b 3 0 3 1,2,2
-24972: a 3 0 3 1,2
-24973: Facts:
-24973: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24973: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24973: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24973: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24973: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24973: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24973: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24973: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24973: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-24973: Goal:
-24973: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-24973: Order:
-24973: kbo
-24973: Leaf order:
-24973: meet 19 2 6 0,2
-24973: join 15 2 3 0,2,2,2
-24973: d 2 0 2 2,2,2,2
-24973: c 3 0 3 1,2,2,2
-24973: b 3 0 3 1,2,2
-24973: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-24974: Facts:
-24974: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24974: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24974: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24974: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24974: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24974: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24974: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24974: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24974: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-24974: Goal:
-24974: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-24974: Order:
-24974: lpo
-24974: Leaf order:
-24974: meet 19 2 6 0,2
-24974: join 15 2 3 0,2,2,2
-24974: d 2 0 2 2,2,2,2
-24974: c 3 0 3 1,2,2,2
-24974: b 3 0 3 1,2,2
-24974: a 3 0 3 1,2
-% SZS status Timeout for LAT162-1.p
-NO CLASH, using fixed ground order
-24990: Facts:
-24990: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24990: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24990: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24990: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24990: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24990: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24990: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24990: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24990: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-24990: Goal:
-24990: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24990: Order:
-24990: nrkbo
-24990: Leaf order:
-24990: join 17 2 4 0,2,2
-24990: meet 20 2 6 0,2
-24990: c 3 0 3 2,2,2,2
-24990: b 3 0 3 1,2,2
-24990: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24991: Facts:
-24991: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24991: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24991: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24991: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24991: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24991: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24991: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24991: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24991: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-24991: Goal:
-24991: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24991: Order:
-24991: kbo
-24991: Leaf order:
-24991: join 17 2 4 0,2,2
-24991: meet 20 2 6 0,2
-24991: c 3 0 3 2,2,2,2
-24991: b 3 0 3 1,2,2
-24991: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-24992: Facts:
-24992: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24992: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24992: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24992: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24992: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24992: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24992: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24992: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24992: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-24992: Goal:
-24992: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-24992: Order:
-24992: lpo
-24992: Leaf order:
-24992: join 17 2 4 0,2,2
-24992: meet 20 2 6 0,2
-24992: c 3 0 3 2,2,2,2
-24992: b 3 0 3 1,2,2
-24992: a 6 0 6 1,2
-% SZS status Timeout for LAT164-1.p
-NO CLASH, using fixed ground order
-25019: Facts:
-NO CLASH, using fixed ground order
-25020: Facts:
-25020: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25020: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25020: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25020: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25020: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25020: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25020: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25020: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25020: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-25020: Goal:
-25020: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-25020: Order:
-25020: kbo
-25020: Leaf order:
-25020: meet 17 2 4 0,2
-25020: join 19 2 4 0,2,2
-25020: c 2 0 2 2,2,2
-25020: b 4 0 4 1,2,2
-25020: a 4 0 4 1,2
-25019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25019: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25019: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25019: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-NO CLASH, using fixed ground order
-25019: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25019: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-25019: Goal:
-25019: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-25019: Order:
-25019: nrkbo
-25019: Leaf order:
-25019: meet 17 2 4 0,2
-25019: join 19 2 4 0,2,2
-25019: c 2 0 2 2,2,2
-25019: b 4 0 4 1,2,2
-25019: a 4 0 4 1,2
-25021: Facts:
-25021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25021: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25021: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25021: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25021: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25021: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-25021: Goal:
-25021: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-25021: Order:
-25021: lpo
-25021: Leaf order:
-25021: meet 17 2 4 0,2
-25021: join 19 2 4 0,2,2
-25021: c 2 0 2 2,2,2
-25021: b 4 0 4 1,2,2
-25021: a 4 0 4 1,2
-% SZS status Timeout for LAT169-1.p
-NO CLASH, using fixed ground order
-25071: Facts:
-25071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25071: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25071: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25071: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25071: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25071: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-25071: Goal:
-25071: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25071: Order:
-25071: nrkbo
-25071: Leaf order:
-25071: join 18 2 4 0,2,2
-25071: meet 19 2 6 0,2
-25071: c 3 0 3 2,2,2,2
-25071: b 3 0 3 1,2,2
-25071: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-25072: Facts:
-25072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25072: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25072: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25072: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25072: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25072: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-25072: Goal:
-25072: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25072: Order:
-25072: kbo
-25072: Leaf order:
-25072: join 18 2 4 0,2,2
-25072: meet 19 2 6 0,2
-25072: c 3 0 3 2,2,2,2
-25072: b 3 0 3 1,2,2
-25072: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-25073: Facts:
-25073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25073: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25073: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25073: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25073: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25073: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-25073: Goal:
-25073: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25073: Order:
-25073: lpo
-25073: Leaf order:
-25073: join 18 2 4 0,2,2
-25073: meet 19 2 6 0,2
-25073: c 3 0 3 2,2,2,2
-25073: b 3 0 3 1,2,2
-25073: a 6 0 6 1,2
-% SZS status Timeout for LAT174-1.p
-NO CLASH, using fixed ground order
-25101: Facts:
-25101: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25101: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25101: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25101: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25101: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25101: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25101: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25101: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25101: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25101: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25101: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25101: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25101: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25101: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25101: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25101: Goal:
-25101: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25101: Order:
-25101: nrkbo
-25101: Leaf order:
-25101: commutator 1 2 0
-25101: associator 1 3 0
-25101: additive_inverse 6 1 0
-25101: add 16 2 0
-25101: additive_identity 8 0 0
-25101: multiply 28 2 6 0,2
-25101: cy 2 0 2 1,2,2,2
-25101: cx 4 0 4 1,2,2
-25101: cz 2 0 2 1,2
-NO CLASH, using fixed ground order
-25102: Facts:
-25102: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25102: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25102: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25102: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25102: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25102: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25102: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25102: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25102: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25102: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-NO CLASH, using fixed ground order
-25103: Facts:
-25103: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25103: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25103: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25103: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25103: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25103: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25103: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25103: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25103: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25102: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25102: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25102: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25102: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25102: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25102: Goal:
-25102: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25102: Order:
-25102: kbo
-25102: Leaf order:
-25102: commutator 1 2 0
-25102: associator 1 3 0
-25102: additive_inverse 6 1 0
-25102: add 16 2 0
-25102: additive_identity 8 0 0
-25102: multiply 28 2 6 0,2
-25102: cy 2 0 2 1,2,2,2
-25102: cx 4 0 4 1,2,2
-25102: cz 2 0 2 1,2
-25103: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25103: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25103: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25103: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25103: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25103: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25103: Goal:
-25103: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25103: Order:
-25103: lpo
-25103: Leaf order:
-25103: commutator 1 2 0
-25103: associator 1 3 0
-25103: additive_inverse 6 1 0
-25103: add 16 2 0
-25103: additive_identity 8 0 0
-25103: multiply 28 2 6 0,2
-25103: cy 2 0 2 1,2,2,2
-25103: cx 4 0 4 1,2,2
-25103: cz 2 0 2 1,2
-% SZS status Timeout for RNG027-5.p
-NO CLASH, using fixed ground order
-25119: Facts:
-25119: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25119: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25119: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25119: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25119: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25119: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25119: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25119: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25119: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25119: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25119: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25119: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25119: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25119: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25119: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25119: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25119: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25119: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25119: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25119: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25119: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25119: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25119: Goal:
-25119: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25119: Order:
-25119: nrkbo
-25119: Leaf order:
-25119: commutator 1 2 0
-25119: associator 1 3 0
-25119: additive_inverse 22 1 0
-25119: add 24 2 0
-25119: additive_identity 8 0 0
-25119: multiply 46 2 6 0,2
-25119: cy 2 0 2 1,2,2,2
-25119: cx 4 0 4 1,2,2
-25119: cz 2 0 2 1,2
-NO CLASH, using fixed ground order
-25120: Facts:
-25120: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25120: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25120: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25120: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25120: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25120: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25120: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25120: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25120: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25120: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25120: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25120: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25120: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25120: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25120: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25120: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25120: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25120: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25120: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25120: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25120: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25120: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25120: Goal:
-25120: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25120: Order:
-25120: kbo
-25120: Leaf order:
-25120: commutator 1 2 0
-25120: associator 1 3 0
-25120: additive_inverse 22 1 0
-25120: add 24 2 0
-25120: additive_identity 8 0 0
-25120: multiply 46 2 6 0,2
-25120: cy 2 0 2 1,2,2,2
-25120: cx 4 0 4 1,2,2
-25120: cz 2 0 2 1,2
-NO CLASH, using fixed ground order
-25121: Facts:
-25121: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25121: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25121: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25121: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25121: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25121: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25121: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25121: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25121: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25121: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25121: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25121: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25121: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25121: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25121: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25121: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25121: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25121: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25121: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25121: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25121: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25121: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25121: Goal:
-25121: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-25121: Order:
-25121: lpo
-25121: Leaf order:
-25121: commutator 1 2 0
-25121: associator 1 3 0
-25121: additive_inverse 22 1 0
-25121: add 24 2 0
-25121: additive_identity 8 0 0
-25121: multiply 46 2 6 0,2
-25121: cy 2 0 2 1,2,2,2
-25121: cx 4 0 4 1,2,2
-25121: cz 2 0 2 1,2
-% SZS status Timeout for RNG027-7.p
-NO CLASH, using fixed ground order
-25148: Facts:
-25148: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25148: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25148: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25148: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25148: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25148: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25148: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25148: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25148: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25148: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25148: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25148: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25148: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25148: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25148: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25148: Goal:
-25148: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25148: Order:
-25148: nrkbo
-25148: Leaf order:
-25148: commutator 1 2 0
-25148: additive_inverse 6 1 0
-25148: add 16 2 0
-25148: additive_identity 8 0 0
-25148: associator 3 3 2 0,2
-25148: z 2 0 2 3,2
-25148: multiply 24 2 2 0,2,2
-25148: y 2 0 2 2,2,2
-25148: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25149: Facts:
-25149: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25149: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25149: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25149: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25149: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25149: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25149: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25149: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25149: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25149: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25149: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25149: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25149: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25149: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25149: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25149: Goal:
-25149: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25149: Order:
-25149: kbo
-25149: Leaf order:
-25149: commutator 1 2 0
-25149: additive_inverse 6 1 0
-25149: add 16 2 0
-25149: additive_identity 8 0 0
-25149: associator 3 3 2 0,2
-25149: z 2 0 2 3,2
-25149: multiply 24 2 2 0,2,2
-25149: y 2 0 2 2,2,2
-25149: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25150: Facts:
-25150: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25150: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25150: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25150: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25150: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25150: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25150: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25150: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25150: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25150: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25150: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25150: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25150: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25150: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25150: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25150: Goal:
-25150: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25150: Order:
-25150: lpo
-25150: Leaf order:
-25150: commutator 1 2 0
-25150: additive_inverse 6 1 0
-25150: add 16 2 0
-25150: additive_identity 8 0 0
-25150: associator 3 3 2 0,2
-25150: z 2 0 2 3,2
-25150: multiply 24 2 2 0,2,2
-25150: y 2 0 2 2,2,2
-25150: x 4 0 4 1,2
-% SZS status Timeout for RNG027-8.p
-NO CLASH, using fixed ground order
-25166: Facts:
-25166: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25166: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25166: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25166: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25166: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25166: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25166: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25166: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25166: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25166: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25166: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25166: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25166: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25166: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25166: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25166: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25166: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25166: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25166: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25166: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25166: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25166: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25166: Goal:
-25166: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25166: Order:
-25166: nrkbo
-25166: Leaf order:
-25166: commutator 1 2 0
-25166: additive_inverse 22 1 0
-25166: add 24 2 0
-25166: additive_identity 8 0 0
-25166: associator 3 3 2 0,2
-25166: z 2 0 2 3,2
-25166: multiply 42 2 2 0,2,2
-25166: y 2 0 2 2,2,2
-25166: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25168: Facts:
-25168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25168: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25168: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25168: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25168: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25168: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25168: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25168: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25168: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25168: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25168: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25168: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25168: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25168: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25168: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25168: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25168: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25168: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25168: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25168: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25168: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25168: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25168: Goal:
-25168: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25168: Order:
-25168: lpo
-25168: Leaf order:
-25168: commutator 1 2 0
-25168: additive_inverse 22 1 0
-25168: add 24 2 0
-25168: additive_identity 8 0 0
-25168: associator 3 3 2 0,2
-25168: z 2 0 2 3,2
-25168: multiply 42 2 2 0,2,2
-25168: y 2 0 2 2,2,2
-25168: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25167: Facts:
-25167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25167: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25167: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25167: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25167: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25167: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25167: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25167: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25167: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25167: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25167: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25167: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25167: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25167: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25167: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25167: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25167: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25167: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25167: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25167: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25167: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25167: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25167: Goal:
-25167: Id : 1, {_}:
- associator x (multiply x y) z =<= multiply (associator x y z) x
- [] by prove_right_moufang
-25167: Order:
-25167: kbo
-25167: Leaf order:
-25167: commutator 1 2 0
-25167: additive_inverse 22 1 0
-25167: add 24 2 0
-25167: additive_identity 8 0 0
-25167: associator 3 3 2 0,2
-25167: z 2 0 2 3,2
-25167: multiply 42 2 2 0,2,2
-25167: y 2 0 2 2,2,2
-25167: x 4 0 4 1,2
-% SZS status Timeout for RNG027-9.p
-NO CLASH, using fixed ground order
-25195: Facts:
-25195: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25195: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25195: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25195: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25195: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25195: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25195: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25195: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25195: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25195: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25195: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25195: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25195: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25195: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25195: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25195: Goal:
-25195: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25195: Order:
-25195: nrkbo
-25195: Leaf order:
-25195: commutator 1 2 0
-25195: associator 1 3 0
-25195: additive_inverse 6 1 0
-25195: add 16 2 0
-25195: additive_identity 8 0 0
-25195: cz 2 0 2 2,2
-25195: multiply 28 2 6 0,2
-25195: cy 2 0 2 1,2,1,2
-25195: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25196: Facts:
-25196: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25196: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25196: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25196: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25196: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25196: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25196: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25196: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25196: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25196: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25196: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25196: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25196: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25196: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25196: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25196: Goal:
-25196: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25196: Order:
-25196: kbo
-25196: Leaf order:
-25196: commutator 1 2 0
-25196: associator 1 3 0
-25196: additive_inverse 6 1 0
-25196: add 16 2 0
-25196: additive_identity 8 0 0
-25196: cz 2 0 2 2,2
-25196: multiply 28 2 6 0,2
-25196: cy 2 0 2 1,2,1,2
-25196: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25197: Facts:
-25197: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25197: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25197: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25197: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25197: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25197: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25197: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25197: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25197: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25197: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25197: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25197: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25197: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25197: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25197: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25197: Goal:
-25197: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25197: Order:
-25197: lpo
-25197: Leaf order:
-25197: commutator 1 2 0
-25197: associator 1 3 0
-25197: additive_inverse 6 1 0
-25197: add 16 2 0
-25197: additive_identity 8 0 0
-25197: cz 2 0 2 2,2
-25197: multiply 28 2 6 0,2
-25197: cy 2 0 2 1,2,1,2
-25197: cx 4 0 4 1,1,2
-% SZS status Timeout for RNG028-5.p
-NO CLASH, using fixed ground order
-25213: Facts:
-25213: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25213: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25213: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25213: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25213: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25213: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25213: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25213: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25213: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25213: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25213: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25213: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25213: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25213: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25213: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25213: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25213: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25213: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25213: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25213: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25213: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25213: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25213: Goal:
-25213: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25213: Order:
-25213: nrkbo
-25213: Leaf order:
-25213: commutator 1 2 0
-25213: associator 1 3 0
-25213: additive_inverse 22 1 0
-25213: add 24 2 0
-25213: additive_identity 8 0 0
-25213: cz 2 0 2 2,2
-25213: multiply 46 2 6 0,2
-25213: cy 2 0 2 1,2,1,2
-25213: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25214: Facts:
-25214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25214: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25214: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25214: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25214: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25214: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25214: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25214: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25214: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25214: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25214: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25214: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25214: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25214: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25214: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25214: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25214: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25214: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25214: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25214: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25214: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25214: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25214: Goal:
-25214: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25214: Order:
-25214: kbo
-25214: Leaf order:
-25214: commutator 1 2 0
-25214: associator 1 3 0
-25214: additive_inverse 22 1 0
-25214: add 24 2 0
-25214: additive_identity 8 0 0
-25214: cz 2 0 2 2,2
-25214: multiply 46 2 6 0,2
-25214: cy 2 0 2 1,2,1,2
-25214: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25215: Facts:
-25215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25215: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25215: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25215: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25215: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25215: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25215: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25215: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25215: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25215: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25215: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25215: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25215: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25215: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25215: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25215: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25215: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25215: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25215: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25215: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25215: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25215: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25215: Goal:
-25215: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-25215: Order:
-25215: lpo
-25215: Leaf order:
-25215: commutator 1 2 0
-25215: associator 1 3 0
-25215: additive_inverse 22 1 0
-25215: add 24 2 0
-25215: additive_identity 8 0 0
-25215: cz 2 0 2 2,2
-25215: multiply 46 2 6 0,2
-25215: cy 2 0 2 1,2,1,2
-25215: cx 4 0 4 1,1,2
-% SZS status Timeout for RNG028-7.p
-NO CLASH, using fixed ground order
-25251: Facts:
-25251: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25251: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25251: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25251: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25251: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25251: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25251: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25251: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25251: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25251: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25251: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25251: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25251: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25251: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25251: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25251: Goal:
-25251: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25251: Order:
-25251: nrkbo
-25251: Leaf order:
-25251: commutator 1 2 0
-25251: additive_inverse 6 1 0
-25251: add 16 2 0
-25251: additive_identity 8 0 0
-25251: associator 3 3 2 0,2
-25251: z 2 0 2 3,2
-25251: multiply 24 2 2 0,2,2
-25251: y 2 0 2 1,2,2
-25251: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25252: Facts:
-25252: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25252: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25252: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25252: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25252: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25252: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25252: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25252: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25252: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25252: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25252: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25252: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25252: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25252: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25252: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25252: Goal:
-25252: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25252: Order:
-25252: kbo
-25252: Leaf order:
-25252: commutator 1 2 0
-25252: additive_inverse 6 1 0
-25252: add 16 2 0
-25252: additive_identity 8 0 0
-25252: associator 3 3 2 0,2
-25252: z 2 0 2 3,2
-25252: multiply 24 2 2 0,2,2
-25252: y 2 0 2 1,2,2
-25252: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25253: Facts:
-25253: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25253: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25253: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25253: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25253: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25253: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25253: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25253: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25253: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25253: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25253: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25253: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25253: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25253: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25253: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25253: Goal:
-25253: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25253: Order:
-25253: lpo
-25253: Leaf order:
-25253: commutator 1 2 0
-25253: additive_inverse 6 1 0
-25253: add 16 2 0
-25253: additive_identity 8 0 0
-25253: associator 3 3 2 0,2
-25253: z 2 0 2 3,2
-25253: multiply 24 2 2 0,2,2
-25253: y 2 0 2 1,2,2
-25253: x 4 0 4 1,2
-% SZS status Timeout for RNG028-8.p
-NO CLASH, using fixed ground order
-25289: Facts:
-25289: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25289: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25289: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25289: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25289: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25289: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25289: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25289: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25289: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25289: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25289: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25289: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25289: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25289: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25289: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25289: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25289: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25289: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25289: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25289: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25289: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25289: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25289: Goal:
-25289: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25289: Order:
-25289: nrkbo
-25289: Leaf order:
-25289: commutator 1 2 0
-25289: additive_inverse 22 1 0
-25289: add 24 2 0
-25289: additive_identity 8 0 0
-25289: associator 3 3 2 0,2
-25289: z 2 0 2 3,2
-25289: multiply 42 2 2 0,2,2
-25289: y 2 0 2 1,2,2
-25289: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25290: Facts:
-25290: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25290: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25290: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25290: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25290: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25290: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25290: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25290: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25290: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25290: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25290: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25290: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25290: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25290: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25290: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25290: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25290: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25290: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25290: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25290: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25290: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25290: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25290: Goal:
-25290: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25290: Order:
-25290: kbo
-25290: Leaf order:
-25290: commutator 1 2 0
-25290: additive_inverse 22 1 0
-25290: add 24 2 0
-25290: additive_identity 8 0 0
-25290: associator 3 3 2 0,2
-25290: z 2 0 2 3,2
-25290: multiply 42 2 2 0,2,2
-25290: y 2 0 2 1,2,2
-25290: x 4 0 4 1,2
-NO CLASH, using fixed ground order
-25291: Facts:
-25291: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25291: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25291: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25291: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25291: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25291: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25291: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25291: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25291: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25291: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25291: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25291: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25291: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25291: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25291: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25291: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25291: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25291: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25291: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25291: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25291: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25291: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25291: Goal:
-25291: Id : 1, {_}:
- associator x (multiply y x) z =<= multiply x (associator x y z)
- [] by prove_left_moufang
-25291: Order:
-25291: lpo
-25291: Leaf order:
-25291: commutator 1 2 0
-25291: additive_inverse 22 1 0
-25291: add 24 2 0
-25291: additive_identity 8 0 0
-25291: associator 3 3 2 0,2
-25291: z 2 0 2 3,2
-25291: multiply 42 2 2 0,2,2
-25291: y 2 0 2 1,2,2
-25291: x 4 0 4 1,2
-% SZS status Timeout for RNG028-9.p
-NO CLASH, using fixed ground order
-25318: Facts:
-25318: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25318: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25318: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25318: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25318: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25318: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25318: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25318: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25318: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25318: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25318: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25318: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25318: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25318: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25318: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25318: Goal:
-25318: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-25318: Order:
-25318: nrkbo
-25318: Leaf order:
-25318: commutator 1 2 0
-25318: associator 1 3 0
-25318: additive_inverse 6 1 0
-25318: add 16 2 0
-25318: additive_identity 8 0 0
-25318: cz 2 0 2 1,2,2
-25318: multiply 28 2 6 0,2
-25318: cy 2 0 2 2,1,2
-25318: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25320: Facts:
-25320: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25320: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25320: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25320: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25320: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25320: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25320: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25320: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25320: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25320: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25320: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25320: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25320: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25320: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25320: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25320: Goal:
-25320: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-25320: Order:
-25320: lpo
-25320: Leaf order:
-25320: commutator 1 2 0
-25320: associator 1 3 0
-25320: additive_inverse 6 1 0
-25320: add 16 2 0
-25320: additive_identity 8 0 0
-25320: cz 2 0 2 1,2,2
-25320: multiply 28 2 6 0,2
-25320: cy 2 0 2 2,1,2
-25320: cx 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25319: Facts:
-25319: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25319: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25319: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25319: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25319: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25319: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25319: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25319: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25319: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25319: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25319: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25319: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25319: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25319: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25319: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25319: Goal:
-25319: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-25319: Order:
-25319: kbo
-25319: Leaf order:
-25319: commutator 1 2 0
-25319: associator 1 3 0
-25319: additive_inverse 6 1 0
-25319: add 16 2 0
-25319: additive_identity 8 0 0
-25319: cz 2 0 2 1,2,2
-25319: multiply 28 2 6 0,2
-25319: cy 2 0 2 2,1,2
-25319: cx 4 0 4 1,1,2
-% SZS status Timeout for RNG029-5.p
-NO CLASH, using fixed ground order
-25337: Facts:
-25337: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25337: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25337: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25337: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25337: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25337: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25337: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25337: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25337: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25337: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25337: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25337: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25337: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25337: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25337: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25337: Goal:
-25337: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25337: Order:
-25337: nrkbo
-25337: Leaf order:
-25337: commutator 1 2 0
-25337: associator 1 3 0
-25337: additive_inverse 6 1 0
-25337: add 16 2 0
-25337: additive_identity 8 0 0
-25337: z 2 0 2 1,2,2
-25337: multiply 28 2 6 0,2
-25337: y 2 0 2 2,1,2
-25337: x 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25338: Facts:
-25338: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25338: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25338: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25338: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25338: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25338: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25338: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25338: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25338: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25338: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25338: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25338: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25338: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25338: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25338: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25338: Goal:
-25338: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25338: Order:
-25338: kbo
-25338: Leaf order:
-25338: commutator 1 2 0
-25338: associator 1 3 0
-25338: additive_inverse 6 1 0
-25338: add 16 2 0
-25338: additive_identity 8 0 0
-25338: z 2 0 2 1,2,2
-25338: multiply 28 2 6 0,2
-25338: y 2 0 2 2,1,2
-25338: x 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25339: Facts:
-25339: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25339: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25339: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25339: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25339: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25339: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25339: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25339: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25339: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25339: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25339: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25339: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25339: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25339: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25339: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25339: Goal:
-25339: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25339: Order:
-25339: lpo
-25339: Leaf order:
-25339: commutator 1 2 0
-25339: associator 1 3 0
-25339: additive_inverse 6 1 0
-25339: add 16 2 0
-25339: additive_identity 8 0 0
-25339: z 2 0 2 1,2,2
-25339: multiply 28 2 6 0,2
-25339: y 2 0 2 2,1,2
-25339: x 4 0 4 1,1,2
-% SZS status Timeout for RNG029-6.p
-NO CLASH, using fixed ground order
-25367: Facts:
-25367: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25367: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25367: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25367: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25367: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25367: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25367: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25367: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25367: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25367: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25367: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25367: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25367: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25367: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25367: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25367: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25367: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25367: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25367: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25367: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25367: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25367: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25367: Goal:
-25367: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25367: Order:
-25367: nrkbo
-25367: Leaf order:
-25367: commutator 1 2 0
-25367: associator 1 3 0
-25367: additive_inverse 22 1 0
-25367: add 24 2 0
-25367: additive_identity 8 0 0
-25367: z 2 0 2 1,2,2
-25367: multiply 46 2 6 0,2
-25367: y 2 0 2 2,1,2
-25367: x 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-25368: Facts:
-25368: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25368: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25368: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-NO CLASH, using fixed ground order
-25369: Facts:
-25369: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25369: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25369: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25369: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25369: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25369: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25369: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25369: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25369: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25369: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25369: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25369: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25369: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25369: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25369: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25369: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25369: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25369: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25369: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25369: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25369: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25369: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25369: Goal:
-25369: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25369: Order:
-25369: lpo
-25369: Leaf order:
-25369: commutator 1 2 0
-25369: associator 1 3 0
-25369: additive_inverse 22 1 0
-25369: add 24 2 0
-25369: additive_identity 8 0 0
-25369: z 2 0 2 1,2,2
-25369: multiply 46 2 6 0,2
-25369: y 2 0 2 2,1,2
-25369: x 4 0 4 1,1,2
-25368: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25368: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25368: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25368: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25368: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25368: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25368: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25368: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25368: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25368: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25368: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25368: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25368: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25368: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25368: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25368: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25368: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25368: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25368: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25368: Goal:
-25368: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-25368: Order:
-25368: kbo
-25368: Leaf order:
-25368: commutator 1 2 0
-25368: associator 1 3 0
-25368: additive_inverse 22 1 0
-25368: add 24 2 0
-25368: additive_identity 8 0 0
-25368: z 2 0 2 1,2,2
-25368: multiply 46 2 6 0,2
-25368: y 2 0 2 2,1,2
-25368: x 4 0 4 1,1,2
-% SZS status Timeout for RNG029-7.p
-NO CLASH, using fixed ground order
-25651: Facts:
-25651: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25651: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25651: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25651: Id : 5, {_}: add c d =>= d [] by absorbtion
-25651: Goal:
-NO CLASH, using fixed ground order
-25652: Facts:
-25652: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25652: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25652: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25652: Id : 5, {_}: add c d =>= d [] by absorbtion
-25652: Goal:
-25652: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25652: Order:
-25652: kbo
-25652: Leaf order:
-25652: d 2 0 0
-25652: c 1 0 0
-25652: add 13 2 3 0,2
-25652: negate 9 1 5 0,1,2
-25652: b 3 0 3 1,2,1,1,2
-25652: a 2 0 2 1,1,1,2
-25651: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25651: Order:
-25651: nrkbo
-25651: Leaf order:
-25651: d 2 0 0
-25651: c 1 0 0
-25651: add 13 2 3 0,2
-25651: negate 9 1 5 0,1,2
-25651: b 3 0 3 1,2,1,1,2
-25651: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-25653: Facts:
-25653: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25653: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25653: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25653: Id : 5, {_}: add c d =>= d [] by absorbtion
-25653: Goal:
-25653: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25653: Order:
-25653: lpo
-25653: Leaf order:
-25653: d 2 0 0
-25653: c 1 0 0
-25653: add 13 2 3 0,2
-25653: negate 9 1 5 0,1,2
-25653: b 3 0 3 1,2,1,1,2
-25653: a 2 0 2 1,1,1,2
-% SZS status Timeout for ROB006-1.p
-NO CLASH, using fixed ground order
-25684: Facts:
-25684: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-25684: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-25684: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-25684: Id : 5, {_}: add c d =>= d [] by absorbtion
-25684: Goal:
-25684: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-25684: Order:
-25684: nrkbo
-25684: Leaf order:
-25684: d 2 0 0
-25684: c 1 0 0
-25684: negate 4 1 0
-25684: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-25685: Facts:
-25685: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-25685: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-25685: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-25685: Id : 5, {_}: add c d =>= d [] by absorbtion
-25685: Goal:
-25685: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-25685: Order:
-25685: kbo
-25685: Leaf order:
-25685: d 2 0 0
-25685: c 1 0 0
-25685: negate 4 1 0
-25685: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-25686: Facts:
-25686: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-25686: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-25686: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-25686: Id : 5, {_}: add c d =>= d [] by absorbtion
-25686: Goal:
-25686: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-25686: Order:
-25686: lpo
-25686: Leaf order:
-25686: d 2 0 0
-25686: c 1 0 0
-25686: negate 4 1 0
-25686: add 11 2 1 0,2
-% SZS status Timeout for ROB006-2.p
-NO CLASH, using fixed ground order
-25702: Facts:
-25702: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25702: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25702: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25702: Id : 5, {_}: add c d =>= c [] by identity_constant
-25702: Goal:
-25702: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25702: Order:
-25702: nrkbo
-25702: Leaf order:
-25702: d 1 0 0
-25702: c 2 0 0
-25702: add 13 2 3 0,2
-25702: negate 9 1 5 0,1,2
-25702: b 3 0 3 1,2,1,1,2
-25702: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-25704: Facts:
-25704: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25704: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25704: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25704: Id : 5, {_}: add c d =>= c [] by identity_constant
-25704: Goal:
-25704: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25704: Order:
-25704: lpo
-25704: Leaf order:
-25704: d 1 0 0
-25704: c 2 0 0
-25704: add 13 2 3 0,2
-25704: negate 9 1 5 0,1,2
-25704: b 3 0 3 1,2,1,1,2
-25704: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-25703: Facts:
-25703: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-25703: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-25703: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-25703: Id : 5, {_}: add c d =>= c [] by identity_constant
-25703: Goal:
-25703: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-25703: Order:
-25703: kbo
-25703: Leaf order:
-25703: d 1 0 0
-25703: c 2 0 0
-25703: add 13 2 3 0,2
-25703: negate 9 1 5 0,1,2
-25703: b 3 0 3 1,2,1,1,2
-25703: a 2 0 2 1,1,1,2
-% SZS status Timeout for ROB026-1.p
-NO CLASH, using fixed ground order
-25731: Facts:
-25731: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25731: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25731: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25731: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25731: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25731: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25731: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25731: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25731: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25731: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25731: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25731: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25731: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25731: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25731: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25731: Goal:
-25731: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =<=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-25731: Order:
-25731: nrkbo
-25731: Leaf order:
-25731: inverse 1 1 0
-25731: multiply 18 2 0
-25731: identity 2 0 0
-25731: least_upper_bound 16 2 3 0,2
-25731: greatest_lower_bound 15 2 2 0,2,2
-25731: c 2 0 2 2,2,2
-25731: b 2 0 2 1,2,2
-25731: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25732: Facts:
-25732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25732: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25732: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25732: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25732: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25732: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25732: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25732: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25732: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25732: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25732: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25732: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25732: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25732: Goal:
-25732: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =<=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-25732: Order:
-25732: kbo
-25732: Leaf order:
-25732: inverse 1 1 0
-25732: multiply 18 2 0
-25732: identity 2 0 0
-25732: least_upper_bound 16 2 3 0,2
-25732: greatest_lower_bound 15 2 2 0,2,2
-25732: c 2 0 2 2,2,2
-25732: b 2 0 2 1,2,2
-25732: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25733: Facts:
-25733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25733: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25733: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25733: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25733: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25733: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25733: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25733: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25733: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25733: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25733: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25733: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25733: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25733: Goal:
-25733: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =<=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-25733: Order:
-25733: lpo
-25733: Leaf order:
-25733: inverse 1 1 0
-25733: multiply 18 2 0
-25733: identity 2 0 0
-25733: least_upper_bound 16 2 3 0,2
-25733: greatest_lower_bound 15 2 2 0,2,2
-25733: c 2 0 2 2,2,2
-25733: b 2 0 2 1,2,2
-25733: a 3 0 3 1,2
-% SZS status Timeout for GRP164-1.p
-NO CLASH, using fixed ground order
-25749: Facts:
-25749: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25749: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25749: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25749: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25749: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25749: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25749: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25749: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25749: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25749: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25749: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25749: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25749: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25749: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25749: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25749: Goal:
-25749: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-25749: Order:
-25749: nrkbo
-25749: Leaf order:
-25749: inverse 1 1 0
-25749: multiply 18 2 0
-25749: identity 2 0 0
-25749: greatest_lower_bound 16 2 3 0,2
-25749: least_upper_bound 15 2 2 0,2,2
-25749: c 2 0 2 2,2,2
-25749: b 2 0 2 1,2,2
-25749: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25750: Facts:
-25750: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25750: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25750: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25750: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25750: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25750: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25750: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25750: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25750: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25750: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25750: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-NO CLASH, using fixed ground order
-25751: Facts:
-25751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25751: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25751: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25751: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25751: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25751: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25751: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25751: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25751: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25751: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25751: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25751: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25751: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25751: Goal:
-25751: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-25751: Order:
-25751: lpo
-25751: Leaf order:
-25751: inverse 1 1 0
-25751: multiply 18 2 0
-25751: identity 2 0 0
-25751: greatest_lower_bound 16 2 3 0,2
-25751: least_upper_bound 15 2 2 0,2,2
-25751: c 2 0 2 2,2,2
-25751: b 2 0 2 1,2,2
-25751: a 3 0 3 1,2
-25750: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25750: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25750: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25750: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25750: Goal:
-25750: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-25750: Order:
-25750: kbo
-25750: Leaf order:
-25750: inverse 1 1 0
-25750: multiply 18 2 0
-25750: identity 2 0 0
-25750: greatest_lower_bound 16 2 3 0,2
-25750: least_upper_bound 15 2 2 0,2,2
-25750: c 2 0 2 2,2,2
-25750: b 2 0 2 1,2,2
-25750: a 3 0 3 1,2
-% SZS status Timeout for GRP164-2.p
-NO CLASH, using fixed ground order
-25782: Facts:
-25782: Id : 2, {_}:
- multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4)
- [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
-25782: Id : 3, {_}:
- multiply ?6 (multiply ?7 (multiply ?7 ?7))
- =?=
- multiply ?7 (multiply ?7 (multiply ?7 ?6))
- [7, 6] by condition ?6 ?7
-25782: Goal:
-25782: Id : 1, {_}:
- multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a (multiply b (multiply a b))))))))))))))))
- =<=
- multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b (multiply b (multiply b b))))))))))))))))
- [] by prove_this
-25782: Order:
-25782: nrkbo
-25782: Leaf order:
-25782: multiply 44 2 34 0,2
-25782: b 18 0 18 1,2,2
-25782: a 18 0 18 1,2
-NO CLASH, using fixed ground order
-25783: Facts:
-25783: Id : 2, {_}:
- multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4)
- [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
-25783: Id : 3, {_}:
- multiply ?6 (multiply ?7 (multiply ?7 ?7))
- =?=
- multiply ?7 (multiply ?7 (multiply ?7 ?6))
- [7, 6] by condition ?6 ?7
-25783: Goal:
-25783: Id : 1, {_}:
- multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a (multiply b (multiply a b))))))))))))))))
- =?=
- multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b (multiply b (multiply b b))))))))))))))))
- [] by prove_this
-25783: Order:
-25783: kbo
-25783: Leaf order:
-25783: multiply 44 2 34 0,2
-25783: b 18 0 18 1,2,2
-25783: a 18 0 18 1,2
-NO CLASH, using fixed ground order
-% SZS status Timeout for GRP196-1.p
-NO CLASH, using fixed ground order
-25809: Facts:
-25809: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-25809: Goal:
-25809: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25809: Order:
-25809: nrkbo
-25809: Leaf order:
-25809: f 18 2 8 0,2
-25809: c 3 0 3 2,1,2,2
-25809: b 4 0 4 1,1,2,2
-25809: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25810: Facts:
-25810: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-25810: Goal:
-25810: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25810: Order:
-25810: kbo
-25810: Leaf order:
-25810: f 18 2 8 0,2
-25810: c 3 0 3 2,1,2,2
-25810: b 4 0 4 1,1,2,2
-25810: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25811: Facts:
-25811: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-25811: Goal:
-25811: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25811: Order:
-25811: lpo
-25811: Leaf order:
-25811: f 18 2 8 0,2
-25811: c 3 0 3 2,1,2,2
-25811: b 4 0 4 1,1,2,2
-25811: a 3 0 3 1,2
-% SZS status Timeout for LAT070-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-25843: Facts:
-25843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25843: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25843: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25843: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25843: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25843: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-25843: Goal:
-25843: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25843: Order:
-25843: kbo
-25843: Leaf order:
-25843: join 17 2 4 0,2,2
-25843: meet 21 2 6 0,2
-25843: c 3 0 3 2,2,2,2
-25843: b 3 0 3 1,2,2
-25843: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-25844: Facts:
-25844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25844: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25844: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25844: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25844: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25844: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-25844: Goal:
-25844: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25844: Order:
-25844: lpo
-25844: Leaf order:
-25844: join 17 2 4 0,2,2
-25844: meet 21 2 6 0,2
-25844: c 3 0 3 2,2,2,2
-25844: b 3 0 3 1,2,2
-25844: a 6 0 6 1,2
-25842: Facts:
-25842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25842: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25842: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25842: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25842: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25842: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-25842: Goal:
-25842: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25842: Order:
-25842: nrkbo
-25842: Leaf order:
-25842: join 17 2 4 0,2,2
-25842: meet 21 2 6 0,2
-25842: c 3 0 3 2,2,2,2
-25842: b 3 0 3 1,2,2
-25842: a 6 0 6 1,2
-% SZS status Timeout for LAT138-1.p
-NO CLASH, using fixed ground order
-25866: Facts:
-25866: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25866: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25866: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25866: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25866: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25866: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25866: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25866: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25866: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25866: Goal:
-25866: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-25866: Order:
-25866: nrkbo
-25866: Leaf order:
-25866: join 17 2 4 0,2,2
-25866: meet 21 2 6 0,2
-25866: c 4 0 4 2,2,2,2
-25866: b 4 0 4 1,2,2
-25866: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-25867: Facts:
-25867: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25867: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25867: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25867: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25867: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25867: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25867: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25867: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25867: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25867: Goal:
-25867: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-25867: Order:
-25867: kbo
-25867: Leaf order:
-25867: join 17 2 4 0,2,2
-25867: meet 21 2 6 0,2
-25867: c 4 0 4 2,2,2,2
-25867: b 4 0 4 1,2,2
-25867: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-25868: Facts:
-25868: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25868: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25868: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25868: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25868: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25868: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25868: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25868: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25868: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25868: Goal:
-25868: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-25868: Order:
-25868: lpo
-25868: Leaf order:
-25868: join 17 2 4 0,2,2
-25868: meet 21 2 6 0,2
-25868: c 4 0 4 2,2,2,2
-25868: b 4 0 4 1,2,2
-25868: a 4 0 4 1,2
-% SZS status Timeout for LAT140-1.p
-NO CLASH, using fixed ground order
-25928: Facts:
-25928: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25928: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25928: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25928: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25928: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25928: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25928: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25928: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25928: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-25928: Goal:
-NO CLASH, using fixed ground order
-25929: Facts:
-25929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25929: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25929: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25929: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25929: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25929: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-25929: Goal:
-25929: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25929: Order:
-25929: kbo
-25929: Leaf order:
-25929: join 16 2 4 0,2,2
-25929: meet 22 2 6 0,2
-25929: c 3 0 3 2,2,2,2
-25929: b 3 0 3 1,2,2
-25929: a 6 0 6 1,2
-25928: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25928: Order:
-25928: nrkbo
-25928: Leaf order:
-25928: join 16 2 4 0,2,2
-25928: meet 22 2 6 0,2
-25928: c 3 0 3 2,2,2,2
-25928: b 3 0 3 1,2,2
-25928: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-25930: Facts:
-25930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25930: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25930: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25930: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25930: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25930: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-25930: Goal:
-25930: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25930: Order:
-25930: lpo
-25930: Leaf order:
-25930: join 16 2 4 0,2,2
-25930: meet 22 2 6 0,2
-25930: c 3 0 3 2,2,2,2
-25930: b 3 0 3 1,2,2
-25930: a 6 0 6 1,2
-% SZS status Timeout for LAT145-1.p
-NO CLASH, using fixed ground order
-25948: Facts:
-25948: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25948: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25948: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25948: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25948: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25948: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25948: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25948: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25948: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-25948: Goal:
-25948: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-25948: Order:
-25948: nrkbo
-25948: Leaf order:
-25948: meet 19 2 5 0,2
-25948: join 19 2 5 0,2,2
-25948: d 3 0 3 2,2,2,2,2
-25948: c 2 0 2 1,2,2,2
-25948: b 4 0 4 1,2,2
-25948: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25949: Facts:
-25949: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25949: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25949: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25949: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25949: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25949: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25949: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25949: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25949: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-25949: Goal:
-25949: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-25949: Order:
-25949: kbo
-25949: Leaf order:
-25949: meet 19 2 5 0,2
-25949: join 19 2 5 0,2,2
-25949: d 3 0 3 2,2,2,2,2
-25949: c 2 0 2 1,2,2,2
-25949: b 4 0 4 1,2,2
-25949: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-25950: Facts:
-25950: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25950: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25950: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25950: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25950: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25950: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25950: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25950: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25950: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-25950: Goal:
-25950: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-25950: Order:
-25950: lpo
-25950: Leaf order:
-25950: meet 19 2 5 0,2
-25950: join 19 2 5 0,2,2
-25950: d 3 0 3 2,2,2,2,2
-25950: c 2 0 2 1,2,2,2
-25950: b 4 0 4 1,2,2
-25950: a 3 0 3 1,2
-% SZS status Timeout for LAT149-1.p
-NO CLASH, using fixed ground order
-26495: Facts:
-26495: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26495: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26495: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26495: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26495: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26495: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26495: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26495: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26495: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-26495: Goal:
-26495: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-26495: Order:
-26495: nrkbo
-26495: Leaf order:
-26495: join 18 2 4 0,2,2
-26495: meet 20 2 6 0,2
-26495: c 2 0 2 2,2,2,2
-26495: b 4 0 4 1,2,2
-26495: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-26496: Facts:
-26496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26496: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26496: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26496: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26496: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26496: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-26496: Goal:
-26496: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-26496: Order:
-26496: kbo
-26496: Leaf order:
-26496: join 18 2 4 0,2,2
-26496: meet 20 2 6 0,2
-26496: c 2 0 2 2,2,2,2
-26496: b 4 0 4 1,2,2
-26496: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-26497: Facts:
-26497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26497: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26497: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26497: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26497: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26497: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-26497: Goal:
-26497: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-26497: Order:
-26497: lpo
-26497: Leaf order:
-26497: join 18 2 4 0,2,2
-26497: meet 20 2 6 0,2
-26497: c 2 0 2 2,2,2,2
-26497: b 4 0 4 1,2,2
-26497: a 6 0 6 1,2
-% SZS status Timeout for LAT153-1.p
-NO CLASH, using fixed ground order
-26513: Facts:
-26513: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26513: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26513: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26513: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26513: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26513: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26513: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26513: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26513: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26513: Goal:
-26513: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-26513: Order:
-26513: nrkbo
-26513: Leaf order:
-26513: join 18 2 4 0,2,2
-26513: meet 20 2 6 0,2
-26513: c 4 0 4 2,2,2,2
-26513: b 4 0 4 1,2,2
-26513: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26514: Facts:
-26514: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26514: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26514: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26514: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26514: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26514: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26514: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26514: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26514: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26514: Goal:
-26514: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-26514: Order:
-26514: kbo
-26514: Leaf order:
-26514: join 18 2 4 0,2,2
-26514: meet 20 2 6 0,2
-26514: c 4 0 4 2,2,2,2
-26514: b 4 0 4 1,2,2
-26514: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26515: Facts:
-26515: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26515: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26515: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26515: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26515: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26515: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26515: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26515: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26515: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26515: Goal:
-26515: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-26515: Order:
-26515: lpo
-26515: Leaf order:
-26515: join 18 2 4 0,2,2
-26515: meet 20 2 6 0,2
-26515: c 4 0 4 2,2,2,2
-26515: b 4 0 4 1,2,2
-26515: a 4 0 4 1,2
-% SZS status Timeout for LAT157-1.p
-NO CLASH, using fixed ground order
-26542: Facts:
-26542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26542: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26542: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26542: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26542: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26542: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26542: Goal:
-26542: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-26542: Order:
-26542: nrkbo
-26542: Leaf order:
-26542: meet 19 2 5 0,2
-26542: join 19 2 5 0,2,2
-26542: d 2 0 2 2,2,2,2,2
-26542: c 3 0 3 1,2,2,2
-26542: b 3 0 3 1,2,2
-26542: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26543: Facts:
-26543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26543: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26543: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26543: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26543: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26543: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26543: Goal:
-26543: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-26543: Order:
-26543: kbo
-26543: Leaf order:
-26543: meet 19 2 5 0,2
-26543: join 19 2 5 0,2,2
-26543: d 2 0 2 2,2,2,2,2
-26543: c 3 0 3 1,2,2,2
-26543: b 3 0 3 1,2,2
-26543: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26544: Facts:
-26544: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26544: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26544: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26544: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26544: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26544: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26544: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26544: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26544: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-26544: Goal:
-26544: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-26544: Order:
-26544: lpo
-26544: Leaf order:
-26544: meet 19 2 5 0,2
-26544: join 19 2 5 0,2,2
-26544: d 2 0 2 2,2,2,2,2
-26544: c 3 0 3 1,2,2,2
-26544: b 3 0 3 1,2,2
-26544: a 4 0 4 1,2
-% SZS status Timeout for LAT158-1.p
-NO CLASH, using fixed ground order
-26561: Facts:
-26561: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26561: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26561: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26561: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26561: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26561: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26561: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26561: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26561: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26561: Goal:
-26561: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26561: Order:
-26561: nrkbo
-26561: Leaf order:
-26561: join 16 2 3 0,2,2
-26561: meet 21 2 7 0,2
-26561: d 3 0 3 2,2,2,2,2
-26561: c 2 0 2 1,2,2,2,2
-26561: b 3 0 3 1,2,2
-26561: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26562: Facts:
-26562: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26562: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26562: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26562: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26562: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26562: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26562: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26562: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26562: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26562: Goal:
-26562: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26562: Order:
-26562: kbo
-26562: Leaf order:
-26562: join 16 2 3 0,2,2
-26562: meet 21 2 7 0,2
-26562: d 3 0 3 2,2,2,2,2
-26562: c 2 0 2 1,2,2,2,2
-26562: b 3 0 3 1,2,2
-26562: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26563: Facts:
-26563: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26563: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26563: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26563: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26563: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26563: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26563: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26563: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26563: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26563: Goal:
-26563: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26563: Order:
-26563: lpo
-26563: Leaf order:
-26563: join 16 2 3 0,2,2
-26563: meet 21 2 7 0,2
-26563: d 3 0 3 2,2,2,2,2
-26563: c 2 0 2 1,2,2,2,2
-26563: b 3 0 3 1,2,2
-26563: a 4 0 4 1,2
-% SZS status Timeout for LAT163-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-26595: Facts:
-26595: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26595: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26595: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26595: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26595: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26595: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26595: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26595: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26595: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26595: Goal:
-26595: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26595: Order:
-26595: kbo
-26595: Leaf order:
-26595: meet 20 2 6 0,2
-26595: join 17 2 4 0,2,2
-26595: d 2 0 2 2,2,2,2,2
-26595: c 3 0 3 1,2,2,2
-26595: b 4 0 4 1,2,2
-26595: a 3 0 3 1,2
-26594: Facts:
-26594: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26594: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26594: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26594: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26594: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26594: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26594: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26594: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26594: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26594: Goal:
-26594: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26594: Order:
-26594: nrkbo
-26594: Leaf order:
-26594: meet 20 2 6 0,2
-26594: join 17 2 4 0,2,2
-26594: d 2 0 2 2,2,2,2,2
-26594: c 3 0 3 1,2,2,2
-26594: b 4 0 4 1,2,2
-26594: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-26596: Facts:
-26596: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26596: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26596: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26596: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26596: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26596: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26596: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26596: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26596: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-26596: Goal:
-26596: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =>=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26596: Order:
-26596: lpo
-26596: Leaf order:
-26596: meet 20 2 6 0,2
-26596: join 17 2 4 0,2,2
-26596: d 2 0 2 2,2,2,2,2
-26596: c 3 0 3 1,2,2,2
-26596: b 4 0 4 1,2,2
-26596: a 3 0 3 1,2
-% SZS status Timeout for LAT165-1.p
-NO CLASH, using fixed ground order
-26645: Facts:
-26645: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26645: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26645: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26645: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26645: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26645: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26645: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26645: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26645: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-26645: Goal:
-26645: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-26645: Order:
-26645: nrkbo
-26645: Leaf order:
-26645: meet 20 2 5 0,2
-26645: join 18 2 5 0,2,2
-26645: d 3 0 3 2,2,2,2,2
-26645: c 2 0 2 1,2,2,2
-26645: b 4 0 4 1,2,2
-26645: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-26646: Facts:
-26646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26646: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26646: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26646: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26646: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26646: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-26646: Goal:
-26646: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-26646: Order:
-26646: kbo
-26646: Leaf order:
-26646: meet 20 2 5 0,2
-26646: join 18 2 5 0,2,2
-26646: d 3 0 3 2,2,2,2,2
-26646: c 2 0 2 1,2,2,2
-26646: b 4 0 4 1,2,2
-26646: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-26647: Facts:
-26647: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26647: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26647: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26647: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26647: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26647: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26647: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26647: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26647: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-26647: Goal:
-26647: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-26647: Order:
-26647: lpo
-26647: Leaf order:
-26647: meet 20 2 5 0,2
-26647: join 18 2 5 0,2,2
-26647: d 3 0 3 2,2,2,2,2
-26647: c 2 0 2 1,2,2,2
-26647: b 4 0 4 1,2,2
-26647: a 3 0 3 1,2
-% SZS status Timeout for LAT166-1.p
-NO CLASH, using fixed ground order
-26677: Facts:
-26677: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26677: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26677: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26677: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26677: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26677: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26677: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26677: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26677: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-26677: Goal:
-26677: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26677: Order:
-26677: kbo
-26677: Leaf order:
-26677: meet 20 2 6 0,2
-26677: join 18 2 4 0,2,2
-26677: d 2 0 2 2,2,2,2,2
-26677: c 3 0 3 1,2,2,2
-26677: b 4 0 4 1,2,2
-26677: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-26676: Facts:
-26676: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26676: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26676: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26676: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26676: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26676: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26676: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26676: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26676: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-26676: Goal:
-26676: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26676: Order:
-26676: nrkbo
-26676: Leaf order:
-26676: meet 20 2 6 0,2
-26676: join 18 2 4 0,2,2
-26676: d 2 0 2 2,2,2,2,2
-26676: c 3 0 3 1,2,2,2
-26676: b 4 0 4 1,2,2
-26676: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-26678: Facts:
-26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26678: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26678: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26678: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26678: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26678: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-26678: Goal:
-26678: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =>=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-26678: Order:
-26678: lpo
-26678: Leaf order:
-26678: meet 20 2 6 0,2
-26678: join 18 2 4 0,2,2
-26678: d 2 0 2 2,2,2,2,2
-26678: c 3 0 3 1,2,2,2
-26678: b 4 0 4 1,2,2
-26678: a 3 0 3 1,2
-% SZS status Timeout for LAT167-1.p
-NO CLASH, using fixed ground order
-26697: Facts:
-26697: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26697: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26697: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26697: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26697: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26697: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26697: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26697: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26697: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26697: Goal:
-26697: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26697: Order:
-26697: nrkbo
-26697: Leaf order:
-26697: join 17 2 3 0,2,2
-26697: meet 20 2 7 0,2
-26697: d 3 0 3 2,2,2,2,2
-26697: c 2 0 2 1,2,2,2,2
-26697: b 3 0 3 1,2,2
-26697: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26698: Facts:
-26698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26698: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26698: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26698: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26698: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26698: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26698: Goal:
-26698: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26698: Order:
-26698: kbo
-26698: Leaf order:
-26698: join 17 2 3 0,2,2
-26698: meet 20 2 7 0,2
-26698: d 3 0 3 2,2,2,2,2
-26698: c 2 0 2 1,2,2,2,2
-26698: b 3 0 3 1,2,2
-26698: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26699: Facts:
-26699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26699: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26699: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26699: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26699: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26699: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26699: Goal:
-26699: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26699: Order:
-26699: lpo
-26699: Leaf order:
-26699: join 17 2 3 0,2,2
-26699: meet 20 2 7 0,2
-26699: d 3 0 3 2,2,2,2,2
-26699: c 2 0 2 1,2,2,2,2
-26699: b 3 0 3 1,2,2
-26699: a 4 0 4 1,2
-% SZS status Timeout for LAT172-1.p
-NO CLASH, using fixed ground order
-26727: Facts:
-26727: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26727: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26727: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26727: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26727: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26727: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26727: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26727: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26727: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26727: Goal:
-26727: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-26727: Order:
-26727: nrkbo
-26727: Leaf order:
-26727: meet 18 2 5 0,2
-26727: join 19 2 5 0,2,2
-26727: d 2 0 2 2,2,2,2,2
-26727: c 3 0 3 1,2,2,2
-26727: b 3 0 3 1,2,2
-26727: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26728: Facts:
-26728: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26728: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26728: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26728: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26728: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26728: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26728: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26728: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26728: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26728: Goal:
-26728: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-26728: Order:
-26728: kbo
-26728: Leaf order:
-26728: meet 18 2 5 0,2
-26728: join 19 2 5 0,2,2
-26728: d 2 0 2 2,2,2,2,2
-26728: c 3 0 3 1,2,2,2
-26728: b 3 0 3 1,2,2
-26728: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26729: Facts:
-26729: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26729: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26729: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26729: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26729: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26729: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26729: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26729: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26729: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-26729: Goal:
-26729: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-26729: Order:
-26729: lpo
-26729: Leaf order:
-26729: meet 18 2 5 0,2
-26729: join 19 2 5 0,2,2
-26729: d 2 0 2 2,2,2,2,2
-26729: c 3 0 3 1,2,2,2
-26729: b 3 0 3 1,2,2
-26729: a 4 0 4 1,2
-% SZS status Timeout for LAT173-1.p
-NO CLASH, using fixed ground order
-26747: Facts:
-26747: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26747: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26747: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26747: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26747: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26747: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26747: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26747: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26747: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26747: Goal:
-26747: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26747: Order:
-26747: kbo
-26747: Leaf order:
-26747: join 18 2 3 0,2,2
-26747: meet 20 2 7 0,2
-26747: d 3 0 3 2,2,2,2,2
-26747: c 2 0 2 1,2,2,2,2
-26747: b 3 0 3 1,2,2
-26747: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26746: Facts:
-26746: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26746: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26746: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26746: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26746: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26746: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26746: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26746: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26746: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26746: Goal:
-26746: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26746: Order:
-26746: nrkbo
-26746: Leaf order:
-26746: join 18 2 3 0,2,2
-26746: meet 20 2 7 0,2
-26746: d 3 0 3 2,2,2,2,2
-26746: c 2 0 2 1,2,2,2,2
-26746: b 3 0 3 1,2,2
-26746: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26748: Facts:
-26748: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26748: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26748: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26748: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26748: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26748: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26748: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26748: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26748: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26748: Goal:
-26748: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-26748: Order:
-26748: lpo
-26748: Leaf order:
-26748: join 18 2 3 0,2,2
-26748: meet 20 2 7 0,2
-26748: d 3 0 3 2,2,2,2,2
-26748: c 2 0 2 1,2,2,2,2
-26748: b 3 0 3 1,2,2
-26748: a 4 0 4 1,2
-% SZS status Timeout for LAT175-1.p
-NO CLASH, using fixed ground order
-26789: Facts:
-26789: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26789: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26789: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26789: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26789: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26789: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26789: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26789: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26789: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26789: Goal:
-26789: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-26789: Order:
-26789: nrkbo
-26789: Leaf order:
-26789: meet 18 2 5 0,2
-26789: join 20 2 5 0,2,2
-26789: d 2 0 2 2,2,2,2,2
-26789: c 3 0 3 1,2,2,2
-26789: b 3 0 3 1,2,2
-26789: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26790: Facts:
-26790: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26790: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26790: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26790: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26790: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26790: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26790: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26790: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26790: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26790: Goal:
-26790: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-26790: Order:
-26790: kbo
-26790: Leaf order:
-26790: meet 18 2 5 0,2
-26790: join 20 2 5 0,2,2
-26790: d 2 0 2 2,2,2,2,2
-26790: c 3 0 3 1,2,2,2
-26790: b 3 0 3 1,2,2
-26790: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-26791: Facts:
-26791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26791: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26791: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26791: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26791: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26791: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-26791: Goal:
-26791: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-26791: Order:
-26791: lpo
-26791: Leaf order:
-26791: meet 18 2 5 0,2
-26791: join 20 2 5 0,2,2
-26791: d 2 0 2 2,2,2,2,2
-26791: c 3 0 3 1,2,2,2
-26791: b 3 0 3 1,2,2
-26791: a 4 0 4 1,2
-% SZS status Timeout for LAT176-1.p
-NO CLASH, using fixed ground order
-27075: Facts:
-27075: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-27075: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-27075: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-27075: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-27075: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-27075: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-27075: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-27075: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-27075: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-27075: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-27075: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-27075: Goal:
-27075: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-27075: Order:
-27075: nrkbo
-27075: Leaf order:
-27075: additive_inverse 2 1 0
-27075: add 14 2 0
-27075: additive_identity 4 0 0
-27075: c 2 0 1 3
-27075: multiply 15 2 1 0,2
-27075: a 2 0 1 2,2
-27075: b 2 0 1 1,2
-NO CLASH, using fixed ground order
-27077: Facts:
-27077: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-27077: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-27077: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-27077: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-27077: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-27077: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-27077: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-27077: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-27077: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-27077: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-27077: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-27077: Goal:
-27077: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-27077: Order:
-27077: lpo
-27077: Leaf order:
-27077: additive_inverse 2 1 0
-27077: add 14 2 0
-27077: additive_identity 4 0 0
-27077: c 2 0 1 3
-27077: multiply 15 2 1 0,2
-27077: a 2 0 1 2,2
-27077: b 2 0 1 1,2
-NO CLASH, using fixed ground order
-27076: Facts:
-27076: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-27076: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-27076: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-27076: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-27076: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-27076: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-27076: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-27076: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-27076: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-27076: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-27076: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-27076: Goal:
-27076: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-27076: Order:
-27076: kbo
-27076: Leaf order:
-27076: additive_inverse 2 1 0
-27076: add 14 2 0
-27076: additive_identity 4 0 0
-27076: c 2 0 1 3
-27076: multiply 15 2 1 0,2
-27076: a 2 0 1 2,2
-27076: b 2 0 1 1,2
-% SZS status Timeout for RNG035-7.p
-NO CLASH, using fixed ground order
-27109: Facts:
-27109: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27109: Goal:
-27109: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27109: Order:
-27109: nrkbo
-27109: Leaf order:
-27109: b 1 0 1 1,2,2
-27109: nand 9 2 3 0,2
-27109: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27110: Facts:
-27110: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27110: Goal:
-27110: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27110: Order:
-27110: kbo
-27110: Leaf order:
-27110: b 1 0 1 1,2,2
-27110: nand 9 2 3 0,2
-27110: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27111: Facts:
-27111: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27111: Goal:
-27111: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27111: Order:
-27111: lpo
-27111: Leaf order:
-27111: b 1 0 1 1,2,2
-27111: nand 9 2 3 0,2
-27111: a 4 0 4 1,1,2
-% SZS status Timeout for BOO077-1.p
-NO CLASH, using fixed ground order
-27127: Facts:
-27127: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27127: Goal:
-27127: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27127: Order:
-27127: nrkbo
-27127: Leaf order:
-27127: nand 12 2 6 0,2
-27127: c 2 0 2 2,2,2,2
-27127: b 3 0 3 1,2,2
-27127: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27128: Facts:
-27128: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27128: Goal:
-27128: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27128: Order:
-27128: kbo
-27128: Leaf order:
-27128: nand 12 2 6 0,2
-27128: c 2 0 2 2,2,2,2
-27128: b 3 0 3 1,2,2
-27128: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27129: Facts:
-27129: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-27129: Goal:
-27129: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27129: Order:
-27129: lpo
-27129: Leaf order:
-27129: nand 12 2 6 0,2
-27129: c 2 0 2 2,2,2,2
-27129: b 3 0 3 1,2,2
-27129: a 3 0 3 1,2
-% SZS status Timeout for BOO078-1.p
-NO CLASH, using fixed ground order
-27161: Facts:
-27161: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27161: Goal:
-27161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27161: Order:
-27161: kbo
-27161: Leaf order:
-27161: b 1 0 1 1,2,2
-27161: nand 9 2 3 0,2
-27161: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27162: Facts:
-27162: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27162: Goal:
-27162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27162: Order:
-27162: lpo
-27162: Leaf order:
-27162: b 1 0 1 1,2,2
-27162: nand 9 2 3 0,2
-27162: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27160: Facts:
-27160: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27160: Goal:
-27160: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27160: Order:
-27160: nrkbo
-27160: Leaf order:
-27160: b 1 0 1 1,2,2
-27160: nand 9 2 3 0,2
-27160: a 4 0 4 1,1,2
-% SZS status Timeout for BOO079-1.p
-NO CLASH, using fixed ground order
-27178: Facts:
-27178: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27178: Goal:
-27178: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27178: Order:
-27178: nrkbo
-27178: Leaf order:
-27178: nand 12 2 6 0,2
-27178: c 2 0 2 2,2,2,2
-27178: b 3 0 3 1,2,2
-27178: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27179: Facts:
-27179: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27179: Goal:
-27179: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27179: Order:
-27179: kbo
-27179: Leaf order:
-27179: nand 12 2 6 0,2
-27179: c 2 0 2 2,2,2,2
-27179: b 3 0 3 1,2,2
-27179: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27180: Facts:
-27180: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-27180: Goal:
-27180: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27180: Order:
-27180: lpo
-27180: Leaf order:
-27180: nand 12 2 6 0,2
-27180: c 2 0 2 2,2,2,2
-27180: b 3 0 3 1,2,2
-27180: a 3 0 3 1,2
-% SZS status Timeout for BOO080-1.p
-NO CLASH, using fixed ground order
-27207: Facts:
-27207: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27207: Goal:
-27207: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27207: Order:
-27207: nrkbo
-27207: Leaf order:
-27207: b 1 0 1 1,2,2
-27207: nand 9 2 3 0,2
-27207: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27208: Facts:
-27208: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27208: Goal:
-27208: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27208: Order:
-27208: kbo
-27208: Leaf order:
-27208: b 1 0 1 1,2,2
-27208: nand 9 2 3 0,2
-27208: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27209: Facts:
-27209: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27209: Goal:
-27209: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27209: Order:
-27209: lpo
-27209: Leaf order:
-27209: b 1 0 1 1,2,2
-27209: nand 9 2 3 0,2
-27209: a 4 0 4 1,1,2
-% SZS status Timeout for BOO081-1.p
-NO CLASH, using fixed ground order
-27227: Facts:
-27227: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27227: Goal:
-27227: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27227: Order:
-27227: nrkbo
-27227: Leaf order:
-27227: nand 12 2 6 0,2
-27227: c 2 0 2 2,2,2,2
-27227: b 3 0 3 1,2,2
-27227: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27228: Facts:
-27228: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27228: Goal:
-27228: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27228: Order:
-27228: kbo
-27228: Leaf order:
-27228: nand 12 2 6 0,2
-27228: c 2 0 2 2,2,2,2
-27228: b 3 0 3 1,2,2
-27228: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27229: Facts:
-27229: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-27229: Goal:
-27229: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27229: Order:
-27229: lpo
-27229: Leaf order:
-27229: nand 12 2 6 0,2
-27229: c 2 0 2 2,2,2,2
-27229: b 3 0 3 1,2,2
-27229: a 3 0 3 1,2
-% SZS status Timeout for BOO082-1.p
-NO CLASH, using fixed ground order
-27257: Facts:
-27257: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27257: Goal:
-27257: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27257: Order:
-27257: nrkbo
-27257: Leaf order:
-27257: b 1 0 1 1,2,2
-27257: nand 9 2 3 0,2
-27257: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27258: Facts:
-27258: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27258: Goal:
-27258: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27258: Order:
-27258: kbo
-27258: Leaf order:
-27258: b 1 0 1 1,2,2
-27258: nand 9 2 3 0,2
-27258: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27259: Facts:
-27259: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27259: Goal:
-27259: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27259: Order:
-27259: lpo
-27259: Leaf order:
-27259: b 1 0 1 1,2,2
-27259: nand 9 2 3 0,2
-27259: a 4 0 4 1,1,2
-% SZS status Timeout for BOO083-1.p
-NO CLASH, using fixed ground order
-27275: Facts:
-27275: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27275: Goal:
-27275: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27275: Order:
-27275: nrkbo
-27275: Leaf order:
-27275: nand 12 2 6 0,2
-27275: c 2 0 2 2,2,2,2
-27275: b 3 0 3 1,2,2
-27275: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27276: Facts:
-27276: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27276: Goal:
-27276: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27276: Order:
-27276: kbo
-27276: Leaf order:
-27276: nand 12 2 6 0,2
-27276: c 2 0 2 2,2,2,2
-27276: b 3 0 3 1,2,2
-27276: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27277: Facts:
-27277: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-27277: Goal:
-27277: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27277: Order:
-27277: lpo
-27277: Leaf order:
-27277: nand 12 2 6 0,2
-27277: c 2 0 2 2,2,2,2
-27277: b 3 0 3 1,2,2
-27277: a 3 0 3 1,2
-% SZS status Timeout for BOO084-1.p
-NO CLASH, using fixed ground order
-27304: Facts:
-27304: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27304: Goal:
-27304: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27304: Order:
-27304: nrkbo
-27304: Leaf order:
-27304: b 1 0 1 1,2,2
-27304: nand 9 2 3 0,2
-27304: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27305: Facts:
-27305: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27305: Goal:
-27305: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27305: Order:
-27305: kbo
-27305: Leaf order:
-27305: b 1 0 1 1,2,2
-27305: nand 9 2 3 0,2
-27305: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27306: Facts:
-27306: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27306: Goal:
-27306: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27306: Order:
-27306: lpo
-27306: Leaf order:
-27306: b 1 0 1 1,2,2
-27306: nand 9 2 3 0,2
-27306: a 4 0 4 1,1,2
-% SZS status Timeout for BOO085-1.p
-NO CLASH, using fixed ground order
-27328: Facts:
-27328: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27328: Goal:
-27328: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27328: Order:
-27328: nrkbo
-27328: Leaf order:
-27328: nand 12 2 6 0,2
-27328: c 2 0 2 2,2,2,2
-27328: b 3 0 3 1,2,2
-27328: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27331: Facts:
-27331: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27331: Goal:
-27331: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27331: Order:
-27331: lpo
-27331: Leaf order:
-27331: nand 12 2 6 0,2
-27331: c 2 0 2 2,2,2,2
-27331: b 3 0 3 1,2,2
-27331: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27329: Facts:
-27329: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-27329: Goal:
-27329: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27329: Order:
-27329: kbo
-27329: Leaf order:
-27329: nand 12 2 6 0,2
-27329: c 2 0 2 2,2,2,2
-27329: b 3 0 3 1,2,2
-27329: a 3 0 3 1,2
-% SZS status Timeout for BOO086-1.p
-NO CLASH, using fixed ground order
-27408: Facts:
-27408: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27408: Goal:
-27408: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27408: Order:
-27408: kbo
-27408: Leaf order:
-27408: b 1 0 1 1,2,2
-27408: nand 9 2 3 0,2
-27408: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27407: Facts:
-27407: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27407: Goal:
-27407: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27407: Order:
-27407: nrkbo
-27407: Leaf order:
-27407: b 1 0 1 1,2,2
-27407: nand 9 2 3 0,2
-27407: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27409: Facts:
-27409: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27409: Goal:
-27409: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27409: Order:
-27409: lpo
-27409: Leaf order:
-27409: b 1 0 1 1,2,2
-27409: nand 9 2 3 0,2
-27409: a 4 0 4 1,1,2
-% SZS status Timeout for BOO087-1.p
-NO CLASH, using fixed ground order
-27425: Facts:
-27425: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27425: Goal:
-27425: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27425: Order:
-27425: nrkbo
-27425: Leaf order:
-27425: nand 12 2 6 0,2
-27425: c 2 0 2 2,2,2,2
-27425: b 3 0 3 1,2,2
-27425: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27426: Facts:
-27426: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27426: Goal:
-27426: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27426: Order:
-27426: kbo
-27426: Leaf order:
-27426: nand 12 2 6 0,2
-27426: c 2 0 2 2,2,2,2
-27426: b 3 0 3 1,2,2
-27426: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27427: Facts:
-27427: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-27427: Goal:
-27427: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27427: Order:
-27427: lpo
-27427: Leaf order:
-27427: nand 12 2 6 0,2
-27427: c 2 0 2 2,2,2,2
-27427: b 3 0 3 1,2,2
-27427: a 3 0 3 1,2
-% SZS status Timeout for BOO088-1.p
-NO CLASH, using fixed ground order
-27458: Facts:
-27458: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27458: Goal:
-27458: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27458: Order:
-27458: nrkbo
-27458: Leaf order:
-27458: b 1 0 1 1,2,2
-27458: nand 9 2 3 0,2
-27458: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27459: Facts:
-27459: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27459: Goal:
-27459: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27459: Order:
-27459: kbo
-27459: Leaf order:
-27459: b 1 0 1 1,2,2
-27459: nand 9 2 3 0,2
-27459: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27460: Facts:
-27460: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27460: Goal:
-27460: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27460: Order:
-27460: lpo
-27460: Leaf order:
-27460: b 1 0 1 1,2,2
-27460: nand 9 2 3 0,2
-27460: a 4 0 4 1,1,2
-% SZS status Timeout for BOO089-1.p
-NO CLASH, using fixed ground order
-27496: Facts:
-27496: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27496: Goal:
-27496: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27496: Order:
-27496: nrkbo
-27496: Leaf order:
-27496: nand 12 2 6 0,2
-27496: c 2 0 2 2,2,2,2
-27496: b 3 0 3 1,2,2
-27496: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27497: Facts:
-27497: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27497: Goal:
-27497: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27497: Order:
-27497: kbo
-27497: Leaf order:
-27497: nand 12 2 6 0,2
-27497: c 2 0 2 2,2,2,2
-27497: b 3 0 3 1,2,2
-27497: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27498: Facts:
-27498: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-27498: Goal:
-27498: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27498: Order:
-27498: lpo
-27498: Leaf order:
-27498: nand 12 2 6 0,2
-27498: c 2 0 2 2,2,2,2
-27498: b 3 0 3 1,2,2
-27498: a 3 0 3 1,2
-% SZS status Timeout for BOO090-1.p
-NO CLASH, using fixed ground order
-27534: Facts:
-27534: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27534: Goal:
-27534: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27534: Order:
-27534: nrkbo
-27534: Leaf order:
-27534: b 1 0 1 1,2,2
-27534: nand 9 2 3 0,2
-27534: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27535: Facts:
-27535: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27535: Goal:
-27535: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27535: Order:
-27535: kbo
-27535: Leaf order:
-27535: b 1 0 1 1,2,2
-27535: nand 9 2 3 0,2
-27535: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27536: Facts:
-27536: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27536: Goal:
-27536: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27536: Order:
-27536: lpo
-27536: Leaf order:
-27536: b 1 0 1 1,2,2
-27536: nand 9 2 3 0,2
-27536: a 4 0 4 1,1,2
-% SZS status Timeout for BOO091-1.p
-NO CLASH, using fixed ground order
-27553: Facts:
-27553: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27553: Goal:
-27553: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27553: Order:
-27553: nrkbo
-27553: Leaf order:
-27553: nand 12 2 6 0,2
-27553: c 2 0 2 2,2,2,2
-27553: b 3 0 3 1,2,2
-27553: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27554: Facts:
-27554: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27554: Goal:
-27554: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27554: Order:
-27554: kbo
-27554: Leaf order:
-27554: nand 12 2 6 0,2
-27554: c 2 0 2 2,2,2,2
-27554: b 3 0 3 1,2,2
-27554: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27555: Facts:
-27555: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-27555: Goal:
-27555: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27555: Order:
-27555: lpo
-27555: Leaf order:
-27555: nand 12 2 6 0,2
-27555: c 2 0 2 2,2,2,2
-27555: b 3 0 3 1,2,2
-27555: a 3 0 3 1,2
-% SZS status Timeout for BOO092-1.p
-NO CLASH, using fixed ground order
-27585: Facts:
-27585: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27585: Goal:
-27585: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27585: Order:
-27585: kbo
-27585: Leaf order:
-27585: b 1 0 1 1,2,2
-27585: nand 9 2 3 0,2
-27585: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27584: Facts:
-27584: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27584: Goal:
-27584: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27584: Order:
-27584: nrkbo
-27584: Leaf order:
-27584: b 1 0 1 1,2,2
-27584: nand 9 2 3 0,2
-27584: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27586: Facts:
-27586: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27586: Goal:
-27586: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27586: Order:
-27586: lpo
-27586: Leaf order:
-27586: b 1 0 1 1,2,2
-27586: nand 9 2 3 0,2
-27586: a 4 0 4 1,1,2
-% SZS status Timeout for BOO093-1.p
-NO CLASH, using fixed ground order
-27602: Facts:
-27602: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27602: Goal:
-27602: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27602: Order:
-27602: nrkbo
-27602: Leaf order:
-27602: nand 12 2 6 0,2
-27602: c 2 0 2 2,2,2,2
-27602: b 3 0 3 1,2,2
-27602: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27603: Facts:
-27603: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27603: Goal:
-27603: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27603: Order:
-27603: kbo
-27603: Leaf order:
-27603: nand 12 2 6 0,2
-27603: c 2 0 2 2,2,2,2
-27603: b 3 0 3 1,2,2
-27603: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27604: Facts:
-27604: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-27604: Goal:
-27604: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27604: Order:
-27604: lpo
-27604: Leaf order:
-27604: nand 12 2 6 0,2
-27604: c 2 0 2 2,2,2,2
-27604: b 3 0 3 1,2,2
-27604: a 3 0 3 1,2
-% SZS status Timeout for BOO094-1.p
-NO CLASH, using fixed ground order
-27635: Facts:
-27635: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27635: Goal:
-27635: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27635: Order:
-27635: nrkbo
-27635: Leaf order:
-27635: b 1 0 1 1,2,2
-27635: nand 9 2 3 0,2
-27635: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27636: Facts:
-27636: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27636: Goal:
-27636: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27636: Order:
-27636: kbo
-27636: Leaf order:
-27636: b 1 0 1 1,2,2
-27636: nand 9 2 3 0,2
-27636: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27637: Facts:
-27637: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27637: Goal:
-27637: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27637: Order:
-27637: lpo
-27637: Leaf order:
-27637: b 1 0 1 1,2,2
-27637: nand 9 2 3 0,2
-27637: a 4 0 4 1,1,2
-% SZS status Timeout for BOO095-1.p
-NO CLASH, using fixed ground order
-27662: Facts:
-27662: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27662: Goal:
-27662: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27662: Order:
-27662: nrkbo
-27662: Leaf order:
-27662: nand 12 2 6 0,2
-27662: c 2 0 2 2,2,2,2
-27662: b 3 0 3 1,2,2
-27662: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27663: Facts:
-27663: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27663: Goal:
-27663: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27663: Order:
-27663: kbo
-27663: Leaf order:
-27663: nand 12 2 6 0,2
-27663: c 2 0 2 2,2,2,2
-27663: b 3 0 3 1,2,2
-27663: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27664: Facts:
-27664: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-27664: Goal:
-27664: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27664: Order:
-27664: lpo
-27664: Leaf order:
-27664: nand 12 2 6 0,2
-27664: c 2 0 2 2,2,2,2
-27664: b 3 0 3 1,2,2
-27664: a 3 0 3 1,2
-% SZS status Timeout for BOO096-1.p
-NO CLASH, using fixed ground order
-27691: Facts:
-27691: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27691: Goal:
-27691: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27691: Order:
-27691: nrkbo
-27691: Leaf order:
-27691: b 1 0 1 1,2,2
-27691: nand 9 2 3 0,2
-27691: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27692: Facts:
-27692: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27692: Goal:
-27692: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27692: Order:
-27692: kbo
-27692: Leaf order:
-27692: b 1 0 1 1,2,2
-27692: nand 9 2 3 0,2
-27692: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27693: Facts:
-27693: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27693: Goal:
-27693: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27693: Order:
-27693: lpo
-27693: Leaf order:
-27693: b 1 0 1 1,2,2
-27693: nand 9 2 3 0,2
-27693: a 4 0 4 1,1,2
-% SZS status Timeout for BOO097-1.p
-NO CLASH, using fixed ground order
-27766: Facts:
-27766: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27766: Goal:
-27766: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27766: Order:
-27766: nrkbo
-27766: Leaf order:
-27766: nand 12 2 6 0,2
-27766: c 2 0 2 2,2,2,2
-27766: b 3 0 3 1,2,2
-27766: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27767: Facts:
-27767: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27767: Goal:
-27767: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27767: Order:
-27767: kbo
-27767: Leaf order:
-27767: nand 12 2 6 0,2
-27767: c 2 0 2 2,2,2,2
-27767: b 3 0 3 1,2,2
-27767: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27768: Facts:
-27768: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-27768: Goal:
-27768: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27768: Order:
-27768: lpo
-27768: Leaf order:
-27768: nand 12 2 6 0,2
-27768: c 2 0 2 2,2,2,2
-27768: b 3 0 3 1,2,2
-27768: a 3 0 3 1,2
-% SZS status Timeout for BOO098-1.p
-NO CLASH, using fixed ground order
-27800: Facts:
-27800: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27800: Goal:
-27800: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27800: Order:
-27800: nrkbo
-27800: Leaf order:
-27800: b 1 0 1 1,2,2
-27800: nand 9 2 3 0,2
-27800: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27801: Facts:
-27801: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27801: Goal:
-27801: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27801: Order:
-27801: kbo
-27801: Leaf order:
-27801: b 1 0 1 1,2,2
-27801: nand 9 2 3 0,2
-27801: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27802: Facts:
-27802: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27802: Goal:
-27802: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27802: Order:
-27802: lpo
-27802: Leaf order:
-27802: b 1 0 1 1,2,2
-27802: nand 9 2 3 0,2
-27802: a 4 0 4 1,1,2
-% SZS status Timeout for BOO099-1.p
-NO CLASH, using fixed ground order
-27864: Facts:
-27864: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27864: Goal:
-27864: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27864: Order:
-27864: nrkbo
-27864: Leaf order:
-27864: nand 12 2 6 0,2
-27864: c 2 0 2 2,2,2,2
-27864: b 3 0 3 1,2,2
-27864: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27865: Facts:
-27865: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27865: Goal:
-27865: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27865: Order:
-27865: kbo
-27865: Leaf order:
-27865: nand 12 2 6 0,2
-27865: c 2 0 2 2,2,2,2
-27865: b 3 0 3 1,2,2
-27865: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27866: Facts:
-27866: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-27866: Goal:
-27866: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27866: Order:
-27866: lpo
-27866: Leaf order:
-27866: nand 12 2 6 0,2
-27866: c 2 0 2 2,2,2,2
-27866: b 3 0 3 1,2,2
-27866: a 3 0 3 1,2
-% SZS status Timeout for BOO100-1.p
-NO CLASH, using fixed ground order
-27893: Facts:
-27893: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27893: Goal:
-27893: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27893: Order:
-27893: nrkbo
-27893: Leaf order:
-27893: b 1 0 1 1,2,2
-27893: nand 9 2 3 0,2
-27893: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27894: Facts:
-27894: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27894: Goal:
-27894: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27894: Order:
-27894: kbo
-27894: Leaf order:
-27894: b 1 0 1 1,2,2
-27894: nand 9 2 3 0,2
-27894: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27895: Facts:
-27895: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27895: Goal:
-27895: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27895: Order:
-27895: lpo
-27895: Leaf order:
-27895: b 1 0 1 1,2,2
-27895: nand 9 2 3 0,2
-27895: a 4 0 4 1,1,2
-% SZS status Timeout for BOO101-1.p
-NO CLASH, using fixed ground order
-27912: Facts:
-27912: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27912: Goal:
-27912: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27912: Order:
-27912: nrkbo
-27912: Leaf order:
-27912: nand 12 2 6 0,2
-27912: c 2 0 2 2,2,2,2
-27912: b 3 0 3 1,2,2
-27912: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27913: Facts:
-27913: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27913: Goal:
-27913: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27913: Order:
-27913: kbo
-27913: Leaf order:
-27913: nand 12 2 6 0,2
-27913: c 2 0 2 2,2,2,2
-27913: b 3 0 3 1,2,2
-27913: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27914: Facts:
-27914: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-27914: Goal:
-27914: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27914: Order:
-27914: lpo
-27914: Leaf order:
-27914: nand 12 2 6 0,2
-27914: c 2 0 2 2,2,2,2
-27914: b 3 0 3 1,2,2
-27914: a 3 0 3 1,2
-% SZS status Timeout for BOO102-1.p
-NO CLASH, using fixed ground order
-27942: Facts:
-27942: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27942: Goal:
-27942: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27942: Order:
-27942: nrkbo
-27942: Leaf order:
-27942: b 1 0 1 1,2,2
-27942: nand 9 2 3 0,2
-27942: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27943: Facts:
-27943: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27943: Goal:
-27943: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27943: Order:
-27943: kbo
-27943: Leaf order:
-27943: b 1 0 1 1,2,2
-27943: nand 9 2 3 0,2
-27943: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27944: Facts:
-27944: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27944: Goal:
-27944: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27944: Order:
-27944: lpo
-27944: Leaf order:
-27944: b 1 0 1 1,2,2
-27944: nand 9 2 3 0,2
-27944: a 4 0 4 1,1,2
-% SZS status Timeout for BOO103-1.p
-NO CLASH, using fixed ground order
-27963: Facts:
-27963: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27963: Goal:
-27963: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27963: Order:
-27963: nrkbo
-27963: Leaf order:
-27963: nand 12 2 6 0,2
-27963: c 2 0 2 2,2,2,2
-27963: b 3 0 3 1,2,2
-27963: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27964: Facts:
-27964: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27964: Goal:
-27964: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27964: Order:
-27964: kbo
-27964: Leaf order:
-27964: nand 12 2 6 0,2
-27964: c 2 0 2 2,2,2,2
-27964: b 3 0 3 1,2,2
-27964: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-27965: Facts:
-27965: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-27965: Goal:
-27965: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-27965: Order:
-27965: lpo
-27965: Leaf order:
-27965: nand 12 2 6 0,2
-27965: c 2 0 2 2,2,2,2
-27965: b 3 0 3 1,2,2
-27965: a 3 0 3 1,2
-% SZS status Timeout for BOO104-1.p
-NO CLASH, using fixed ground order
-27992: Facts:
-27992: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-27992: Goal:
-27992: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27992: Order:
-27992: nrkbo
-27992: Leaf order:
-27992: b 1 0 1 1,2,2
-27992: nand 9 2 3 0,2
-27992: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27993: Facts:
-27993: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-27993: Goal:
-27993: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27993: Order:
-27993: kbo
-27993: Leaf order:
-27993: b 1 0 1 1,2,2
-27993: nand 9 2 3 0,2
-27993: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-27994: Facts:
-27994: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-27994: Goal:
-27994: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-27994: Order:
-27994: lpo
-27994: Leaf order:
-27994: b 1 0 1 1,2,2
-27994: nand 9 2 3 0,2
-27994: a 4 0 4 1,1,2
-% SZS status Timeout for BOO105-1.p
-NO CLASH, using fixed ground order
-28010: Facts:
-28010: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-28010: Goal:
-28010: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28010: Order:
-28010: nrkbo
-28010: Leaf order:
-28010: nand 12 2 6 0,2
-28010: c 2 0 2 2,2,2,2
-28010: b 3 0 3 1,2,2
-28010: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28011: Facts:
-28011: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-28011: Goal:
-28011: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28011: Order:
-28011: kbo
-28011: Leaf order:
-28011: nand 12 2 6 0,2
-28011: c 2 0 2 2,2,2,2
-28011: b 3 0 3 1,2,2
-28011: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28012: Facts:
-28012: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-28012: Goal:
-28012: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28012: Order:
-28012: lpo
-28012: Leaf order:
-28012: nand 12 2 6 0,2
-28012: c 2 0 2 2,2,2,2
-28012: b 3 0 3 1,2,2
-28012: a 3 0 3 1,2
-% SZS status Timeout for BOO106-1.p
-NO CLASH, using fixed ground order
-28046: Facts:
-28046: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28046: Goal:
-28046: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-28046: Order:
-28046: nrkbo
-28046: Leaf order:
-28046: b 1 0 1 1,2,2
-28046: nand 9 2 3 0,2
-28046: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-28047: Facts:
-28047: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28047: Goal:
-28047: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-28047: Order:
-28047: kbo
-28047: Leaf order:
-28047: b 1 0 1 1,2,2
-28047: nand 9 2 3 0,2
-28047: a 4 0 4 1,1,2
-NO CLASH, using fixed ground order
-28048: Facts:
-28048: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28048: Goal:
-28048: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-28048: Order:
-28048: lpo
-28048: Leaf order:
-28048: b 1 0 1 1,2,2
-28048: nand 9 2 3 0,2
-28048: a 4 0 4 1,1,2
-% SZS status Timeout for BOO107-1.p
-NO CLASH, using fixed ground order
-28069: Facts:
-28069: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28069: Goal:
-28069: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28069: Order:
-28069: nrkbo
-28069: Leaf order:
-28069: nand 12 2 6 0,2
-28069: c 2 0 2 2,2,2,2
-28069: b 3 0 3 1,2,2
-28069: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28070: Facts:
-28070: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28070: Goal:
-28070: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28070: Order:
-28070: kbo
-28070: Leaf order:
-28070: nand 12 2 6 0,2
-28070: c 2 0 2 2,2,2,2
-28070: b 3 0 3 1,2,2
-28070: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28071: Facts:
-28071: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-28071: Goal:
-28071: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-28071: Order:
-28071: lpo
-28071: Leaf order:
-28071: nand 12 2 6 0,2
-28071: c 2 0 2 2,2,2,2
-28071: b 3 0 3 1,2,2
-28071: a 3 0 3 1,2
-% SZS status Timeout for BOO108-1.p
-CLASH, statistics insufficient
-28456: Facts:
-28456: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28456: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28456: Goal:
-28456: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28456: Order:
-28456: nrkbo
-28456: Leaf order:
-28456: b 1 0 0
-28456: s 1 0 0
-28456: apply 14 2 3 0,2
-28456: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28457: Facts:
-28457: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28457: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28457: Goal:
-28457: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28457: Order:
-28457: kbo
-28457: Leaf order:
-28457: b 1 0 0
-28457: s 1 0 0
-28457: apply 14 2 3 0,2
-28457: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28458: Facts:
-28458: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28458: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28458: Goal:
-28458: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28458: Order:
-28458: lpo
-28458: Leaf order:
-28458: b 1 0 0
-28458: s 1 0 0
-28458: apply 14 2 3 0,2
-28458: f 3 1 3 0,2,2
-% SZS status Timeout for COL067-1.p
-CLASH, statistics insufficient
-28873: Facts:
-28873: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28873: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28873: Goal:
-28873: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-28873: Order:
-28873: nrkbo
-28873: Leaf order:
-28873: b 1 0 0
-28873: s 1 0 0
-28873: apply 12 2 1 0,3
-28873: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-28874: Facts:
-28874: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28874: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28874: Goal:
-28874: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-28874: Order:
-28874: kbo
-28874: Leaf order:
-28874: b 1 0 0
-28874: s 1 0 0
-28874: apply 12 2 1 0,3
-28874: combinator 1 0 1 1,3
-CLASH, statistics insufficient
-28875: Facts:
-28875: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-28875: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-28875: Goal:
-28875: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-28875: Order:
-28875: lpo
-28875: Leaf order:
-28875: b 1 0 0
-28875: s 1 0 0
-28875: apply 12 2 1 0,3
-28875: combinator 1 0 1 1,3
-% SZS status Timeout for COL068-1.p
-CLASH, statistics insufficient
-28902: Facts:
-28902: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-28902: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-28902: Goal:
-28902: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28902: Order:
-28902: nrkbo
-28902: Leaf order:
-28902: l 1 0 0
-28902: b 1 0 0
-28902: apply 12 2 3 0,2
-28902: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28903: Facts:
-28903: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-28903: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-28903: Goal:
-28903: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28903: Order:
-28903: kbo
-28903: Leaf order:
-28903: l 1 0 0
-28903: b 1 0 0
-28903: apply 12 2 3 0,2
-28903: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28904: Facts:
-28904: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-28904: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-28904: Goal:
-28904: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-28904: Order:
-28904: lpo
-28904: Leaf order:
-28904: l 1 0 0
-28904: b 1 0 0
-28904: apply 12 2 3 0,2
-28904: f 3 1 3 0,2,2
-% SZS status Timeout for COL069-1.p
-CLASH, statistics insufficient
-28921: Facts:
-28921: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-28921: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-28921: Goal:
-28921: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-28921: Order:
-28921: nrkbo
-28921: Leaf order:
-28921: m 1 0 0
-28921: b 1 0 0
-28921: apply 10 2 3 0,2
-28921: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28922: Facts:
-28922: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-28922: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-28922: Goal:
-28922: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-28922: Order:
-28922: kbo
-28922: Leaf order:
-28922: m 1 0 0
-28922: b 1 0 0
-28922: apply 10 2 3 0,2
-28922: f 3 1 3 0,2,2
-CLASH, statistics insufficient
-28923: Facts:
-28923: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-28923: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-28923: Goal:
-28923: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-28923: Order:
-28923: lpo
-28923: Leaf order:
-28923: m 1 0 0
-28923: b 1 0 0
-28923: apply 10 2 3 0,2
-28923: f 3 1 3 0,2,2
-% SZS status Timeout for COL087-1.p
-NO CLASH, using fixed ground order
-28951: Facts:
-28951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-28951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-28951: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-28951: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-28951: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-28951: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-28951: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-28951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-28951: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-28951: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-28951: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-28951: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-28951: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-28951: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-28951: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-28951: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-28951: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-28951: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-28951: Goal:
-28951: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-28951: Order:
-28951: nrkbo
-28951: Leaf order:
-28951: inverse 1 1 0
-28951: identity 5 0 0
-28951: least_upper_bound 17 2 1 0,2
-28951: greatest_lower_bound 18 2 5 0,1,2
-28951: multiply 21 2 3 0,2,1,2
-28951: c 5 0 3 2,2,1,2
-28951: b 5 0 3 1,2,1,2
-28951: a 7 0 5 1,1,2
-NO CLASH, using fixed ground order
-28952: Facts:
-28952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-28952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-28952: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-28952: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-28952: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-28952: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-28952: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-28952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-28952: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-28952: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-28952: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-28952: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-28952: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-28952: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-28952: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-28952: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-28952: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-28952: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-28952: Goal:
-28952: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-28952: Order:
-28952: kbo
-28952: Leaf order:
-28952: inverse 1 1 0
-28952: identity 5 0 0
-28952: least_upper_bound 17 2 1 0,2
-28952: greatest_lower_bound 18 2 5 0,1,2
-28952: multiply 21 2 3 0,2,1,2
-28952: c 5 0 3 2,2,1,2
-28952: b 5 0 3 1,2,1,2
-28952: a 7 0 5 1,1,2
-NO CLASH, using fixed ground order
-28953: Facts:
-28953: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-28953: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-28953: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-28953: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-28953: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-28953: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-28953: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-28953: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-28953: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-28953: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-28953: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-28953: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-28953: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-28953: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-28953: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-28953: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-28953: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-28953: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-28953: Goal:
-28953: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-28953: Order:
-28953: lpo
-28953: Leaf order:
-28953: inverse 1 1 0
-28953: identity 5 0 0
-28953: least_upper_bound 17 2 1 0,2
-28953: greatest_lower_bound 18 2 5 0,1,2
-28953: multiply 21 2 3 0,2,1,2
-28953: c 5 0 3 2,2,1,2
-28953: b 5 0 3 1,2,1,2
-28953: a 7 0 5 1,1,2
-% SZS status Timeout for GRP177-1.p
-NO CLASH, using fixed ground order
-28970: Facts:
-28970: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-28970: Goal:
-28970: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-28970: Order:
-28970: nrkbo
-28970: Leaf order:
-28970: f 17 2 8 0,2
-28970: c 3 0 3 2,1,2,2
-28970: b 4 0 4 1,1,2,2
-28970: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28971: Facts:
-28971: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-28971: Goal:
-28971: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-28971: Order:
-28971: kbo
-28971: Leaf order:
-28971: f 17 2 8 0,2
-28971: c 3 0 3 2,1,2,2
-28971: b 4 0 4 1,1,2,2
-28971: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-28972: Facts:
-28972: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-28972: Goal:
-28972: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-28972: Order:
-28972: lpo
-28972: Leaf order:
-28972: f 17 2 8 0,2
-28972: c 3 0 3 2,1,2,2
-28972: b 4 0 4 1,1,2,2
-28972: a 3 0 3 1,2
-% SZS status Timeout for LAT071-1.p
-NO CLASH, using fixed ground order
-29000: Facts:
-29000: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-29000: Goal:
-29000: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29000: Order:
-29000: nrkbo
-29000: Leaf order:
-29000: f 18 2 8 0,2
-29000: c 3 0 3 2,1,2,2
-29000: b 4 0 4 1,1,2,2
-29000: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29001: Facts:
-29001: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-29001: Goal:
-29001: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29001: Order:
-29001: kbo
-29001: Leaf order:
-29001: f 18 2 8 0,2
-29001: c 3 0 3 2,1,2,2
-29001: b 4 0 4 1,1,2,2
-29001: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29002: Facts:
-29002: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-29002: Goal:
-29002: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-29002: Order:
-29002: lpo
-29002: Leaf order:
-29002: f 18 2 8 0,2
-29002: c 3 0 3 2,1,2,2
-29002: b 4 0 4 1,1,2,2
-29002: a 3 0 3 1,2
-% SZS status Timeout for LAT072-1.p
-NO CLASH, using fixed ground order
-29018: Facts:
-29018: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-29018: Goal:
-29018: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-29018: Order:
-29018: nrkbo
-29018: Leaf order:
-29018: f 18 2 8 0,2
-29018: c 3 0 3 1,2,2,2,2
-29018: b 3 0 3 1,2,2
-29018: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29019: Facts:
-29019: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-29019: Goal:
-29019: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-29019: Order:
-29019: kbo
-29019: Leaf order:
-29019: f 18 2 8 0,2
-29019: c 3 0 3 1,2,2,2,2
-29019: b 3 0 3 1,2,2
-29019: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29020: Facts:
-29020: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-29020: Goal:
-29020: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-29020: Order:
-29020: lpo
-29020: Leaf order:
-29020: f 18 2 8 0,2
-29020: c 3 0 3 1,2,2,2,2
-29020: b 3 0 3 1,2,2
-29020: a 4 0 4 1,2
-% SZS status Timeout for LAT073-1.p
-NO CLASH, using fixed ground order
-29047: Facts:
-29047: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29047: Goal:
-29047: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29047: Order:
-29047: nrkbo
-29047: Leaf order:
-29047: f 19 2 8 0,2
-29047: c 3 0 3 2,1,2,2
-29047: b 4 0 4 1,1,2,2
-29047: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29048: Facts:
-29048: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29048: Goal:
-29048: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29048: Order:
-29048: kbo
-29048: Leaf order:
-29048: f 19 2 8 0,2
-29048: c 3 0 3 2,1,2,2
-29048: b 4 0 4 1,1,2,2
-29048: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29049: Facts:
-29049: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29049: Goal:
-29049: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-29049: Order:
-29049: lpo
-29049: Leaf order:
-29049: f 19 2 8 0,2
-29049: c 3 0 3 2,1,2,2
-29049: b 4 0 4 1,1,2,2
-29049: a 3 0 3 1,2
-% SZS status Timeout for LAT074-1.p
-NO CLASH, using fixed ground order
-29065: Facts:
-29065: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29065: Goal:
-29065: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-29065: Order:
-29065: nrkbo
-29065: Leaf order:
-29065: f 19 2 8 0,2
-29065: c 3 0 3 1,2,2,2,2
-29065: b 3 0 3 1,2,2
-29065: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29066: Facts:
-29066: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29066: Goal:
-29066: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-29066: Order:
-29066: kbo
-29066: Leaf order:
-29066: f 19 2 8 0,2
-29066: c 3 0 3 1,2,2,2,2
-29066: b 3 0 3 1,2,2
-29066: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29067: Facts:
-29067: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-29067: Goal:
-29067: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-29067: Order:
-29067: lpo
-29067: Leaf order:
-29067: f 19 2 8 0,2
-29067: c 3 0 3 1,2,2,2,2
-29067: b 3 0 3 1,2,2
-29067: a 4 0 4 1,2
-% SZS status Timeout for LAT075-1.p
-NO CLASH, using fixed ground order
-29098: Facts:
-29098: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29098: Goal:
-29098: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29098: Order:
-29098: nrkbo
-29098: Leaf order:
-29098: f 20 2 8 0,2
-29098: c 3 0 3 2,1,2,2
-29098: b 4 0 4 1,1,2,2
-29098: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29099: Facts:
-29099: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29099: Goal:
-29099: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29099: Order:
-29099: kbo
-29099: Leaf order:
-29099: f 20 2 8 0,2
-29099: c 3 0 3 2,1,2,2
-29099: b 4 0 4 1,1,2,2
-29099: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29100: Facts:
-29100: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29100: Goal:
-29100: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-29100: Order:
-29100: lpo
-29100: Leaf order:
-29100: f 20 2 8 0,2
-29100: c 3 0 3 2,1,2,2
-29100: b 4 0 4 1,1,2,2
-29100: a 3 0 3 1,2
-% SZS status Timeout for LAT076-1.p
-NO CLASH, using fixed ground order
-29161: Facts:
-NO CLASH, using fixed ground order
-29162: Facts:
-29162: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29162: Goal:
-29162: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-29162: Order:
-29162: kbo
-29162: Leaf order:
-29162: f 20 2 8 0,2
-29162: c 3 0 3 1,2,2,2,2
-29162: b 3 0 3 1,2,2
-29162: a 4 0 4 1,2
-29161: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29161: Goal:
-29161: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-29161: Order:
-29161: nrkbo
-29161: Leaf order:
-29161: f 20 2 8 0,2
-29161: c 3 0 3 1,2,2,2,2
-29161: b 3 0 3 1,2,2
-29161: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29163: Facts:
-29163: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-29163: Goal:
-29163: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-29163: Order:
-29163: lpo
-29163: Leaf order:
-29163: f 20 2 8 0,2
-29163: c 3 0 3 1,2,2,2,2
-29163: b 3 0 3 1,2,2
-29163: a 4 0 4 1,2
-% SZS status Timeout for LAT077-1.p
-NO CLASH, using fixed ground order
-29191: Facts:
-29191: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29191: Goal:
-29191: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29191: Order:
-29191: nrkbo
-29191: Leaf order:
-29191: f 20 2 8 0,2
-29191: c 3 0 3 2,1,2,2
-29191: b 4 0 4 1,1,2,2
-29191: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29192: Facts:
-29192: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29192: Goal:
-29192: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-29192: Order:
-29192: kbo
-29192: Leaf order:
-29192: f 20 2 8 0,2
-29192: c 3 0 3 2,1,2,2
-29192: b 4 0 4 1,1,2,2
-29192: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29193: Facts:
-29193: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29193: Goal:
-29193: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-29193: Order:
-29193: lpo
-29193: Leaf order:
-29193: f 20 2 8 0,2
-29193: c 3 0 3 2,1,2,2
-29193: b 4 0 4 1,1,2,2
-29193: a 3 0 3 1,2
-% SZS status Timeout for LAT078-1.p
-NO CLASH, using fixed ground order
-29210: Facts:
-29210: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29210: Goal:
-29210: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-29210: Order:
-29210: nrkbo
-29210: Leaf order:
-29210: f 20 2 8 0,2
-29210: c 3 0 3 1,2,2,2,2
-29210: b 3 0 3 1,2,2
-29210: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29211: Facts:
-29211: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29211: Goal:
-29211: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-29211: Order:
-29211: kbo
-29211: Leaf order:
-29211: f 20 2 8 0,2
-29211: c 3 0 3 1,2,2,2,2
-29211: b 3 0 3 1,2,2
-29211: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29212: Facts:
-29212: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-29212: Goal:
-29212: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-29212: Order:
-29212: lpo
-29212: Leaf order:
-29212: f 20 2 8 0,2
-29212: c 3 0 3 1,2,2,2,2
-29212: b 3 0 3 1,2,2
-29212: a 4 0 4 1,2
-% SZS status Timeout for LAT079-1.p
-NO CLASH, using fixed ground order
-29240: Facts:
-29240: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29240: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29240: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29240: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29240: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29240: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29240: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29240: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29240: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-29240: Goal:
-29240: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-29240: Order:
-29240: nrkbo
-29240: Leaf order:
-29240: join 16 2 3 0,2,2
-29240: meet 20 2 5 0,2
-29240: c 3 0 3 2,2,2,2
-29240: b 3 0 3 1,2,2
-29240: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29241: Facts:
-29241: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29241: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29241: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29241: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29241: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29241: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29241: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29241: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29241: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-29241: Goal:
-29241: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-29241: Order:
-29241: kbo
-29241: Leaf order:
-29241: join 16 2 3 0,2,2
-29241: meet 20 2 5 0,2
-29241: c 3 0 3 2,2,2,2
-29241: b 3 0 3 1,2,2
-29241: a 4 0 4 1,2
-NO CLASH, using fixed ground order
-29242: Facts:
-29242: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29242: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29242: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29242: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29242: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29242: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29242: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29242: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29242: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-29242: Goal:
-29242: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-29242: Order:
-29242: lpo
-29242: Leaf order:
-29242: join 16 2 3 0,2,2
-29242: meet 20 2 5 0,2
-29242: c 3 0 3 2,2,2,2
-29242: b 3 0 3 1,2,2
-29242: a 4 0 4 1,2
-% SZS status Timeout for LAT139-1.p
-NO CLASH, using fixed ground order
-29258: Facts:
-29258: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29258: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29258: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29258: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29258: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29258: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29258: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29258: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29258: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-29258: Goal:
-29258: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29258: Order:
-29258: nrkbo
-29258: Leaf order:
-29258: join 17 2 4 0,2,2
-29258: meet 21 2 6 0,2
-29258: c 3 0 3 2,2,2,2
-29258: b 3 0 3 1,2,2
-29258: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-29259: Facts:
-29259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29259: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29259: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29259: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29259: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29259: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-29259: Goal:
-29259: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29259: Order:
-29259: kbo
-29259: Leaf order:
-29259: join 17 2 4 0,2,2
-29259: meet 21 2 6 0,2
-29259: c 3 0 3 2,2,2,2
-NO CLASH, using fixed ground order
-29260: Facts:
-29260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29260: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29260: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29260: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29260: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29260: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-29260: Goal:
-29260: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29260: Order:
-29260: lpo
-29260: Leaf order:
-29260: join 17 2 4 0,2,2
-29260: meet 21 2 6 0,2
-29260: c 3 0 3 2,2,2,2
-29260: b 3 0 3 1,2,2
-29260: a 6 0 6 1,2
-29259: b 3 0 3 1,2,2
-29259: a 6 0 6 1,2
-% SZS status Timeout for LAT141-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-29297: Facts:
-29297: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29297: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29297: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29297: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29297: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29297: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29297: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29297: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29297: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-29297: Goal:
-29297: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-29297: Order:
-29297: kbo
-29297: Leaf order:
-29297: meet 18 2 5 0,2
-29297: d 2 0 2 2,2,2,2
-29297: join 18 2 5 0,1,2,2
-29297: c 2 0 2 2,1,2,2
-29297: b 5 0 5 1,1,2,2
-29297: a 3 0 3 1,2
-29296: Facts:
-29296: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29296: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29296: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29296: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29296: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29296: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29296: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29296: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29296: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-29296: Goal:
-29296: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-29296: Order:
-29296: nrkbo
-29296: Leaf order:
-29296: meet 18 2 5 0,2
-29296: d 2 0 2 2,2,2,2
-29296: join 18 2 5 0,1,2,2
-29296: c 2 0 2 2,1,2,2
-29296: b 5 0 5 1,1,2,2
-29296: a 3 0 3 1,2
-NO CLASH, using fixed ground order
-29298: Facts:
-29298: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29298: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29298: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29298: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29298: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29298: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29298: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29298: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29298: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-29298: Goal:
-29298: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-29298: Order:
-29298: lpo
-29298: Leaf order:
-29298: meet 18 2 5 0,2
-29298: d 2 0 2 2,2,2,2
-29298: join 18 2 5 0,1,2,2
-29298: c 2 0 2 2,1,2,2
-29298: b 5 0 5 1,1,2,2
-29298: a 3 0 3 1,2
-% SZS status Timeout for LAT161-1.p
-NO CLASH, using fixed ground order
-29316: Facts:
-29316: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29316: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29316: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29316: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29316: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29316: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29316: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29316: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29316: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-29316: Goal:
-29316: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29316: Order:
-29316: nrkbo
-29316: Leaf order:
-29316: join 19 2 4 0,2,2
-29316: meet 19 2 6 0,2
-29316: c 3 0 3 2,2,2,2
-29316: b 3 0 3 1,2,2
-29316: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-29317: Facts:
-29317: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29317: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29317: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29317: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29317: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29317: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29317: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29317: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29317: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-29317: Goal:
-29317: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29317: Order:
-29317: kbo
-29317: Leaf order:
-29317: join 19 2 4 0,2,2
-29317: meet 19 2 6 0,2
-29317: c 3 0 3 2,2,2,2
-29317: b 3 0 3 1,2,2
-29317: a 6 0 6 1,2
-NO CLASH, using fixed ground order
-29318: Facts:
-29318: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29318: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29318: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29318: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29318: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29318: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29318: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29318: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29318: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-29318: Goal:
-29318: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29318: Order:
-29318: lpo
-29318: Leaf order:
-29318: join 19 2 4 0,2,2
-29318: meet 19 2 6 0,2
-29318: c 3 0 3 2,2,2,2
-29318: b 3 0 3 1,2,2
-29318: a 6 0 6 1,2
-% SZS status Timeout for LAT177-1.p
-NO CLASH, using fixed ground order
-29346: Facts:
-29346: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-29346: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-NO CLASH, using fixed ground order
-29347: Facts:
-29347: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-29347: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-29347: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-29347: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-29347: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-29347: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-29347: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-29347: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-29347: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =>=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-29347: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-29347: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-29347: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-29347: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-NO CLASH, using fixed ground order
-29346: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-29346: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-29346: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-29346: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-29346: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-29345: Facts:
-29346: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-29346: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =<=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-29345: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-29345: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-29346: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-29345: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-29346: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-29345: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-29346: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-29346: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-29346: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =<=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-29345: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-29345: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-29345: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-29346: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =<=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-29345: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-29346: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =<=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-29345: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =<=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-29346: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =<=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-29345: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-29345: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-29345: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-29345: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-29345: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =<=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-29345: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =<=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-29345: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =<=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-29345: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =<=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-29345: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-29347: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =<=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-29345: Id : 20, {_}:
- associator ?50 ?51 ?52
- =<=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-29345: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-29347: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =<=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-29347: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =<=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-29347: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =<=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-29347: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-29347: Id : 20, {_}:
- associator ?50 ?51 ?52
- =<=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-29347: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-29347: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-29347: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-29347: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =>=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-29347: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =<=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-29347: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =>=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-29347: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =<=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-29347: Goal:
-29347: Id : 1, {_}:
- s a b c d =>= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29347: Order:
-29347: lpo
-29347: Leaf order:
-29347: commutator 1 2 0
-29347: associator 6 3 0
-29347: multiply 51 2 0
-29347: additive_identity 11 0 0
-29347: add 22 2 0
-29347: additive_inverse 20 1 1 0,3
-29347: s 3 4 2 0,2
-29347: d 2 0 2 4,2
-29347: c 2 0 2 3,2
-29347: b 2 0 2 2,2
-29347: a 2 0 2 1,2
-29346: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-29345: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-29345: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-29345: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =<=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-29345: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =?=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-29345: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =?=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-29345: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =?=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-29345: Goal:
-29345: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29345: Order:
-29345: nrkbo
-29345: Leaf order:
-29345: commutator 1 2 0
-29345: associator 6 3 0
-29345: multiply 51 2 0
-29345: additive_identity 11 0 0
-29345: add 22 2 0
-29345: additive_inverse 20 1 1 0,3
-29345: s 3 4 2 0,2
-29345: d 2 0 2 4,2
-29345: c 2 0 2 3,2
-29345: b 2 0 2 2,2
-29345: a 2 0 2 1,2
-29346: Id : 20, {_}:
- associator ?50 ?51 ?52
- =<=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-29346: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-29346: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-29346: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-29346: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =<=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-29346: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =<=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-29346: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =>=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-29346: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =<=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-29346: Goal:
-29346: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29346: Order:
-29346: kbo
-29346: Leaf order:
-29346: commutator 1 2 0
-29346: associator 6 3 0
-29346: multiply 51 2 0
-29346: additive_identity 11 0 0
-29346: add 22 2 0
-29346: additive_inverse 20 1 1 0,3
-29346: s 3 4 2 0,2
-29346: d 2 0 2 4,2
-29346: c 2 0 2 3,2
-29346: b 2 0 2 2,2
-29346: a 2 0 2 1,2
-% SZS status Timeout for RNG010-5.p
-NO CLASH, using fixed ground order
-29364: Facts:
-29364: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29364: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29364: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29364: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29364: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29364: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29364: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29364: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29364: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29364: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29364: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29364: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29364: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29364: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29364: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29364: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =<=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-29364: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =<=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-29364: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =>=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-29364: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =<=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-29364: Goal:
-29364: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29364: Order:
-29364: kbo
-29364: Leaf order:
-29364: commutator 1 2 0
-29364: associator 4 3 0
-29364: multiply 43 2 0
-29364: add 18 2 0
-29364: additive_identity 8 0 0
-29364: additive_inverse 9 1 1 0,3
-29364: s 3 4 2 0,2
-29364: d 2 0 2 4,2
-29364: c 2 0 2 3,2
-29364: b 2 0 2 2,2
-29364: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-29363: Facts:
-29363: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29363: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29363: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29363: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29363: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29363: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29363: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29363: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29363: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29363: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29363: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29363: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29363: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29363: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29363: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29363: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =<=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-29363: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =?=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-29363: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =?=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-29363: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =?=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-29363: Goal:
-29363: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29363: Order:
-29363: nrkbo
-29363: Leaf order:
-29363: commutator 1 2 0
-29363: associator 4 3 0
-29363: multiply 43 2 0
-29363: add 18 2 0
-29363: additive_identity 8 0 0
-29363: additive_inverse 9 1 1 0,3
-29363: s 3 4 2 0,2
-29363: d 2 0 2 4,2
-29363: c 2 0 2 3,2
-29363: b 2 0 2 2,2
-29363: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-29365: Facts:
-29365: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29365: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29365: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29365: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29365: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29365: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29365: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29365: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29365: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29365: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29365: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29365: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29365: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29365: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29365: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29365: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =>=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-29365: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =<=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-29365: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =>=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-29365: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =<=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-29365: Goal:
-29365: Id : 1, {_}:
- s a b c d =>= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29365: Order:
-29365: lpo
-29365: Leaf order:
-29365: commutator 1 2 0
-29365: associator 4 3 0
-29365: multiply 43 2 0
-29365: add 18 2 0
-29365: additive_identity 8 0 0
-29365: additive_inverse 9 1 1 0,3
-29365: s 3 4 2 0,2
-29365: d 2 0 2 4,2
-29365: c 2 0 2 3,2
-29365: b 2 0 2 2,2
-29365: a 2 0 2 1,2
-% SZS status Timeout for RNG010-6.p
-NO CLASH, using fixed ground order
-29396: Facts:
-29396: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29396: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29396: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29396: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29396: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29396: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29396: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29396: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29396: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29396: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29396: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29396: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29396: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29396: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29396: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29396: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29396: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =<=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29396: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =<=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29396: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29396: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29396: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29396: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29396: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =<=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-29396: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =?=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-29396: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =?=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-29396: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =?=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-29396: Goal:
-29396: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29396: Order:
-29396: nrkbo
-29396: Leaf order:
-29396: commutator 1 2 0
-29396: associator 4 3 0
-29396: multiply 61 2 0
-29396: add 26 2 0
-29396: additive_identity 8 0 0
-29396: additive_inverse 25 1 1 0,3
-29396: s 3 4 2 0,2
-29396: d 2 0 2 4,2
-29396: c 2 0 2 3,2
-29396: b 2 0 2 2,2
-29396: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-29397: Facts:
-29397: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29397: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29397: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29397: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29397: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29397: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29397: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29397: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29397: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29397: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29397: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29397: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29397: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29397: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29397: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29397: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29397: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =<=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29397: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =<=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29397: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29397: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29397: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29397: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29397: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =<=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-29397: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =<=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-29397: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =>=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-29397: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =<=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-29397: Goal:
-29397: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29397: Order:
-29397: kbo
-29397: Leaf order:
-29397: commutator 1 2 0
-29397: associator 4 3 0
-29397: multiply 61 2 0
-29397: add 26 2 0
-29397: additive_identity 8 0 0
-29397: additive_inverse 25 1 1 0,3
-29397: s 3 4 2 0,2
-29397: d 2 0 2 4,2
-29397: c 2 0 2 3,2
-29397: b 2 0 2 2,2
-29397: a 2 0 2 1,2
-NO CLASH, using fixed ground order
-29398: Facts:
-29398: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29398: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29398: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29398: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29398: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29398: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29398: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29398: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29398: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29398: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29398: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29398: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29398: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29398: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29398: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29398: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29398: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =<=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29398: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =<=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29398: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29398: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29398: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29398: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29398: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =>=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-29398: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =<=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-29398: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =>=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-29398: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =<=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-29398: Goal:
-29398: Id : 1, {_}:
- s a b c d =>= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-29398: Order:
-29398: lpo
-29398: Leaf order:
-29398: commutator 1 2 0
-29398: associator 4 3 0
-29398: multiply 61 2 0
-29398: add 26 2 0
-29398: additive_identity 8 0 0
-29398: additive_inverse 25 1 1 0,3
-29398: s 3 4 2 0,2
-29398: d 2 0 2 4,2
-29398: c 2 0 2 3,2
-29398: b 2 0 2 2,2
-29398: a 2 0 2 1,2
-% SZS status Timeout for RNG010-7.p
-NO CLASH, using fixed ground order
-29437: Facts:
-29437: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29437: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29437: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29437: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29437: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29437: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29437: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29437: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29437: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29437: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29437: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29437: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29437: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29437: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29437: Goal:
-29437: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29437: Order:
-29437: nrkbo
-29437: Leaf order:
-29437: commutator 1 2 0
-29437: additive_inverse 6 1 0
-29437: additive_identity 9 0 1 3
-29437: add 17 2 1 0,2
-29437: multiply 22 2 4 0,1,2
-29437: associator 7 3 6 0,1,1,2
-29437: y 6 0 6 3,1,1,2
-29437: x 12 0 12 1,1,1,2
-NO CLASH, using fixed ground order
-29438: Facts:
-29438: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29438: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29438: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29438: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29438: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29438: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29438: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29438: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29438: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29438: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29438: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29438: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29438: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29438: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29438: Goal:
-29438: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29438: Order:
-29438: kbo
-29438: Leaf order:
-29438: commutator 1 2 0
-29438: additive_inverse 6 1 0
-29438: additive_identity 9 0 1 3
-29438: add 17 2 1 0,2
-29438: multiply 22 2 4 0,1,2
-29438: associator 7 3 6 0,1,1,2
-29438: y 6 0 6 3,1,1,2
-29438: x 12 0 12 1,1,1,2
-NO CLASH, using fixed ground order
-29439: Facts:
-29439: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29439: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29439: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29439: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29439: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29439: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29439: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29439: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29439: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29439: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29439: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29439: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29439: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29439: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29439: Goal:
-29439: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29439: Order:
-29439: lpo
-29439: Leaf order:
-29439: commutator 1 2 0
-29439: additive_inverse 6 1 0
-29439: additive_identity 9 0 1 3
-29439: add 17 2 1 0,2
-29439: multiply 22 2 4 0,1,2
-29439: associator 7 3 6 0,1,1,2
-29439: y 6 0 6 3,1,1,2
-29439: x 12 0 12 1,1,1,2
-% SZS status Timeout for RNG030-6.p
-NO CLASH, using fixed ground order
-29722: Facts:
-29722: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29722: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29722: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29722: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29722: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29722: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29722: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29722: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29722: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29722: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29722: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29722: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29722: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29722: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29722: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29722: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29722: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29722: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29722: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29722: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29722: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29722: Goal:
-29722: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29722: Order:
-29722: nrkbo
-29722: Leaf order:
-29722: commutator 1 2 0
-29722: additive_inverse 22 1 0
-29722: additive_identity 9 0 1 3
-29722: add 25 2 1 0,2
-29722: multiply 40 2 4 0,1,2add
-29722: associator 7 3 6 0,1,1,2
-29722: y 6 0 6 3,1,1,2
-29722: x 12 0 12 1,1,1,2
-NO CLASH, using fixed ground order
-29723: Facts:
-29723: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29723: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29723: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29723: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29723: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29723: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29723: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29723: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29723: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29723: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29723: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29723: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29723: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29723: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29723: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29723: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29723: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29723: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29723: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29723: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29723: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29723: Goal:
-29723: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29723: Order:
-29723: kbo
-29723: Leaf order:
-29723: commutator 1 2 0
-29723: additive_inverse 22 1 0
-29723: additive_identity 9 0 1 3
-29723: add 25 2 1 0,2
-29723: multiply 40 2 4 0,1,2add
-29723: associator 7 3 6 0,1,1,2
-29723: y 6 0 6 3,1,1,2
-29723: x 12 0 12 1,1,1,2
-NO CLASH, using fixed ground order
-29724: Facts:
-29724: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29724: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29724: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29724: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29724: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29724: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29724: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29724: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29724: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29724: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29724: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29724: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29724: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29724: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29724: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29724: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29724: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29724: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29724: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29724: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29724: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29724: Goal:
-29724: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-29724: Order:
-29724: lpo
-29724: Leaf order:
-29724: commutator 1 2 0
-29724: additive_inverse 22 1 0
-29724: additive_identity 9 0 1 3
-29724: add 25 2 1 0,2
-29724: multiply 40 2 4 0,1,2add
-29724: associator 7 3 6 0,1,1,2
-29724: y 6 0 6 3,1,1,2
-29724: x 12 0 12 1,1,1,2
-% SZS status Timeout for RNG030-7.p
-NO CLASH, using fixed ground order
-29762: Facts:
-29762: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29762: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29762: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29762: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29762: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29762: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29762: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29762: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29762: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29762: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29762: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29762: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29762: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29762: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29762: Goal:
-29762: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29762: Order:
-29762: nrkbo
-29762: Leaf order:
-29762: commutator 1 2 0
-29762: additive_inverse 6 1 0
-29762: additive_identity 9 0 1 3
-29762: add 21 2 5 0,2
-29762: multiply 30 2 12 0,1,1,1,1,1,2
-29762: associator 19 3 18 0,1,1,1,1,1,1,2
-29762: y 18 0 18 3,1,1,1,1,1,1,2
-29762: x 36 0 36 1,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-29763: Facts:
-29763: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29763: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29763: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29763: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29763: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29763: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29763: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-NO CLASH, using fixed ground order
-29764: Facts:
-29764: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29764: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29764: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29764: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29764: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29764: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29764: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29764: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29764: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29764: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29764: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29764: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29764: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29764: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29764: Goal:
-29764: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29764: Order:
-29764: lpo
-29764: Leaf order:
-29764: commutator 1 2 0
-29764: additive_inverse 6 1 0
-29764: additive_identity 9 0 1 3
-29764: add 21 2 5 0,2
-29764: multiply 30 2 12 0,1,1,1,1,1,2
-29764: associator 19 3 18 0,1,1,1,1,1,1,2
-29764: y 18 0 18 3,1,1,1,1,1,1,2
-29764: x 36 0 36 1,1,1,1,1,1,1,2
-29763: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29763: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29763: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29763: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29763: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29763: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-29763: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-29763: Goal:
-29763: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29763: Order:
-29763: kbo
-29763: Leaf order:
-29763: commutator 1 2 0
-29763: additive_inverse 6 1 0
-29763: additive_identity 9 0 1 3
-29763: add 21 2 5 0,2
-29763: multiply 30 2 12 0,1,1,1,1,1,2
-29763: associator 19 3 18 0,1,1,1,1,1,1,2
-29763: y 18 0 18 3,1,1,1,1,1,1,2
-29763: x 36 0 36 1,1,1,1,1,1,1,2
-% SZS status Timeout for RNG032-6.p
-NO CLASH, using fixed ground order
-29792: Facts:
-29792: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29792: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29792: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29792: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29792: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29792: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29792: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29792: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29792: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29792: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29792: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29792: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29792: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29792: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29792: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29792: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29792: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29792: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29792: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29792: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29792: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29792: Goal:
-29792: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29792: Order:
-29792: nrkbo
-29792: Leaf order:
-29792: commutator 1 2 0
-29792: additive_inverse 22 1 0
-29792: additive_identity 9 0 1 3
-29792: add 29 2 5 0,2
-29792: multiply 48 2 12 0,1,1,1,1,1,2add
-29792: associator 19 3 18 0,1,1,1,1,1,1,2
-29792: y 18 0 18 3,1,1,1,1,1,1,2
-29792: x 36 0 36 1,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-29793: Facts:
-29793: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29793: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29793: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29793: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29793: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29793: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29793: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29793: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29793: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29793: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29793: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29793: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29793: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29793: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29793: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29793: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29793: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29793: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29793: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29793: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29793: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29793: Goal:
-29793: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29793: Order:
-29793: kbo
-29793: Leaf order:
-29793: commutator 1 2 0
-29793: additive_inverse 22 1 0
-29793: additive_identity 9 0 1 3
-29793: add 29 2 5 0,2
-29793: multiply 48 2 12 0,1,1,1,1,1,2add
-29793: associator 19 3 18 0,1,1,1,1,1,1,2
-29793: y 18 0 18 3,1,1,1,1,1,1,2
-29793: x 36 0 36 1,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-29794: Facts:
-29794: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29794: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29794: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29794: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29794: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29794: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29794: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29794: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29794: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29794: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29794: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29794: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29794: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29794: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29794: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29794: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29794: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29794: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29794: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29794: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-29794: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-29794: Goal:
-29794: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-29794: Order:
-29794: lpo
-29794: Leaf order:
-29794: commutator 1 2 0
-29794: additive_inverse 22 1 0
-29794: additive_identity 9 0 1 3
-29794: add 29 2 5 0,2
-29794: multiply 48 2 12 0,1,1,1,1,1,2add
-29794: associator 19 3 18 0,1,1,1,1,1,1,2
-29794: y 18 0 18 3,1,1,1,1,1,1,2
-29794: x 36 0 36 1,1,1,1,1,1,1,2
-% SZS status Timeout for RNG032-7.p
-NO CLASH, using fixed ground order
-29810: Facts:
-29810: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29810: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29810: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29810: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29810: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29810: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29810: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29810: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29810: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29810: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29810: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29810: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29810: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29810: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29810: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29810: Goal:
-29810: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29810: Order:
-29810: nrkbo
-29810: Leaf order:
-29810: additive_inverse 6 1 0
-29810: additive_identity 8 0 0
-29810: add 18 2 2 0,2
-29810: commutator 2 2 1 0,3,2,2
-29810: associator 5 3 4 0,1,2
-29810: w 4 0 4 3,1,2
-29810: z 4 0 4 2,1,2
-29810: multiply 25 2 3 0,1,1,2
-29810: y 4 0 4 2,1,1,2
-29810: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29811: Facts:
-29811: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29811: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29811: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29811: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29811: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29811: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29811: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29811: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29811: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29811: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29811: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29811: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29811: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29811: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29811: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29811: Goal:
-29811: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29811: Order:
-29811: kbo
-29811: Leaf order:
-29811: additive_inverse 6 1 0
-29811: additive_identity 8 0 0
-29811: add 18 2 2 0,2
-29811: commutator 2 2 1 0,3,2,2
-29811: associator 5 3 4 0,1,2
-29811: w 4 0 4 3,1,2
-29811: z 4 0 4 2,1,2
-29811: multiply 25 2 3 0,1,1,2
-29811: y 4 0 4 2,1,1,2
-29811: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29812: Facts:
-29812: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29812: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29812: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29812: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29812: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29812: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29812: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29812: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29812: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29812: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29812: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29812: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29812: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29812: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29812: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29812: Goal:
-29812: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29812: Order:
-29812: lpo
-29812: Leaf order:
-29812: additive_inverse 6 1 0
-29812: additive_identity 8 0 0
-29812: add 18 2 2 0,2
-29812: commutator 2 2 1 0,3,2,2
-29812: associator 5 3 4 0,1,2
-29812: w 4 0 4 3,1,2
-29812: z 4 0 4 2,1,2
-29812: multiply 25 2 3 0,1,1,2
-29812: y 4 0 4 2,1,1,2
-29812: x 4 0 4 1,1,1,2
-% SZS status Timeout for RNG033-6.p
-NO CLASH, using fixed ground order
-29844: Facts:
-29844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29844: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29844: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29844: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29844: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29844: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29844: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29844: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29844: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29844: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29844: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29844: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29844: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29844: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29844: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29844: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29844: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29844: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29844: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29844: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29844: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29844: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29844: Goal:
-29844: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29844: Order:
-29844: nrkbo
-29844: Leaf order:
-29844: additive_inverse 22 1 0
-29844: additive_identity 8 0 0
-29844: add 26 2 2 0,2
-29844: commutator 2 2 1 0,3,2,2
-29844: associator 5 3 4 0,1,2
-29844: w 4 0 4 3,1,2
-29844: z 4 0 4 2,1,2
-29844: multiply 43 2 3 0,1,1,2
-29844: y 4 0 4 2,1,1,2
-29844: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29846: Facts:
-29846: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29846: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29846: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29846: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29846: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29846: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29846: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29846: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29846: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29846: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29846: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29846: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29846: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29846: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29846: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29846: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29846: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29846: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29846: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29846: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29846: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29846: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29846: Goal:
-29846: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29846: Order:
-29846: lpo
-29846: Leaf order:
-29846: additive_inverse 22 1 0
-29846: additive_identity 8 0 0
-29846: add 26 2 2 0,2
-29846: commutator 2 2 1 0,3,2,2
-29846: associator 5 3 4 0,1,2
-29846: w 4 0 4 3,1,2
-29846: z 4 0 4 2,1,2
-29846: multiply 43 2 3 0,1,1,2
-29846: y 4 0 4 2,1,1,2
-29846: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29845: Facts:
-29845: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29845: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29845: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29845: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29845: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29845: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29845: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29845: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29845: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29845: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29845: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29845: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29845: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29845: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29845: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29845: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29845: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29845: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29845: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29845: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29845: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29845: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29845: Goal:
-29845: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29845: Order:
-29845: kbo
-29845: Leaf order:
-29845: additive_inverse 22 1 0
-29845: additive_identity 8 0 0
-29845: add 26 2 2 0,2
-29845: commutator 2 2 1 0,3,2,2
-29845: associator 5 3 4 0,1,2
-29845: w 4 0 4 3,1,2
-29845: z 4 0 4 2,1,2
-29845: multiply 43 2 3 0,1,1,2
-29845: y 4 0 4 2,1,1,2
-29845: x 4 0 4 1,1,1,2
-% SZS status Timeout for RNG033-7.p
-NO CLASH, using fixed ground order
-29862: Facts:
-29862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29862: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29862: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29862: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29862: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29862: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29862: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29862: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29862: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29862: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29862: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29862: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29862: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29862: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29862: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29862: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =?=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-29862: Goal:
-29862: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29862: Order:
-29862: nrkbo
-29862: Leaf order:
-29862: additive_inverse 6 1 0
-29862: additive_identity 8 0 0
-29862: add 18 2 2 0,2
-29862: commutator 2 2 1 0,3,2,2
-29862: associator 5 3 4 0,1,2
-29862: w 4 0 4 3,1,2
-29862: z 4 0 4 2,1,2
-29862: multiply 31 2 3 0,1,1,2
-29862: y 4 0 4 2,1,1,2
-29862: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29863: Facts:
-29863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29863: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29863: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29863: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29863: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29863: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29863: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29863: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29863: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29863: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29863: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29863: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29863: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29863: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29863: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29863: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =<=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-29863: Goal:
-29863: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29863: Order:
-29863: kbo
-29863: Leaf order:
-29863: additive_inverse 6 1 0
-29863: additive_identity 8 0 0
-29863: add 18 2 2 0,2
-29863: commutator 2 2 1 0,3,2,2
-29863: associator 5 3 4 0,1,2
-29863: w 4 0 4 3,1,2
-29863: z 4 0 4 2,1,2
-29863: multiply 31 2 3 0,1,1,2
-29863: y 4 0 4 2,1,1,2
-29863: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29864: Facts:
-29864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29864: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29864: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29864: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29864: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29864: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29864: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29864: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29864: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29864: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29864: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29864: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29864: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29864: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29864: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29864: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =<=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-29864: Goal:
-29864: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29864: Order:
-29864: lpo
-29864: Leaf order:
-29864: additive_inverse 6 1 0
-29864: additive_identity 8 0 0
-29864: add 18 2 2 0,2
-29864: commutator 2 2 1 0,3,2,2
-29864: associator 5 3 4 0,1,2
-29864: w 4 0 4 3,1,2
-29864: z 4 0 4 2,1,2
-29864: multiply 31 2 3 0,1,1,2
-29864: y 4 0 4 2,1,1,2
-29864: x 4 0 4 1,1,1,2
-% SZS status Timeout for RNG033-8.p
-NO CLASH, using fixed ground order
-29900: Facts:
-29900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29900: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29900: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29900: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29900: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29900: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29900: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29900: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29900: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29900: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29900: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29900: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29900: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29900: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29900: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29900: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29900: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29900: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29900: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29900: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29900: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29900: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29900: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =?=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-29900: Goal:
-29900: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29900: Order:
-29900: nrkbo
-29900: Leaf order:
-29900: additive_inverse 22 1 0
-29900: additive_identity 8 0 0
-29900: add 26 2 2 0,2
-29900: commutator 2 2 1 0,3,2,2
-29900: associator 5 3 4 0,1,2
-29900: w 4 0 4 3,1,2
-29900: z 4 0 4 2,1,2
-29900: multiply 49 2 3 0,1,1,2
-29900: y 4 0 4 2,1,1,2
-29900: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29901: Facts:
-29901: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29901: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29901: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29901: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29901: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29901: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29901: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29901: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29901: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29901: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29901: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29901: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29901: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29901: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29901: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29901: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29901: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29901: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29901: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29901: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29901: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29901: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29901: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =<=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-29901: Goal:
-29901: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29901: Order:
-29901: kbo
-29901: Leaf order:
-29901: additive_inverse 22 1 0
-29901: additive_identity 8 0 0
-29901: add 26 2 2 0,2
-29901: commutator 2 2 1 0,3,2,2
-29901: associator 5 3 4 0,1,2
-29901: w 4 0 4 3,1,2
-29901: z 4 0 4 2,1,2
-29901: multiply 49 2 3 0,1,1,2
-29901: y 4 0 4 2,1,1,2
-29901: x 4 0 4 1,1,1,2
-NO CLASH, using fixed ground order
-29902: Facts:
-29902: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29902: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29902: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29902: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29902: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29902: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29902: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29902: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29902: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29902: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29902: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29902: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29902: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29902: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29902: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29902: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29902: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29902: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29902: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29902: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29902: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29902: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29902: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =<=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-29902: Goal:
-29902: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =<=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-29902: Order:
-29902: lpo
-29902: Leaf order:
-29902: additive_inverse 22 1 0
-29902: additive_identity 8 0 0
-29902: add 26 2 2 0,2
-29902: commutator 2 2 1 0,3,2,2
-29902: associator 5 3 4 0,1,2
-29902: w 4 0 4 3,1,2
-29902: z 4 0 4 2,1,2
-29902: multiply 49 2 3 0,1,1,2
-29902: y 4 0 4 2,1,1,2
-29902: x 4 0 4 1,1,1,2
-% SZS status Timeout for RNG033-9.p
-NO CLASH, using fixed ground order
-29918: Facts:
-29918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29918: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29918: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-29918: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-29918: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-29918: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-29918: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-29918: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29918: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29918: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-29918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-29918: Goal:
-29918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-29918: Order:
-29918: nrkbo
-29918: Leaf order:
-29918: additive_inverse 2 1 0
-29918: add 14 2 0
-29918: additive_identity 4 0 0
-29918: c 2 0 1 3
-29918: multiply 16 2 1 0,2
-29918: a 2 0 1 2,2
-29918: b 2 0 1 1,2
-NO CLASH, using fixed ground order
-29919: Facts:
-29919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29919: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29919: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-29919: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-29919: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-29919: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-29919: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-29919: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29919: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29919: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-29919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-29919: Goal:
-29919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-29919: Order:
-29919: kbo
-29919: Leaf order:
-29919: additive_inverse 2 1 0
-29919: add 14 2 0
-29919: additive_identity 4 0 0
-NO CLASH, using fixed ground order
-29920: Facts:
-29920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29920: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29920: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-29920: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-29920: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-29920: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-29920: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-29920: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29920: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29920: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-29920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-29920: Goal:
-29920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-29920: Order:
-29920: lpo
-29920: Leaf order:
-29920: additive_inverse 2 1 0
-29920: add 14 2 0
-29920: additive_identity 4 0 0
-29920: c 2 0 1 3
-29920: multiply 16 2 1 0,2
-29920: a 2 0 1 2,2
-29920: b 2 0 1 1,2
-29919: c 2 0 1 3
-29919: multiply 16 2 1 0,2
-29919: a 2 0 1 2,2
-29919: b 2 0 1 1,2
-% SZS status Timeout for RNG036-7.p
-NO CLASH, using fixed ground order
-29951: Facts:
-29951: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29951: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29951: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29951: Goal:
-29951: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29951: Order:
-29951: nrkbo
-29951: Leaf order:
-29951: add 12 2 3 0,2
-29951: negate 9 1 5 0,1,2
-29951: b 3 0 3 1,2,1,1,2
-29951: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-29952: Facts:
-29952: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29952: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29952: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29952: Goal:
-29952: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29952: Order:
-29952: kbo
-29952: Leaf order:
-29952: add 12 2 3 0,2
-29952: negate 9 1 5 0,1,2
-29952: b 3 0 3 1,2,1,1,2
-29952: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-29953: Facts:
-29953: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29953: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29953: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29953: Goal:
-29953: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29953: Order:
-29953: lpo
-29953: Leaf order:
-29953: add 12 2 3 0,2
-29953: negate 9 1 5 0,1,2
-29953: b 3 0 3 1,2,1,1,2
-29953: a 2 0 2 1,1,1,2
-% SZS status Timeout for ROB001-1.p
-NO CLASH, using fixed ground order
-29969: Facts:
-29969: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29969: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29969: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29969: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-29969: Goal:
-29969: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29969: Order:
-29969: nrkbo
-29969: Leaf order:
-29969: add 13 2 3 0,2
-29969: negate 11 1 5 0,1,2
-29969: b 5 0 3 1,2,1,1,2
-29969: a 3 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-29970: Facts:
-29970: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29970: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29970: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29970: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-29970: Goal:
-29970: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29970: Order:
-29970: kbo
-29970: Leaf order:
-29970: add 13 2 3 0,2
-29970: negate 11 1 5 0,1,2
-29970: b 5 0 3 1,2,1,1,2
-29970: a 3 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-29971: Facts:
-29971: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-29971: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-29971: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-29971: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-29971: Goal:
-29971: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-29971: Order:
-29971: lpo
-29971: Leaf order:
-29971: add 13 2 3 0,2
-29971: negate 11 1 5 0,1,2
-29971: b 5 0 3 1,2,1,1,2
-29971: a 3 0 2 1,1,1,2
-% SZS status Timeout for ROB007-1.p
-NO CLASH, using fixed ground order
-29998: Facts:
-29998: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-29998: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-29998: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-29998: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-29998: Goal:
-29998: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-29998: Order:
-29998: nrkbo
-29998: Leaf order:
-29998: b 2 0 0
-29998: a 1 0 0
-29998: negate 6 1 0
-29998: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-29999: Facts:
-29999: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-29999: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-29999: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-29999: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-29999: Goal:
-29999: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-29999: Order:
-29999: kbo
-29999: Leaf order:
-29999: b 2 0 0
-29999: a 1 0 0
-29999: negate 6 1 0
-29999: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-30000: Facts:
-30000: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30000: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30000: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30000: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-30000: Goal:
-30000: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30000: Order:
-30000: lpo
-30000: Leaf order:
-30000: b 2 0 0
-30000: a 1 0 0
-30000: negate 6 1 0
-30000: add 11 2 1 0,2
-% SZS status Timeout for ROB007-2.p
-NO CLASH, using fixed ground order
-30074: Facts:
-30074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-NO CLASH, using fixed ground order
-30075: Facts:
-30075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30075: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30075: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30075: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30075: Goal:
-30075: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30075: Order:
-30075: kbo
-30075: Leaf order:
-30075: add 13 2 3 0,2
-30075: negate 11 1 5 0,1,2
-30075: b 5 0 3 1,2,1,1,2
-30075: a 3 0 2 1,1,1,2
-30074: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30074: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30074: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30074: Goal:
-30074: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30074: Order:
-30074: nrkbo
-30074: Leaf order:
-30074: add 13 2 3 0,2
-30074: negate 11 1 5 0,1,2
-30074: b 5 0 3 1,2,1,1,2
-30074: a 3 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-30076: Facts:
-30076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30076: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30076: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30076: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30076: Goal:
-30076: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30076: Order:
-30076: lpo
-30076: Leaf order:
-30076: add 13 2 3 0,2
-30076: negate 11 1 5 0,1,2
-30076: b 5 0 3 1,2,1,1,2
-30076: a 3 0 2 1,1,1,2
-% SZS status Timeout for ROB020-1.p
-NO CLASH, using fixed ground order
-30104: Facts:
-30104: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30104: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30104: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30104: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30104: Goal:
-30104: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30104: Order:
-30104: nrkbo
-30104: Leaf order:
-30104: b 2 0 0
-30104: a 1 0 0
-30104: negate 6 1 0
-30104: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-30105: Facts:
-30105: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30105: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30105: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30105: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30105: Goal:
-30105: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30105: Order:
-30105: kbo
-30105: Leaf order:
-30105: b 2 0 0
-30105: a 1 0 0
-30105: negate 6 1 0
-30105: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-30106: Facts:
-30106: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30106: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30106: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30106: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-30106: Goal:
-30106: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30106: Order:
-30106: lpo
-30106: Leaf order:
-30106: b 2 0 0
-30106: a 1 0 0
-30106: negate 6 1 0
-30106: add 11 2 1 0,2
-% SZS status Timeout for ROB020-2.p
-NO CLASH, using fixed ground order
-30123: Facts:
-30123: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30123: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30123: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30123: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-30123: Goal:
-30123: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30123: Order:
-30123: nrkbo
-30123: Leaf order:
-30123: add 16 2 3 0,2
-30123: negate 13 1 5 0,1,2
-30123: b 5 0 3 1,2,1,1,2
-30123: a 6 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-30124: Facts:
-30124: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30124: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30124: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30124: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-30124: Goal:
-30124: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30124: Order:
-30124: kbo
-30124: Leaf order:
-30124: add 16 2 3 0,2
-30124: negate 13 1 5 0,1,2
-30124: b 5 0 3 1,2,1,1,2
-30124: a 6 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-30125: Facts:
-30125: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30125: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30125: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30125: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-30125: Goal:
-30125: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30125: Order:
-30125: lpo
-30125: Leaf order:
-30125: add 16 2 3 0,2
-30125: negate 13 1 5 0,1,2
-30125: b 5 0 3 1,2,1,1,2
-30125: a 6 0 2 1,1,1,2
-% SZS status Timeout for ROB024-1.p
-NO CLASH, using fixed ground order
-30152: Facts:
-30152: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30152: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30152: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30152: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-30152: Goal:
-30152: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30152: Order:
-30152: nrkbo
-30152: Leaf order:
-30152: c 2 0 0
-30152: add 12 2 3 0,2
-30152: negate 11 1 5 0,1,2
-30152: b 3 0 3 1,2,1,1,2
-30152: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-30153: Facts:
-30153: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30153: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30153: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30153: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-30153: Goal:
-30153: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30153: Order:
-30153: kbo
-30153: Leaf order:
-30153: c 2 0 0
-30153: add 12 2 3 0,2
-30153: negate 11 1 5 0,1,2
-30153: b 3 0 3 1,2,1,1,2
-30153: a 2 0 2 1,1,1,2
-NO CLASH, using fixed ground order
-30154: Facts:
-30154: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-30154: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-30154: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-30154: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-30154: Goal:
-30154: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-30154: Order:
-30154: lpo
-30154: Leaf order:
-30154: c 2 0 0
-30154: add 12 2 3 0,2
-30154: negate 11 1 5 0,1,2
-30154: b 3 0 3 1,2,1,1,2
-30154: a 2 0 2 1,1,1,2
-% SZS status Timeout for ROB027-1.p
-NO CLASH, using fixed ground order
-30170: Facts:
-30170: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-30170: Id : 3, {_}:
- add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30170: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30170: Goal:
-30170: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-30170: Order:
-30170: nrkbo
-30170: Leaf order:
-30170: negate 6 1 2 0,2
-30170: add 10 2 1 0,1,2
-NO CLASH, using fixed ground order
-30171: Facts:
-30171: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-30171: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30171: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30171: Goal:
-30171: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-30171: Order:
-30171: kbo
-30171: Leaf order:
-30171: negate 6 1 2 0,2
-30171: add 10 2 1 0,1,2
-NO CLASH, using fixed ground order
-30172: Facts:
-30172: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-30172: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30172: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30172: Goal:
-30172: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-30172: Order:
-30172: lpo
-30172: Leaf order:
-30172: negate 6 1 2 0,2
-30172: add 10 2 1 0,1,2
-% SZS status Timeout for ROB031-1.p
-NO CLASH, using fixed ground order
-30204: Facts:
-30204: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-NO CLASH, using fixed ground order
-30205: Facts:
-30205: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-30205: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30205: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30205: Goal:
-30205: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-30205: Order:
-30205: kbo
-30205: Leaf order:
-30205: negate 4 1 0
-30205: add 10 2 1 0,2
-30204: Id : 3, {_}:
- add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30204: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30204: Goal:
-30204: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-30204: Order:
-30204: nrkbo
-30204: Leaf order:
-30204: negate 4 1 0
-30204: add 10 2 1 0,2
-NO CLASH, using fixed ground order
-30206: Facts:
-30206: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-30206: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-30206: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-30206: Goal:
-30206: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-30206: Order:
-30206: lpo
-30206: Leaf order:
-30206: negate 4 1 0
-30206: add 10 2 1 0,2
-% SZS status Timeout for ROB032-1.p
+++ /dev/null
-CLASH, statistics insufficient
-CLASH, statistics insufficient
-22279: Facts:
-22279: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22279: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22279: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22279: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22279: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-22279: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-22279: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-22279: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-22279: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-22279: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-22279: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-22279: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-22279: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-22279: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-22279: Goal:
-22279: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22279: Order:
-22279: kbo
-22279: Leaf order:
-22279: a 2 0 2 1,2
-22279: b 2 0 2 1,2,2
-22279: c 2 0 2 2,2,2
-22279: multiplicative_identity 4 0 0
-22279: additive_identity 4 0 0
-22279: inverse 4 1 0
-22279: add 16 2 0 multiply
-22279: multiply 20 2 4 0,2add
-CLASH, statistics insufficient
-22280: Facts:
-22280: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22280: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22280: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22280: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22280: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =>=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-22280: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =>=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-22280: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-22280: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-22280: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-22280: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-22280: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-22280: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-22280: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-22280: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-22280: Goal:
-22280: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22280: Order:
-22280: lpo
-22280: Leaf order:
-22280: a 2 0 2 1,2
-22280: b 2 0 2 1,2,2
-22280: c 2 0 2 2,2,2
-22280: multiplicative_identity 4 0 0
-22280: additive_identity 4 0 0
-22280: inverse 4 1 0
-22280: add 16 2 0 multiply
-22280: multiply 20 2 4 0,2add
-22278: Facts:
-22278: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22278: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22278: Id : 4, {_}:
- add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22278: Id : 5, {_}:
- add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22278: Id : 6, {_}:
- multiply (add ?16 ?17) ?18
- =<=
- add (multiply ?16 ?18) (multiply ?17 ?18)
- [18, 17, 16] by distributivity3 ?16 ?17 ?18
-22278: Id : 7, {_}:
- multiply ?20 (add ?21 ?22)
- =<=
- add (multiply ?20 ?21) (multiply ?20 ?22)
- [22, 21, 20] by distributivity4 ?20 ?21 ?22
-22278: Id : 8, {_}:
- add ?24 (inverse ?24) =>= multiplicative_identity
- [24] by additive_inverse1 ?24
-22278: Id : 9, {_}:
- add (inverse ?26) ?26 =>= multiplicative_identity
- [26] by additive_inverse2 ?26
-22278: Id : 10, {_}:
- multiply ?28 (inverse ?28) =>= additive_identity
- [28] by multiplicative_inverse1 ?28
-22278: Id : 11, {_}:
- multiply (inverse ?30) ?30 =>= additive_identity
- [30] by multiplicative_inverse2 ?30
-22278: Id : 12, {_}:
- multiply ?32 multiplicative_identity =>= ?32
- [32] by multiplicative_id1 ?32
-22278: Id : 13, {_}:
- multiply multiplicative_identity ?34 =>= ?34
- [34] by multiplicative_id2 ?34
-22278: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-22278: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-22278: Goal:
-22278: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22278: Order:
-22278: nrkbo
-22278: Leaf order:
-22278: a 2 0 2 1,2
-22278: b 2 0 2 1,2,2
-22278: c 2 0 2 2,2,2
-22278: multiplicative_identity 4 0 0
-22278: additive_identity 4 0 0
-22278: inverse 4 1 0
-22278: add 16 2 0 multiply
-22278: multiply 20 2 4 0,2add
-Statistics :
-Max weight : 22
-Found proof, 16.771241s
-% SZS status Unsatisfiable for BOO007-2.p
-% SZS output start CNFRefutation for BOO007-2.p
-Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
-Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
-Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
-Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
-Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
-Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
-Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
-Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
-Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
-Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
-Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
-Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2
-Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3
-Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
-Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3
-Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2
-Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2
-Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3
-Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2
-Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3
-Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
-Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3
-Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
-Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3
-Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3
-Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
-Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3
-Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2
-Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2
-Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2
-Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2
-Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3
-Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2
-Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3
-Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2
-Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3
-Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3
-Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2
-Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3
-Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3
-Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3
-Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2
-Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2
-Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
-Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3
-Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2
-Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2
-Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2
-Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3
-Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3
-Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2
-Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
-Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3
-Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2
-Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2
-Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2
-Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3
-Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3
-Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3
-Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3
-Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2
-Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2
-Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2
-Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3
-Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
-Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2
-Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3
-Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3
-Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3
-Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2
-Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3
-Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2
-Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2
-Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3
-Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2
-Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3
-Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3
-Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3
-Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2
-Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3
-Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2
-Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3
-Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2
-Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2
-Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3
-Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2
-Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3
-Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3
-Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3
-Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3
-Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3
-Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3
-Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3
-Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2
-Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3
-Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3
-Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3
-Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2
-Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3
-Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3
-Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3
-Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2
-Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3
-Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2
-Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3
-Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-2.p
-22279: solved BOO007-2.p in 8.384524 using kbo
-22279: status Unsatisfiable for BOO007-2.p
-CLASH, statistics insufficient
-22287: Facts:
-22287: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22287: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22287: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22287: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22287: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-22287: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-22287: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-22287: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-22287: Goal:
-22287: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22287: Order:
-22287: nrkbo
-22287: Leaf order:
-22287: additive_identity 2 0 0
-22287: multiplicative_identity 2 0 0
-22287: a 2 0 2 1,2
-22287: b 2 0 2 1,2,2
-22287: c 2 0 2 2,2,2
-22287: inverse 2 1 0
-22287: add 9 2 0 multiply
-22287: multiply 13 2 4 0,2add
-CLASH, statistics insufficient
-22288: Facts:
-22288: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22288: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22288: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22288: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =<=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22288: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-22288: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-22288: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-22288: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-22288: Goal:
-22288: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22288: Order:
-22288: kbo
-22288: Leaf order:
-22288: additive_identity 2 0 0
-22288: multiplicative_identity 2 0 0
-22288: a 2 0 2 1,2
-22288: b 2 0 2 1,2,2
-22288: c 2 0 2 2,2,2
-22288: inverse 2 1 0
-22288: add 9 2 0 multiply
-22288: multiply 13 2 4 0,2add
-CLASH, statistics insufficient
-22289: Facts:
-22289: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-22289: Id : 3, {_}:
- multiply ?5 ?6 =?= multiply ?6 ?5
- [6, 5] by commutativity_of_multiply ?5 ?6
-22289: Id : 4, {_}:
- add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
- [10, 9, 8] by distributivity1 ?8 ?9 ?10
-22289: Id : 5, {_}:
- multiply ?12 (add ?13 ?14)
- =>=
- add (multiply ?12 ?13) (multiply ?12 ?14)
- [14, 13, 12] by distributivity2 ?12 ?13 ?14
-22289: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-22289: Id : 7, {_}:
- multiply ?18 multiplicative_identity =>= ?18
- [18] by multiplicative_id1 ?18
-22289: Id : 8, {_}:
- add ?20 (inverse ?20) =>= multiplicative_identity
- [20] by additive_inverse1 ?20
-22289: Id : 9, {_}:
- multiply ?22 (inverse ?22) =>= additive_identity
- [22] by multiplicative_inverse1 ?22
-22289: Goal:
-22289: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22289: Order:
-22289: lpo
-22289: Leaf order:
-22289: additive_identity 2 0 0
-22289: multiplicative_identity 2 0 0
-22289: a 2 0 2 1,2
-22289: b 2 0 2 1,2,2
-22289: c 2 0 2 2,2,2
-22289: inverse 2 1 0
-22289: add 9 2 0 multiply
-22289: multiply 13 2 4 0,2add
-Statistics :
-Max weight : 25
-Found proof, 23.744275s
-% SZS status Unsatisfiable for BOO007-4.p
-% SZS output start CNFRefutation for BOO007-4.p
-Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114
-Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
-Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
-Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
-Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
-Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
-Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
-Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
-Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64
-Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3
-Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3
-Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3
-Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3
-Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3
-Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3
-Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3
-Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3
-Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3
-Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3
-Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2
-Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2
-Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2
-Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3
-Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2
-Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3
-Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3
-Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2
-Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2
-Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3
-Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3
-Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2
-Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2
-Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3
-Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2
-Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2
-Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2
-Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2
-Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2
-Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3
-Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3
-Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2
-Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3
-Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3
-Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3
-Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3
-Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3
-Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3
-Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3
-Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3
-Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3
-Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3
-Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3
-Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3
-Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2
-Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2
-Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3
-Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3
-Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3
-Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3
-Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3
-Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3
-Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3
-Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3
-Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3
-Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2
-Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2
-Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3
-Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3
-Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2
-Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3
-Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3
-Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2
-Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3
-Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2
-Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3
-Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2
-Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3
-Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2
-Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3
-Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3
-Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2
-Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3
-Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2
-Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3
-Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3
-Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2
-Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2
-Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3
-Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2
-Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3
-Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2
-Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3
-Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for BOO007-4.p
-22288: solved BOO007-4.p in 11.836739 using kbo
-22288: status Unsatisfiable for BOO007-4.p
-CLASH, statistics insufficient
-22303: Facts:
-22303: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-22303: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-22303: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-22303: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-22303: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-22303: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-22303: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-22303: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-22303: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-22303: Id : 11, {_}:
- add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-22303: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-22303: Goal:
-22303: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-22303: Order:
-22303: nrkbo
-22303: Leaf order:
-22303: n1 1 0 0
-22303: n0 1 0 0
-22303: b 2 0 2 1,2,2
-22303: c 2 0 2 2,2,2
-22303: a 3 0 3 1,2
-22303: inverse 4 1 0
-22303: add 21 2 2 0,2,2multiply
-22303: multiply 22 2 3 0,2add
-CLASH, statistics insufficient
-22304: Facts:
-22304: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-22304: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-22304: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-22304: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-22304: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-22304: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-22304: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-22304: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-22304: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-22304: Id : 11, {_}:
- add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-22304: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-CLASH, statistics insufficient
-22305: Facts:
-22305: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =>=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-22305: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-22305: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-22305: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-22305: Id : 6, {_}:
- multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
- [19, 18, 17] by l2 ?17 ?18 ?19
-22305: Id : 7, {_}:
- multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
- [23, 22, 21] by l4 ?21 ?22 ?23
-22305: Id : 8, {_}:
- add (multiply ?25 (inverse ?25)) ?26 =>= ?26
- [26, 25] by property3_dual ?25 ?26
-22305: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-22305: Id : 10, {_}:
- multiply ?30 (inverse ?30) =>= n0
- [30] by multiplicative_inverse ?30
-22305: Id : 11, {_}:
- add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
- [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-22305: Id : 12, {_}:
- multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
- [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-22305: Goal:
-22305: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-22305: Order:
-22305: lpo
-22305: Leaf order:
-22305: n1 1 0 0
-22305: n0 1 0 0
-22305: b 2 0 2 1,2,2
-22305: c 2 0 2 2,2,2
-22305: a 3 0 3 1,2
-22305: inverse 4 1 0
-22305: add 21 2 2 0,2,2multiply
-22305: multiply 22 2 3 0,2add
-22304: Goal:
-22304: Id : 1, {_}:
- multiply a (add b c) =<= add (multiply b a) (multiply c a)
- [] by prove_multiply_add_property
-22304: Order:
-22304: kbo
-22304: Leaf order:
-22304: n1 1 0 0
-22304: n0 1 0 0
-22304: b 2 0 2 1,2,2
-22304: c 2 0 2 2,2,2
-22304: a 3 0 3 1,2
-22304: inverse 4 1 0
-22304: add 21 2 2 0,2,2multiply
-22304: multiply 22 2 3 0,2add
-Statistics :
-Max weight : 29
-Found proof, 45.037592s
-% SZS status Unsatisfiable for BOO031-1.p
-% SZS output start CNFRefutation for BOO031-1.p
-Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
-Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
-Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
-Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
-Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191
-Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
-Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
-Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
-Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60
-Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
-Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
-Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130
-Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
-Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
-Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2
-Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2
-Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2
-Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2
-Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2
-Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2
-Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2
-Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2
-Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2
-Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2
-Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3
-Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2
-Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2
-Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3
-Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2
-Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3
-Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2
-Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2
-Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2
-Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3
-Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2
-Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2
-Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2
-Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2
-Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2
-Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2
-Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2
-Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2
-Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3
-Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2
-Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3
-Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2
-Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3
-Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2
-Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2
-Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2
-Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3
-Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3
-Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3
-Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2
-Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2
-Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2
-Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2
-Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2
-Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2
-Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3
-Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2
-Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3
-Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3
-Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3
-Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2
-Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2
-Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2
-Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2
-Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3
-Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3
-Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3
-Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2
-Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2
-Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3
-Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2
-Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3
-Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2
-Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2
-Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2
-Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2
-Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2
-Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2
-Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2
-Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2
-Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2
-Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2
-Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3
-Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2
-Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2
-Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3
-Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2
-Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2
-Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3
-Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2
-Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3
-Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3
-Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2
-Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3
-Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2
-Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2
-Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2
-Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2
-Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2
-Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2
-Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2
-Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2
-Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2
-Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3
-Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2
-Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2
-Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3
-Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3
-Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3
-Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3
-Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3
-Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3
-Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2
-Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
-% SZS output end CNFRefutation for BOO031-1.p
-22304: solved BOO031-1.p in 22.545408 using kbo
-22304: status Unsatisfiable for BOO031-1.p
-NO CLASH, using fixed ground order
-22316: Facts:
-22316: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22316: Goal:
-22316: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
-22316: Order:
-22316: nrkbo
-22316: Leaf order:
-22316: b 2 0 2 1,2
-22316: a 2 0 2 2,2
-22316: inverse 7 1 0
-22316: add 8 2 2 0,2
-NO CLASH, using fixed ground order
-22317: Facts:
-22317: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22317: Goal:
-22317: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
-22317: Order:
-22317: kbo
-22317: Leaf order:
-22317: b 2 0 2 1,2
-22317: a 2 0 2 2,2
-22317: inverse 7 1 0
-22317: add 8 2 2 0,2
-NO CLASH, using fixed ground order
-22318: Facts:
-22318: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22318: Goal:
-22318: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
-22318: Order:
-22318: lpo
-22318: Leaf order:
-22318: b 2 0 2 1,2
-22318: a 2 0 2 2,2
-22318: inverse 7 1 0
-22318: add 8 2 2 0,2
-Statistics :
-Max weight : 70
-Found proof, 10.385052s
-% SZS status Unsatisfiable for BOO072-1.p
-% SZS output start CNFRefutation for BOO072-1.p
-Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
-Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
-Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
-Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
-Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
-Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
-Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
-Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
-Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
-Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
-Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
-Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
-Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
-Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
-Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
-Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
-Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
-Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
-Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
-Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
-Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
-Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
-Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
-Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
-Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
-Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
-Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
-Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
-Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
-Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
-Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
-Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
-Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
-Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
-Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
-Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
-Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
-Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
-Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
-Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
-Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
-Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
-Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
-Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
-Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
-Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
-Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
-Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3
-Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2
-Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3
-Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3
-Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2
-Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
-Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
-Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
-Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
-Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
-Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
-Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
-Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
-Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
-Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
-Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
-Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
-Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
-Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
-Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
-Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
-Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
-Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
-Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
-Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
-Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
-Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
-Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
-Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3
-Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2
-Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
-Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
-Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
-Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
-Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
-Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
-Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
-Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3
-Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3
-Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2
-Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2
-Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2
-Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3
-Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2
-Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3
-Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3
-Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3
-Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3
-Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2
-Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2
-Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3
-Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3
-Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3
-Id : 21981, {_}: add b a === add b a [] by Demod 1 with 21454 at 3
-Id : 1, {_}: add b a =<= add a b [] by huntinton_1
-% SZS output end CNFRefutation for BOO072-1.p
-22316: solved BOO072-1.p in 10.380648 using nrkbo
-22316: status Unsatisfiable for BOO072-1.p
-NO CLASH, using fixed ground order
-22328: Facts:
-22328: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22328: Goal:
-22328: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-22328: Order:
-22328: nrkbo
-22328: Leaf order:
-22328: a 2 0 2 1,1,2
-22328: b 2 0 2 2,1,2
-22328: c 2 0 2 2,2
-22328: inverse 7 1 0
-22328: add 10 2 4 0,2
-NO CLASH, using fixed ground order
-22329: Facts:
-22329: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22329: Goal:
-22329: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-22329: Order:
-22329: kbo
-22329: Leaf order:
-22329: a 2 0 2 1,1,2
-22329: b 2 0 2 2,1,2
-22329: c 2 0 2 2,2
-22329: inverse 7 1 0
-22329: add 10 2 4 0,2
-NO CLASH, using fixed ground order
-22330: Facts:
-22330: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22330: Goal:
-22330: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
-22330: Order:
-22330: lpo
-22330: Leaf order:
-22330: a 2 0 2 1,1,2
-22330: b 2 0 2 2,1,2
-22330: c 2 0 2 2,2
-22330: inverse 7 1 0
-22330: add 10 2 4 0,2
-% SZS status Timeout for BOO073-1.p
-NO CLASH, using fixed ground order
-22390: Facts:
-22390: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22390: Goal:
-22390: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-22390: Order:
-22390: nrkbo
-22390: Leaf order:
-22390: b 2 0 2 2,1,1,2
-22390: a 3 0 3 1,1,1,1,2
-22390: inverse 12 1 5 0,1,2
-22390: add 9 2 3 0,2
-NO CLASH, using fixed ground order
-22391: Facts:
-22391: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22391: Goal:
-22391: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-22391: Order:
-22391: kbo
-22391: Leaf order:
-22391: b 2 0 2 2,1,1,2
-22391: a 3 0 3 1,1,1,1,2
-22391: inverse 12 1 5 0,1,2
-22391: add 9 2 3 0,2
-NO CLASH, using fixed ground order
-22392: Facts:
-22392: Id : 2, {_}:
- inverse
- (add (inverse (add (inverse (add ?2 ?3)) ?4))
- (inverse
- (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
- =>=
- ?4
- [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-22392: Goal:
-22392: Id : 1, {_}:
- add (inverse (add (inverse a) b))
- (inverse (add (inverse a) (inverse b)))
- =>=
- a
- [] by huntinton_3
-22392: Order:
-22392: lpo
-22392: Leaf order:
-22392: b 2 0 2 2,1,1,2
-22392: a 3 0 3 1,1,1,1,2
-22392: inverse 12 1 5 0,1,2
-22392: add 9 2 3 0,2
-Statistics :
-Max weight : 70
-Found proof, 9.195802s
-% SZS status Unsatisfiable for BOO074-1.p
-% SZS output start CNFRefutation for BOO074-1.p
-Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
-Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
-Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
-Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
-Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
-Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
-Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
-Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
-Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
-Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
-Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
-Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
-Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
-Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
-Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
-Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
-Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
-Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
-Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
-Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
-Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
-Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
-Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
-Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
-Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
-Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
-Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
-Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
-Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
-Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
-Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
-Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
-Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
-Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
-Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
-Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
-Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
-Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
-Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
-Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
-Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
-Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
-Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
-Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
-Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
-Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
-Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
-Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
-Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
-Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
-Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
-Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
-Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
-Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
-Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
-Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
-Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
-Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
-Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
-Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
-Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
-Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
-Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
-Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
-Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
-Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
-Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
-Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
-Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
-Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
-Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
-Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
-Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
-Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
-Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
-Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
-Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
-Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
-Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
-Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
-Id : 18617, {_}: a === a [] by Demod 18616 with 1733 at 2
-Id : 18616, {_}: inverse (inverse a) =>= a [] by Demod 18615 with 1761 at 2
-Id : 18615, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18614 with 18480 at 1,2,2
-Id : 18614, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2
-Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3
-% SZS output end CNFRefutation for BOO074-1.p
-22390: solved BOO074-1.p in 9.212575 using nrkbo
-22390: status Unsatisfiable for BOO074-1.p
-NO CLASH, using fixed ground order
-22397: Facts:
-22397: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22397: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22397: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-22397: Goal:
-22397: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22397: Order:
-22397: nrkbo
-22397: Leaf order:
-22397: strong_fixed_point 3 0 2 1,2
-22397: fixed_pt 3 0 3 2,2
-22397: w 4 0 0
-22397: b 6 0 0
-22397: apply 19 2 3 0,2
-NO CLASH, using fixed ground order
-22398: Facts:
-22398: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22398: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22398: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-22398: Goal:
-22398: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22398: Order:
-22398: kbo
-22398: Leaf order:
-22398: strong_fixed_point 3 0 2 1,2
-22398: fixed_pt 3 0 3 2,2
-22398: w 4 0 0
-22398: b 6 0 0
-22398: apply 19 2 3 0,2
-NO CLASH, using fixed ground order
-22399: Facts:
-22399: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22399: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22399: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
- [] by strong_fixed_point
-22399: Goal:
-22399: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22399: Order:
-22399: lpo
-22399: Leaf order:
-22399: strong_fixed_point 3 0 2 1,2
-22399: fixed_pt 3 0 3 2,2
-22399: w 4 0 0
-22399: b 6 0 0
-22399: apply 19 2 3 0,2
-% SZS status Timeout for COL003-12.p
-NO CLASH, using fixed ground order
-22420: Facts:
-22420: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22420: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22420: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-22420: Goal:
-22420: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22420: Order:
-22420: nrkbo
-22420: Leaf order:
-22420: strong_fixed_point 3 0 2 1,2
-22420: fixed_pt 3 0 3 2,2
-22420: w 4 0 0
-22420: b 7 0 0
-22420: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22421: Facts:
-22421: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22421: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22421: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-22421: Goal:
-22421: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22421: Order:
-22421: kbo
-22421: Leaf order:
-22421: strong_fixed_point 3 0 2 1,2
-22421: fixed_pt 3 0 3 2,2
-22421: w 4 0 0
-22421: b 7 0 0
-22421: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22422: Facts:
-22422: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22422: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22422: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
- [] by strong_fixed_point
-22422: Goal:
-22422: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22422: Order:
-22422: lpo
-22422: Leaf order:
-22422: strong_fixed_point 3 0 2 1,2
-22422: fixed_pt 3 0 3 2,2
-22422: w 4 0 0
-22422: b 7 0 0
-22422: apply 20 2 3 0,2
-% SZS status Timeout for COL003-17.p
-NO CLASH, using fixed ground order
-22445: Facts:
-22445: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22445: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22445: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-22445: Goal:
-22445: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22445: Order:
-22445: nrkbo
-22445: Leaf order:
-22445: strong_fixed_point 3 0 2 1,2
-22445: fixed_pt 3 0 3 2,2
-22445: w 4 0 0
-22445: b 7 0 0
-22445: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22446: Facts:
-22446: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22446: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22446: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-22446: Goal:
-22446: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22446: Order:
-22446: kbo
-22446: Leaf order:
-22446: strong_fixed_point 3 0 2 1,2
-22446: fixed_pt 3 0 3 2,2
-22446: w 4 0 0
-22446: b 7 0 0
-22446: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22447: Facts:
-22447: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22447: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22447: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply (apply b (apply w w)) (apply b w)))
- (apply (apply b b) b)
- [] by strong_fixed_point
-22447: Goal:
-22447: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22447: Order:
-22447: lpo
-22447: Leaf order:
-22447: strong_fixed_point 3 0 2 1,2
-22447: fixed_pt 3 0 3 2,2
-22447: w 4 0 0
-22447: b 7 0 0
-22447: apply 20 2 3 0,2
-% SZS status Timeout for COL003-18.p
-NO CLASH, using fixed ground order
-22471: Facts:
-22471: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22471: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22471: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-22471: Goal:
-22471: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22471: Order:
-22471: nrkbo
-22471: Leaf order:
-22471: strong_fixed_point 3 0 2 1,2
-22471: fixed_pt 3 0 3 2,2
-22471: w 4 0 0
-22471: b 7 0 0
-22471: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22472: Facts:
-22472: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22472: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22472: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-22472: Goal:
-22472: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22472: Order:
-22472: kbo
-22472: Leaf order:
-22472: strong_fixed_point 3 0 2 1,2
-22472: fixed_pt 3 0 3 2,2
-22472: w 4 0 0
-22472: b 7 0 0
-22472: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-22473: Facts:
-22473: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-22473: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-22473: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
- [] by strong_fixed_point
-22473: Goal:
-22473: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-22473: Order:
-22473: lpo
-22473: Leaf order:
-22473: strong_fixed_point 3 0 2 1,2
-22473: fixed_pt 3 0 3 2,2
-22473: w 4 0 0
-22473: b 7 0 0
-22473: apply 20 2 3 0,2
-% SZS status Timeout for COL003-19.p
-CLASH, statistics insufficient
-22495: Facts:
-22495: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-22495: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-22495: Goal:
-22495: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-22495: Order:
-22495: nrkbo
-22495: Leaf order:
-22495: o 1 0 0
-22495: q1 1 0 0
-22495: combinator 1 0 1 1,3
-22495: apply 10 2 1 0,3
-CLASH, statistics insufficient
-22496: Facts:
-22496: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-22496: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-22496: Goal:
-22496: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-22496: Order:
-22496: kbo
-22496: Leaf order:
-22496: o 1 0 0
-22496: q1 1 0 0
-22496: combinator 1 0 1 1,3
-22496: apply 10 2 1 0,3
-CLASH, statistics insufficient
-22497: Facts:
-22497: Id : 2, {_}:
- apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
- [4, 3] by o_definition ?3 ?4
-22497: Id : 3, {_}:
- apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7)
- [8, 7, 6] by q1_definition ?6 ?7 ?8
-22497: Goal:
-22497: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-22497: Order:
-22497: lpo
-22497: Leaf order:
-22497: o 1 0 0
-22497: q1 1 0 0
-22497: combinator 1 0 1 1,3
-22497: apply 10 2 1 0,3
-% SZS status Timeout for COL011-1.p
-CLASH, statistics insufficient
-22518: Facts:
-22518: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22518: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22518: Id : 4, {_}:
- apply (apply t ?9) ?10 =>= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-22518: Goal:
-22518: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22518: Order:
-22518: nrkbo
-22518: Leaf order:
-22518: b 1 0 0
-22518: m 1 0 0
-22518: t 1 0 0
-22518: f 3 1 3 0,2,2
-22518: apply 13 2 3 0,2
-CLASH, statistics insufficient
-22519: Facts:
-22519: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22519: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22519: Id : 4, {_}:
- apply (apply t ?9) ?10 =>= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-22519: Goal:
-22519: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22519: Order:
-22519: kbo
-22519: Leaf order:
-22519: b 1 0 0
-22519: m 1 0 0
-22519: t 1 0 0
-22519: f 3 1 3 0,2,2
-22519: apply 13 2 3 0,2
-CLASH, statistics insufficient
-22520: Facts:
-22520: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22520: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22520: Id : 4, {_}:
- apply (apply t ?9) ?10 =?= apply ?10 ?9
- [10, 9] by t_definition ?9 ?10
-22520: Goal:
-22520: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22520: Order:
-22520: lpo
-22520: Leaf order:
-22520: b 1 0 0
-22520: m 1 0 0
-22520: t 1 0 0
-22520: f 3 1 3 0,2,2
-22520: apply 13 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 62
-Found proof, 0.520019s
-% SZS status Unsatisfiable for COL034-1.p
-% SZS output start CNFRefutation for COL034-1.p
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2
-Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2
-Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2
-Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3
-Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2
-Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3
-Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL034-1.p
-22518: solved COL034-1.p in 0.528032 using nrkbo
-22518: status Unsatisfiable for COL034-1.p
-CLASH, statistics insufficient
-22525: Facts:
-22525: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22525: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22525: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22525: Goal:
-22525: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22525: Order:
-22525: nrkbo
-22525: Leaf order:
-22525: s 1 0 0
-22525: b 1 0 0
-22525: c 1 0 0
-22525: f 3 1 3 0,2,2
-22525: apply 19 2 3 0,2
-CLASH, statistics insufficient
-22526: Facts:
-22526: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22526: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22526: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22526: Goal:
-22526: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22526: Order:
-22526: kbo
-22526: Leaf order:
-22526: s 1 0 0
-22526: b 1 0 0
-22526: c 1 0 0
-22526: f 3 1 3 0,2,2
-22526: apply 19 2 3 0,2
-CLASH, statistics insufficient
-22527: Facts:
-22527: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22527: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22527: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22527: Goal:
-22527: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22527: Order:
-22527: lpo
-22527: Leaf order:
-22527: s 1 0 0
-22527: b 1 0 0
-22527: c 1 0 0
-22527: f 3 1 3 0,2,2
-22527: apply 19 2 3 0,2
-% SZS status Timeout for COL037-1.p
-CLASH, statistics insufficient
-22551: Facts:
-22551: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22551: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22551: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-22551: Goal:
-22551: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22551: Order:
-22551: nrkbo
-22551: Leaf order:
-22551: b 1 0 0
-22551: m 1 0 0
-22551: c 1 0 0
-22551: f 3 1 3 0,2,2
-22551: apply 15 2 3 0,2
-CLASH, statistics insufficient
-22552: Facts:
-22552: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22552: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22552: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-22552: Goal:
-22552: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22552: Order:
-22552: kbo
-22552: Leaf order:
-22552: b 1 0 0
-22552: m 1 0 0
-22552: c 1 0 0
-22552: f 3 1 3 0,2,2
-22552: apply 15 2 3 0,2
-CLASH, statistics insufficient
-22553: Facts:
-22553: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22553: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-22553: Id : 4, {_}:
- apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10
- [11, 10, 9] by c_definition ?9 ?10 ?11
-22553: Goal:
-22553: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22553: Order:
-22553: lpo
-22553: Leaf order:
-22553: b 1 0 0
-22553: m 1 0 0
-22553: c 1 0 0
-22553: f 3 1 3 0,2,2
-22553: apply 15 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 54
-Found proof, 1.136025s
-% SZS status Unsatisfiable for COL041-1.p
-% SZS output start CNFRefutation for COL041-1.p
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
-Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2
-Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2
-Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3
-Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL041-1.p
-22551: solved COL041-1.p in 1.14407 using nrkbo
-22551: status Unsatisfiable for COL041-1.p
-CLASH, statistics insufficient
-22558: Facts:
-22558: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22558: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-22558: Goal:
-22558: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22558: Order:
-22558: nrkbo
-22558: Leaf order:
-22558: b 1 0 0
-22558: n 1 0 0
-22558: f 3 1 3 0,2,2
-22558: apply 14 2 3 0,2
-CLASH, statistics insufficient
-22559: Facts:
-22559: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22559: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-22559: Goal:
-22559: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22559: Order:
-22559: kbo
-22559: Leaf order:
-22559: b 1 0 0
-22559: n 1 0 0
-22559: f 3 1 3 0,2,2
-22559: apply 14 2 3 0,2
-CLASH, statistics insufficient
-22560: Facts:
-22560: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22560: Id : 3, {_}:
- apply (apply (apply n ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?9) ?8) ?9
- [9, 8, 7] by n_definition ?7 ?8 ?9
-22560: Goal:
-22560: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-22560: Order:
-22560: lpo
-22560: Leaf order:
-22560: b 1 0 0
-22560: n 1 0 0
-22560: f 3 1 3 0,2,2
-22560: apply 14 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 88
-Found proof, 25.425976s
-% SZS status Unsatisfiable for COL044-1.p
-% SZS output start CNFRefutation for COL044-1.p
-Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13
-Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2
-Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2
-Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2
-Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2
-Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3
-Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3
-Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL044-1.p
-22559: solved COL044-1.p in 12.720795 using kbo
-22559: status Unsatisfiable for COL044-1.p
-CLASH, statistics insufficient
-22570: Facts:
-22570: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-CLASH, statistics insufficient
-22571: Facts:
-22571: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22571: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-22571: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-22571: Goal:
-22571: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22571: Order:
-22571: kbo
-22571: Leaf order:
-22571: b 1 0 0
-22571: w 1 0 0
-22571: m 1 0 0
-22571: f 3 1 3 0,2,2
-22571: apply 14 2 3 0,2
-CLASH, statistics insufficient
-22572: Facts:
-22572: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-22572: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-22572: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-22572: Goal:
-22572: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22572: Order:
-22572: lpo
-22572: Leaf order:
-22572: b 1 0 0
-22572: w 1 0 0
-22572: m 1 0 0
-22572: f 3 1 3 0,2,2
-22572: apply 14 2 3 0,2
-22570: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-22570: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-22570: Goal:
-22570: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22570: Order:
-22570: nrkbo
-22570: Leaf order:
-22570: b 1 0 0
-22570: w 1 0 0
-22570: m 1 0 0
-22570: f 3 1 3 0,2,2
-22570: apply 14 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 54
-Found proof, 12.496351s
-% SZS status Unsatisfiable for COL049-1.p
-% SZS output start CNFRefutation for COL049-1.p
-Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8
-Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2
-Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3
-Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3
-Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2
-Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2
-Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3
-Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
-% SZS output end CNFRefutation for COL049-1.p
-22570: solved COL049-1.p in 6.296392 using nrkbo
-22570: status Unsatisfiable for COL049-1.p
-CLASH, statistics insufficient
-22586: Facts:
-22586: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22586: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22586: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22586: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-22586: Goal:
-22586: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22586: Order:
-22586: nrkbo
-22586: Leaf order:
-22586: s 1 0 0
-22586: b 1 0 0
-22586: c 1 0 0
-22586: i 1 0 0
-22586: f 3 1 3 0,2,2
-22586: apply 20 2 3 0,2
-CLASH, statistics insufficient
-22587: Facts:
-22587: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22587: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22587: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22587: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-22587: Goal:
-22587: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22587: Order:
-22587: kbo
-22587: Leaf order:
-22587: s 1 0 0
-22587: b 1 0 0
-22587: c 1 0 0
-22587: i 1 0 0
-22587: f 3 1 3 0,2,2
-22587: apply 20 2 3 0,2
-CLASH, statistics insufficient
-22588: Facts:
-22588: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-22588: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-22588: Id : 4, {_}:
- apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
- [13, 12, 11] by c_definition ?11 ?12 ?13
-22588: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-22588: Goal:
-22588: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-22588: Order:
-22588: lpo
-22588: Leaf order:
-22588: s 1 0 0
-22588: b 1 0 0
-22588: c 1 0 0
-22588: i 1 0 0
-22588: f 3 1 3 0,2,2
-22588: apply 20 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 84
-Found proof, 2.121776s
-% SZS status Unsatisfiable for COL057-1.p
-% SZS output start CNFRefutation for COL057-1.p
-Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
-Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
-Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
-Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3
-Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3
-Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2
-Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3
-Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
-% SZS output end CNFRefutation for COL057-1.p
-22586: solved COL057-1.p in 2.124132 using nrkbo
-22586: status Unsatisfiable for COL057-1.p
-NO CLASH, using fixed ground order
-22593: Facts:
-22593: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-22593: Goal:
-22593: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22593: Order:
-22593: nrkbo
-22593: Leaf order:
-22593: a 2 0 2 1,2
-22593: b 2 0 2 1,2,2
-22593: c 2 0 2 2,2,2
-22593: inverse 5 1 0
-22593: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-22594: Facts:
-22594: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-22594: Goal:
-22594: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22594: Order:
-22594: kbo
-22594: Leaf order:
-22594: a 2 0 2 1,2
-22594: b 2 0 2 1,2,2
-22594: c 2 0 2 2,2,2
-22594: inverse 5 1 0
-22594: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-22595: Facts:
-22595: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-22595: Goal:
-22595: Id : 1, {_}:
- multiply a (multiply b c) =<= multiply (multiply a b) c
- [] by prove_associativity
-22595: Order:
-22595: lpo
-22595: Leaf order:
-22595: a 2 0 2 1,2
-22595: b 2 0 2 1,2,2
-22595: c 2 0 2 2,2,2
-22595: inverse 5 1 0
-22595: multiply 10 2 4 0,2
-Statistics :
-Max weight : 62
-Found proof, 23.394494s
-% SZS status Unsatisfiable for GRP014-1.p
-% SZS output start CNFRefutation for GRP014-1.p
-Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
-Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
-Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
-Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
-Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
-Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
-Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
-Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
-Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
-Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
-Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
-Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
-Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
-Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
-Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
-Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
-Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
-Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
-Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
-Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
-Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
-Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
-Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
-Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
-Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
-Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
-Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
-Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
-Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
-Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
-Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
-Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
-Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
-Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
-Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
-Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
-Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
-Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
-Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
-Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
-Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
-Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
-Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
-Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
-Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
-Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
-Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
-Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
-Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
-Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
-Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
-Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
-Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
-Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
-Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
-Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
-Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
-Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
-Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
-Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
-Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
-Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
-Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
-Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
-Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
-Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
-Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
-Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
-Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
-Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
-Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
-Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
-Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
-Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
-Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
-Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
-Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
-Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
-Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
-Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
-Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
-Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
-Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
-Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
-Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
-Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
-Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
-Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
-Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
-Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
-Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
-Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
-Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
-Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
-Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
-Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
-Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
-Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
-Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
-Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
-Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
-Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
-Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
-Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
-Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
-Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
-Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
-Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
-Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
-Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
-Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
-Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
-Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
-Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
-Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
-Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
-Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
-Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
-Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
-Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
-Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
-Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3
-Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
-% SZS output end CNFRefutation for GRP014-1.p
-22593: solved GRP014-1.p in 11.760735 using nrkbo
-22593: status Unsatisfiable for GRP014-1.p
-CLASH, statistics insufficient
-22602: Facts:
-22602: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22602: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22602: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22602: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22602: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22602: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22602: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22602: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22602: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22602: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22602: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22602: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22602: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22602: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22602: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22602: Id : 17, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-22602: Id : 18, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-22602: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-22602: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-22602: Goal:
-22602: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22602: Order:
-22602: nrkbo
-22602: Leaf order:
-22602: a 3 0 3 2
-22602: identity 4 0 0
-22602: inverse 1 1 0
-22602: positive_part 2 1 1 0,1,3
-22602: negative_part 2 1 1 0,2,3
-22602: greatest_lower_bound 19 2 0
-22602: least_upper_bound 19 2 0
-22602: multiply 19 2 1 0,3
-CLASH, statistics insufficient
-22603: Facts:
-22603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22603: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22603: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22603: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22603: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22603: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22603: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22603: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22603: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22603: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22603: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22603: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22603: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22603: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22603: Id : 17, {_}:
- positive_part ?50 =<= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-22603: Id : 18, {_}:
- negative_part ?52 =<= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-22603: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-22603: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =<=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-22603: Goal:
-22603: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22603: Order:
-22603: kbo
-22603: Leaf order:
-22603: a 3 0 3 2
-22603: identity 4 0 0
-22603: inverse 1 1 0
-22603: positive_part 2 1 1 0,1,3
-22603: negative_part 2 1 1 0,2,3
-22603: greatest_lower_bound 19 2 0
-22603: least_upper_bound 19 2 0
-22603: multiply 19 2 1 0,3
-CLASH, statistics insufficient
-22604: Facts:
-22604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22604: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22604: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22604: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22604: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22604: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22604: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22604: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22604: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22604: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22604: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22604: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22604: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22604: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22604: Id : 17, {_}:
- positive_part ?50 =>= least_upper_bound ?50 identity
- [50] by lat4_1 ?50
-22604: Id : 18, {_}:
- negative_part ?52 =>= greatest_lower_bound ?52 identity
- [52] by lat4_2 ?52
-22604: Id : 19, {_}:
- least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
- =<=
- greatest_lower_bound (least_upper_bound ?54 ?55)
- (least_upper_bound ?54 ?56)
- [56, 55, 54] by lat4_3 ?54 ?55 ?56
-22604: Id : 20, {_}:
- greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
- =>=
- least_upper_bound (greatest_lower_bound ?58 ?59)
- (greatest_lower_bound ?58 ?60)
- [60, 59, 58] by lat4_4 ?58 ?59 ?60
-22604: Goal:
-22604: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22604: Order:
-22604: lpo
-22604: Leaf order:
-22604: a 3 0 3 2
-22604: identity 4 0 0
-22604: inverse 1 1 0
-22604: positive_part 2 1 1 0,1,3
-22604: negative_part 2 1 1 0,2,3
-22604: greatest_lower_bound 19 2 0
-22604: least_upper_bound 19 2 0
-22604: multiply 19 2 1 0,3
-Statistics :
-Max weight : 20
-Found proof, 10.348100s
-% SZS status Unsatisfiable for GRP167-1.p
-% SZS output start CNFRefutation for GRP167-1.p
-Id : 185, {_}: multiply ?584 (greatest_lower_bound ?585 ?586) =<= greatest_lower_bound (multiply ?584 ?585) (multiply ?584 ?586) [586, 585, 584] by monotony_glb1 ?584 ?585 ?586
-Id : 218, {_}: multiply (least_upper_bound ?658 ?659) ?660 =<= least_upper_bound (multiply ?658 ?660) (multiply ?659 ?660) [660, 659, 658] by monotony_lub2 ?658 ?659 ?660
-Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
-Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 250, {_}: multiply (greatest_lower_bound ?735 ?736) ?737 =<= greatest_lower_bound (multiply ?735 ?737) (multiply ?736 ?737) [737, 736, 735] by monotony_glb2 ?735 ?736 ?737
-Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
-Id : 364, {_}: greatest_lower_bound ?996 (least_upper_bound ?997 ?998) =<= least_upper_bound (greatest_lower_bound ?996 ?997) (greatest_lower_bound ?996 ?998) [998, 997, 996] by lat4_4 ?996 ?997 ?998
-Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 155, {_}: multiply ?513 (least_upper_bound ?514 ?515) =<= least_upper_bound (multiply ?513 ?514) (multiply ?513 ?515) [515, 514, 513] by monotony_lub1 ?513 ?514 ?515
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =?= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71
-Id : 27, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= multiply ?76 identity [77, 76] by Super 25 with 3 at 2,3
-Id : 643, {_}: multiply (multiply ?1439 (inverse ?1440)) ?1440 =>= multiply ?1439 identity [1440, 1439] by Super 25 with 3 at 2,3
-Id : 645, {_}: multiply identity ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Super 643 with 3 at 1,2
-Id : 656, {_}: ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Demod 645 with 2 at 2
-Id : 26, {_}: multiply (multiply ?73 identity) ?74 =>= multiply ?73 ?74 [74, 73] by Super 25 with 2 at 2,3
-Id : 1111, {_}: multiply ?2369 ?2370 =<= multiply (inverse (inverse ?2369)) ?2370 [2370, 2369] by Super 26 with 656 at 1,2
-Id : 2348, {_}: ?1444 =<= multiply ?1444 identity [1444] by Demod 656 with 1111 at 3
-Id : 2350, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= ?76 [77, 76] by Demod 27 with 2348 at 3
-Id : 2372, {_}: inverse (inverse ?4335) =<= multiply ?4335 identity [4335] by Super 2348 with 1111 at 3
-Id : 2377, {_}: inverse (inverse ?4335) =>= ?4335 [4335] by Demod 2372 with 2348 at 3
-Id : 25971, {_}: multiply (multiply ?35046 ?35047) (inverse ?35047) =>= ?35046 [35047, 35046] by Super 2350 with 2377 at 2,1,2
-Id : 161, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= least_upper_bound identity (multiply (inverse ?536) ?537) [537, 536] by Super 155 with 3 at 1,3
-Id : 279, {_}: least_upper_bound identity ?790 =>= positive_part ?790 [790] by Super 6 with 17 at 3
-Id : 4991, {_}: multiply (inverse ?8728) (least_upper_bound ?8728 ?8729) =>= positive_part (multiply (inverse ?8728) ?8729) [8729, 8728] by Demod 161 with 279 at 3
-Id : 5015, {_}: multiply (inverse ?8798) (positive_part ?8798) =?= positive_part (multiply (inverse ?8798) identity) [8798] by Super 4991 with 17 at 2,2
-Id : 5066, {_}: multiply (inverse ?8872) (positive_part ?8872) =>= positive_part (inverse ?8872) [8872] by Demod 5015 with 2348 at 1,3
-Id : 5077, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part (inverse (inverse ?8900)) [8900] by Super 5066 with 2377 at 1,2
-Id : 5091, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part ?8900 [8900] by Demod 5077 with 2377 at 1,3
-Id : 25993, {_}: multiply (positive_part ?35122) (inverse (positive_part (inverse ?35122))) =>= ?35122 [35122] by Super 25971 with 5091 at 1,2
-Id : 2406, {_}: multiply (multiply ?4349 ?4350) (inverse ?4350) =>= ?4349 [4350, 4349] by Super 2350 with 2377 at 2,1,2
-Id : 4974, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= positive_part (multiply (inverse ?536) ?537) [537, 536] by Demod 161 with 279 at 3
-Id : 373, {_}: greatest_lower_bound ?1035 (least_upper_bound ?1036 identity) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Super 364 with 18 at 2,3
-Id : 397, {_}: greatest_lower_bound ?1035 (positive_part ?1036) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Demod 373 with 17 at 2,2
-Id : 256, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= greatest_lower_bound identity (multiply ?759 ?758) [759, 758] by Super 250 with 3 at 1,3
-Id : 296, {_}: greatest_lower_bound identity ?821 =>= negative_part ?821 [821] by Super 5 with 18 at 3
-Id : 17350, {_}: multiply (greatest_lower_bound (inverse ?24308) ?24309) ?24308 =>= negative_part (multiply ?24309 ?24308) [24309, 24308] by Demod 256 with 296 at 3
-Id : 17377, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part (multiply identity ?24398) [24398] by Super 17350 with 18 at 1,2
-Id : 17420, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part ?24398 [24398] by Demod 17377 with 2 at 1,3
-Id : 17441, {_}: multiply (greatest_lower_bound (negative_part (inverse ?24443)) ?24444) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Super 16 with 17420 at 1,3
-Id : 455, {_}: greatest_lower_bound identity (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Super 7 with 296 at 1,3
-Id : 465, {_}: negative_part (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 455 with 296 at 2
-Id : 299, {_}: greatest_lower_bound ?828 (greatest_lower_bound ?829 identity) =>= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Super 7 with 18 at 3
-Id : 309, {_}: greatest_lower_bound ?828 (negative_part ?829) =<= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Demod 299 with 18 at 2,2
-Id : 831, {_}: greatest_lower_bound ?1150 (negative_part ?1151) =?= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 465 with 309 at 2
-Id : 17491, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Demod 17441 with 831 at 1,2
-Id : 17492, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24444, 24443] by Demod 17491 with 5 at 3
-Id : 17323, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= negative_part (multiply ?759 ?758) [759, 758] by Demod 256 with 296 at 3
-Id : 17493, {_}: negative_part (multiply (negative_part ?24444) ?24443) =<= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24443, 24444] by Demod 17492 with 17323 at 2
-Id : 5044, {_}: multiply (inverse ?8798) (positive_part ?8798) =>= positive_part (inverse ?8798) [8798] by Demod 5015 with 2348 at 1,3
-Id : 25992, {_}: multiply (positive_part (inverse ?35120)) (inverse (positive_part ?35120)) =>= inverse ?35120 [35120] by Super 25971 with 5044 at 1,2
-Id : 65949, {_}: negative_part (multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239))) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Super 17493 with 25992 at 1,3
-Id : 285, {_}: greatest_lower_bound ?806 (positive_part ?806) =>= ?806 [806] by Super 12 with 17 at 2,2
-Id : 575, {_}: greatest_lower_bound (positive_part ?1304) ?1304 =>= ?1304 [1304] by Super 5 with 285 at 3
-Id : 424, {_}: least_upper_bound identity (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Super 8 with 279 at 1,3
-Id : 433, {_}: positive_part (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 424 with 279 at 2
-Id : 282, {_}: least_upper_bound ?797 (least_upper_bound ?798 identity) =>= positive_part (least_upper_bound ?797 ?798) [798, 797] by Super 8 with 17 at 3
-Id : 292, {_}: least_upper_bound ?797 (positive_part ?798) =<= positive_part (least_upper_bound ?797 ?798) [798, 797] by Demod 282 with 17 at 2,2
-Id : 749, {_}: least_upper_bound ?1119 (positive_part ?1120) =?= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 433 with 292 at 2
-Id : 758, {_}: least_upper_bound (positive_part (positive_part ?1606)) ?1606 =>= positive_part ?1606 [1606] by Super 9 with 749 at 2
-Id : 606, {_}: least_upper_bound ?1347 (positive_part ?1348) =<= positive_part (least_upper_bound ?1347 ?1348) [1348, 1347] by Demod 282 with 17 at 2,2
-Id : 616, {_}: least_upper_bound ?1379 (positive_part identity) =>= positive_part (positive_part ?1379) [1379] by Super 606 with 17 at 1,3
-Id : 278, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2
-Id : 628, {_}: least_upper_bound ?1379 identity =<= positive_part (positive_part ?1379) [1379] by Demod 616 with 278 at 2,2
-Id : 629, {_}: positive_part ?1379 =<= positive_part (positive_part ?1379) [1379] by Demod 628 with 17 at 2
-Id : 798, {_}: least_upper_bound (positive_part ?1606) ?1606 =>= positive_part ?1606 [1606] by Demod 758 with 629 at 1,2
-Id : 5005, {_}: multiply (inverse (positive_part ?8766)) (positive_part ?8766) =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Super 4991 with 798 at 2,2
-Id : 5040, {_}: identity =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Demod 5005 with 3 at 2
-Id : 5691, {_}: greatest_lower_bound identity (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Super 575 with 5040 at 1,2
-Id : 5736, {_}: negative_part (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Demod 5691 with 296 at 2
-Id : 770, {_}: least_upper_bound ?1642 (positive_part ?1643) =?= least_upper_bound (positive_part ?1642) ?1643 [1643, 1642] by Demod 433 with 292 at 2
-Id : 456, {_}: least_upper_bound identity (negative_part ?1153) =>= identity [1153] by Super 11 with 296 at 2,2
-Id : 464, {_}: positive_part (negative_part ?1153) =>= identity [1153] by Demod 456 with 279 at 2
-Id : 772, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= least_upper_bound identity ?1648 [1648, 1647] by Super 770 with 464 at 1,3
-Id : 812, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= positive_part ?1648 [1648, 1647] by Demod 772 with 279 at 3
-Id : 5068, {_}: multiply (inverse (negative_part ?8875)) identity =>= positive_part (inverse (negative_part ?8875)) [8875] by Super 5066 with 464 at 2,2
-Id : 5087, {_}: inverse (negative_part ?8875) =<= positive_part (inverse (negative_part ?8875)) [8875] by Demod 5068 with 2348 at 2
-Id : 5099, {_}: least_upper_bound (negative_part ?8914) (inverse (negative_part ?8915)) =>= positive_part (inverse (negative_part ?8915)) [8915, 8914] by Super 812 with 5087 at 2,2
-Id : 5137, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= positive_part (inverse (negative_part ?8915)) [8914, 8915] by Demod 5099 with 6 at 2
-Id : 5138, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= inverse (negative_part ?8915) [8914, 8915] by Demod 5137 with 5087 at 3
-Id : 7238, {_}: multiply (inverse (inverse (negative_part ?11513))) (inverse (negative_part ?11513)) =?= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Super 4974 with 5138 at 2,2
-Id : 7311, {_}: identity =<= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Demod 7238 with 3 at 2
-Id : 7312, {_}: identity =<= positive_part (multiply (negative_part ?11513) (negative_part ?11514)) [11514, 11513] by Demod 7311 with 2377 at 1,1,3
-Id : 11865, {_}: negative_part (multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Super 5736 with 7312 at 1,1,1,2
-Id : 2405, {_}: multiply ?4347 (inverse ?4347) =>= identity [4347] by Super 3 with 2377 at 1,2
-Id : 2415, {_}: identity =<= inverse identity [] by Super 2 with 2405 at 2
-Id : 11917, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11865 with 2415 at 1,1,2
-Id : 11918, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =>= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11917 with 7312 at 1,1,3
-Id : 11919, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11918 with 2 at 1,2
-Id : 11920, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply identity (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11919 with 2415 at 1,3
-Id : 13421, {_}: negative_part (multiply (negative_part ?18780) (negative_part ?18781)) =>= multiply (negative_part ?18780) (negative_part ?18781) [18781, 18780] by Demod 11920 with 2 at 3
-Id : 5075, {_}: multiply (inverse (positive_part ?8895)) (positive_part ?8895) =>= positive_part (inverse (positive_part ?8895)) [8895] by Super 5066 with 629 at 2,2
-Id : 5090, {_}: identity =<= positive_part (inverse (positive_part ?8895)) [8895] by Demod 5075 with 3 at 2
-Id : 5175, {_}: greatest_lower_bound identity (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Super 575 with 5090 at 1,2
-Id : 5216, {_}: negative_part (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Demod 5175 with 296 at 2
-Id : 13433, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (negative_part (inverse (positive_part ?18823))) [18823, 18822] by Super 13421 with 5216 at 2,1,2
-Id : 13543, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (inverse (positive_part ?18823)) [18823, 18822] by Demod 13433 with 5216 at 2,3
-Id : 66057, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Demod 65949 with 13543 at 2
-Id : 66058, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66057 with 5216 at 2,3
-Id : 451, {_}: negative_part (least_upper_bound identity ?1143) =>= identity [1143] by Super 12 with 296 at 2
-Id : 469, {_}: negative_part (positive_part ?1143) =>= identity [1143] by Demod 451 with 279 at 1,2
-Id : 66059, {_}: multiply identity (inverse (positive_part ?78239)) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66058 with 469 at 1,2
-Id : 66060, {_}: inverse (positive_part ?78239) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66059 with 2 at 2
-Id : 66290, {_}: greatest_lower_bound (inverse ?78524) (positive_part (inverse (positive_part ?78524))) =>= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Super 397 with 66060 at 1,3
-Id : 66456, {_}: greatest_lower_bound (inverse ?78524) identity =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66290 with 5090 at 2,2
-Id : 66457, {_}: greatest_lower_bound identity (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66456 with 5 at 2
-Id : 66458, {_}: negative_part (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66457 with 296 at 2
-Id : 80743, {_}: multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Super 4974 with 66458 at 2,2
-Id : 80871, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Demod 80743 with 2377 at 1,2
-Id : 80872, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (positive_part ?90706) (negative_part (inverse ?90706))) [90706] by Demod 80871 with 2377 at 1,1,3
-Id : 224, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= least_upper_bound identity (multiply ?682 ?681) [682, 681] by Super 218 with 3 at 1,3
-Id : 15127, {_}: multiply (least_upper_bound (inverse ?21966) ?21967) ?21966 =>= positive_part (multiply ?21967 ?21966) [21967, 21966] by Demod 224 with 279 at 3
-Id : 5107, {_}: least_upper_bound (inverse (negative_part ?8933)) (positive_part ?8934) =>= least_upper_bound (inverse (negative_part ?8933)) ?8934 [8934, 8933] by Super 749 with 5087 at 1,3
-Id : 15147, {_}: multiply (least_upper_bound (inverse (negative_part ?22031)) ?22032) (negative_part ?22031) =>= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22032, 22031] by Super 15127 with 5107 at 1,2
-Id : 15100, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= positive_part (multiply ?682 ?681) [682, 681] by Demod 224 with 279 at 3
-Id : 15182, {_}: positive_part (multiply ?22032 (negative_part ?22031)) =<= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22031, 22032] by Demod 15147 with 15100 at 2
-Id : 80873, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply ?90706 (negative_part (inverse ?90706))) [90706] by Demod 80872 with 15182 at 3
-Id : 191, {_}: multiply (inverse ?607) (greatest_lower_bound ?607 ?608) =>= greatest_lower_bound identity (multiply (inverse ?607) ?608) [608, 607] by Super 185 with 3 at 1,3
-Id : 14063, {_}: multiply (inverse ?19549) (greatest_lower_bound ?19549 ?19550) =>= negative_part (multiply (inverse ?19549) ?19550) [19550, 19549] by Demod 191 with 296 at 3
-Id : 14093, {_}: multiply (inverse ?19640) (negative_part ?19640) =?= negative_part (multiply (inverse ?19640) identity) [19640] by Super 14063 with 18 at 2,2
-Id : 14179, {_}: multiply (inverse ?19758) (negative_part ?19758) =>= negative_part (inverse ?19758) [19758] by Demod 14093 with 2348 at 1,3
-Id : 14205, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part (inverse (inverse ?19826)) [19826] by Super 14179 with 2377 at 1,2
-Id : 14261, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part ?19826 [19826] by Demod 14205 with 2377 at 1,3
-Id : 80874, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= positive_part (negative_part ?90706) [90706] by Demod 80873 with 14261 at 1,3
-Id : 80875, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= identity [90706] by Demod 80874 with 464 at 3
-Id : 81247, {_}: multiply identity (inverse (negative_part (inverse ?91006))) =>= positive_part ?91006 [91006] by Super 2406 with 80875 at 1,2
-Id : 81627, {_}: inverse (negative_part (inverse ?91433)) =>= positive_part ?91433 [91433] by Demod 81247 with 2 at 2
-Id : 81628, {_}: inverse (negative_part ?91435) =<= positive_part (inverse ?91435) [91435] by Super 81627 with 2377 at 1,1,2
-Id : 82425, {_}: multiply (positive_part ?35122) (inverse (inverse (negative_part ?35122))) =>= ?35122 [35122] by Demod 25993 with 81628 at 1,2,2
-Id : 82501, {_}: multiply (positive_part ?35122) (negative_part ?35122) =>= ?35122 [35122] by Demod 82425 with 2377 at 2,2
-Id : 82875, {_}: a === a [] by Demod 1 with 82501 at 3
-Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-1.p
-22602: solved GRP167-1.p in 10.376648 using nrkbo
-22602: status Unsatisfiable for GRP167-1.p
-CLASH, statistics insufficient
-22609: Facts:
-22609: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22609: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22609: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22609: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22609: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22609: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22609: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22609: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22609: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22609: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22609: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22609: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22609: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22609: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22609: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22609: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-22609: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-22609: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-22609: Id : 20, {_}:
- positive_part ?56 =<= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-22609: Id : 21, {_}:
- negative_part ?58 =<= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-22609: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-22609: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =<=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-22609: Goal:
-22609: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22609: Order:
-22609: nrkbo
-22609: Leaf order:
-22609: a 3 0 3 2
-22609: identity 6 0 0
-22609: positive_part 2 1 1 0,1,3
-22609: negative_part 2 1 1 0,2,3
-22609: inverse 7 1 0
-22609: greatest_lower_bound 19 2 0
-22609: least_upper_bound 19 2 0
-22609: multiply 21 2 1 0,3
-CLASH, statistics insufficient
-22610: Facts:
-22610: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22610: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22610: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22610: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22610: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-CLASH, statistics insufficient
-22611: Facts:
-22611: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22611: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22611: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22611: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22610: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22610: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22610: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22610: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22610: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22610: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22610: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22610: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22610: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22610: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22610: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-22610: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-22610: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-22610: Id : 20, {_}:
- positive_part ?56 =<= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-22610: Id : 21, {_}:
- negative_part ?58 =<= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-22610: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-22610: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =<=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-22610: Goal:
-22610: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22610: Order:
-22610: kbo
-22610: Leaf order:
-22610: a 3 0 3 2
-22610: identity 6 0 0
-22610: positive_part 2 1 1 0,1,3
-22610: negative_part 2 1 1 0,2,3
-22610: inverse 7 1 0
-22610: greatest_lower_bound 19 2 0
-22610: least_upper_bound 19 2 0
-22610: multiply 21 2 1 0,3
-22611: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22611: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22611: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22611: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22611: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22611: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22611: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22611: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22611: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22611: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22611: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22611: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-22611: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-22611: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by lat4_3 ?53 ?54
-22611: Id : 20, {_}:
- positive_part ?56 =>= least_upper_bound ?56 identity
- [56] by lat4_4 ?56
-22611: Id : 21, {_}:
- negative_part ?58 =>= greatest_lower_bound ?58 identity
- [58] by lat4_5 ?58
-22611: Id : 22, {_}:
- least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
- =<=
- greatest_lower_bound (least_upper_bound ?60 ?61)
- (least_upper_bound ?60 ?62)
- [62, 61, 60] by lat4_6 ?60 ?61 ?62
-22611: Id : 23, {_}:
- greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
- =>=
- least_upper_bound (greatest_lower_bound ?64 ?65)
- (greatest_lower_bound ?64 ?66)
- [66, 65, 64] by lat4_7 ?64 ?65 ?66
-22611: Goal:
-22611: Id : 1, {_}:
- a =<= multiply (positive_part a) (negative_part a)
- [] by prove_lat4
-22611: Order:
-22611: lpo
-22611: Leaf order:
-22611: a 3 0 3 2
-22611: identity 6 0 0
-22611: positive_part 2 1 1 0,1,3
-22611: negative_part 2 1 1 0,2,3
-22611: inverse 7 1 0
-22611: greatest_lower_bound 19 2 0
-22611: least_upper_bound 19 2 0
-22611: multiply 21 2 1 0,3
-Statistics :
-Max weight : 16
-Found proof, 6.082892s
-% SZS status Unsatisfiable for GRP167-2.p
-% SZS output start CNFRefutation for GRP167-2.p
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
-Id : 221, {_}: multiply (least_upper_bound ?664 ?665) ?666 =<= least_upper_bound (multiply ?664 ?666) (multiply ?665 ?666) [666, 665, 664] by monotony_lub2 ?664 ?665 ?666
-Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
-Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 17, {_}: inverse identity =>= identity [] by lat4_1
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =?= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
-Id : 302, {_}: inverse (multiply ?849 ?850) =<= multiply (inverse ?850) (inverse ?849) [850, 849] by lat4_3 ?849 ?850
-Id : 1638, {_}: inverse (multiply ?3326 (inverse ?3327)) =>= multiply ?3327 (inverse ?3326) [3327, 3326] by Super 302 with 18 at 1,3
-Id : 30, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= multiply ?82 identity [83, 82] by Super 28 with 3 at 2,3
-Id : 303, {_}: inverse (multiply identity ?852) =<= multiply (inverse ?852) identity [852] by Super 302 with 17 at 2,3
-Id : 587, {_}: inverse ?1361 =<= multiply (inverse ?1361) identity [1361] by Demod 303 with 2 at 1,2
-Id : 589, {_}: inverse (inverse ?1364) =<= multiply ?1364 identity [1364] by Super 587 with 18 at 1,3
-Id : 603, {_}: ?1364 =<= multiply ?1364 identity [1364] by Demod 589 with 18 at 2
-Id : 645, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= ?82 [83, 82] by Demod 30 with 603 at 3
-Id : 1648, {_}: inverse ?3357 =<= multiply ?3358 (inverse (multiply ?3357 (inverse (inverse ?3358)))) [3358, 3357] by Super 1638 with 645 at 1,2
-Id : 306, {_}: inverse (multiply ?859 (inverse ?860)) =>= multiply ?860 (inverse ?859) [860, 859] by Super 302 with 18 at 1,3
-Id : 1667, {_}: inverse ?3357 =<= multiply ?3358 (multiply (inverse ?3358) (inverse ?3357)) [3358, 3357] by Demod 1648 with 306 at 2,3
-Id : 48018, {_}: inverse ?56639 =<= multiply ?56640 (inverse (multiply ?56639 ?56640)) [56640, 56639] by Demod 1667 with 19 at 2,3
-Id : 657, {_}: multiply ?1476 (least_upper_bound ?1477 identity) =?= least_upper_bound (multiply ?1476 ?1477) ?1476 [1477, 1476] by Super 13 with 603 at 2,3
-Id : 4078, {_}: multiply ?7362 (positive_part ?7363) =<= least_upper_bound (multiply ?7362 ?7363) ?7362 [7363, 7362] by Demod 657 with 20 at 2,2
-Id : 4080, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= least_upper_bound identity (inverse ?7367) [7367] by Super 4078 with 3 at 1,3
-Id : 320, {_}: least_upper_bound identity ?881 =>= positive_part ?881 [881] by Super 6 with 20 at 3
-Id : 4115, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= positive_part (inverse ?7367) [7367] by Demod 4080 with 320 at 3
-Id : 618, {_}: multiply (multiply ?1420 (inverse ?1421)) ?1421 =>= multiply ?1420 identity [1421, 1420] by Super 28 with 3 at 2,3
-Id : 620, {_}: multiply (multiply ?1425 ?1426) (inverse ?1426) =>= multiply ?1425 identity [1426, 1425] by Super 618 with 18 at 2,1,2
-Id : 34073, {_}: multiply (multiply ?41189 ?41190) (inverse ?41190) =>= ?41189 [41190, 41189] by Demod 620 with 603 at 3
-Id : 651, {_}: multiply ?1462 (greatest_lower_bound ?1463 identity) =?= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Super 14 with 603 at 2,3
-Id : 676, {_}: multiply ?1462 (negative_part ?1463) =<= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Demod 651 with 21 at 2,2
-Id : 227, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= least_upper_bound identity (multiply ?688 ?687) [688, 687] by Super 221 with 3 at 1,3
-Id : 14335, {_}: multiply (least_upper_bound (inverse ?21902) ?21903) ?21902 =>= positive_part (multiply ?21903 ?21902) [21903, 21902] by Demod 227 with 320 at 3
-Id : 14360, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part (multiply identity ?21984) [21984] by Super 14335 with 20 at 1,2
-Id : 14399, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part ?21984 [21984] by Demod 14360 with 2 at 1,3
-Id : 14409, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= greatest_lower_bound (positive_part ?22003) (positive_part (inverse ?22003)) [22003] by Super 676 with 14399 at 1,3
-Id : 504, {_}: least_upper_bound identity (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Super 22 with 320 at 2,3
-Id : 513, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Demod 504 with 320 at 2
-Id : 514, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (positive_part ?1268) (positive_part ?1269) [1269, 1268] by Demod 513 with 320 at 1,3
-Id : 14487, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= positive_part (greatest_lower_bound ?22003 (inverse ?22003)) [22003] by Demod 14409 with 514 at 3
-Id : 501, {_}: least_upper_bound identity (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Super 8 with 320 at 1,3
-Id : 518, {_}: positive_part (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 501 with 320 at 2
-Id : 317, {_}: least_upper_bound ?872 (least_upper_bound ?873 identity) =>= positive_part (least_upper_bound ?872 ?873) [873, 872] by Super 8 with 20 at 3
-Id : 329, {_}: least_upper_bound ?872 (positive_part ?873) =<= positive_part (least_upper_bound ?872 ?873) [873, 872] by Demod 317 with 20 at 2,2
-Id : 975, {_}: least_upper_bound ?1262 (positive_part ?1263) =?= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 518 with 329 at 2
-Id : 4147, {_}: multiply (inverse ?7493) (positive_part ?7493) =>= positive_part (inverse ?7493) [7493] by Demod 4080 with 320 at 3
-Id : 337, {_}: greatest_lower_bound identity ?912 =>= negative_part ?912 [912] by Super 5 with 21 at 3
-Id : 533, {_}: least_upper_bound identity (negative_part ?1296) =>= identity [1296] by Super 11 with 337 at 2,2
-Id : 549, {_}: positive_part (negative_part ?1296) =>= identity [1296] by Demod 533 with 320 at 2
-Id : 4149, {_}: multiply (inverse (negative_part ?7496)) identity =>= positive_part (inverse (negative_part ?7496)) [7496] by Super 4147 with 549 at 2,2
-Id : 4174, {_}: inverse (negative_part ?7496) =<= positive_part (inverse (negative_part ?7496)) [7496] by Demod 4149 with 603 at 2
-Id : 4193, {_}: least_upper_bound (inverse (negative_part ?7552)) (positive_part ?7553) =>= least_upper_bound (inverse (negative_part ?7552)) ?7553 [7553, 7552] by Super 975 with 4174 at 1,3
-Id : 14357, {_}: multiply (least_upper_bound (inverse (negative_part ?21975)) ?21976) (negative_part ?21975) =>= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21976, 21975] by Super 14335 with 4193 at 1,2
-Id : 14303, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= positive_part (multiply ?688 ?687) [688, 687] by Demod 227 with 320 at 3
-Id : 14396, {_}: positive_part (multiply ?21976 (negative_part ?21975)) =<= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21975, 21976] by Demod 14357 with 14303 at 2
-Id : 15618, {_}: positive_part (multiply (inverse ?23238) (negative_part ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Super 14396 with 14487 at 1,3
-Id : 4791, {_}: multiply ?8267 (negative_part ?8268) =<= greatest_lower_bound (multiply ?8267 ?8268) ?8267 [8268, 8267] by Demod 651 with 21 at 2,2
-Id : 4793, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= greatest_lower_bound identity (inverse ?8272) [8272] by Super 4791 with 3 at 1,3
-Id : 4834, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= negative_part (inverse ?8272) [8272] by Demod 4793 with 337 at 3
-Id : 15709, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Demod 15618 with 4834 at 1,2
-Id : 774, {_}: least_upper_bound ?1603 (positive_part ?1604) =<= positive_part (least_upper_bound ?1603 ?1604) [1604, 1603] by Demod 317 with 20 at 2,2
-Id : 784, {_}: least_upper_bound ?1635 (positive_part identity) =>= positive_part (positive_part ?1635) [1635] by Super 774 with 20 at 1,3
-Id : 322, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
-Id : 796, {_}: least_upper_bound ?1635 identity =<= positive_part (positive_part ?1635) [1635] by Demod 784 with 322 at 2,2
-Id : 797, {_}: positive_part ?1635 =<= positive_part (positive_part ?1635) [1635] by Demod 796 with 20 at 2
-Id : 15710, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15709 with 797 at 3
-Id : 15711, {_}: identity =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15710 with 549 at 2
-Id : 15820, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= identity [22003] by Demod 14487 with 15711 at 3
-Id : 34109, {_}: multiply identity (inverse (negative_part ?41304)) =>= positive_part (inverse ?41304) [41304] by Super 34073 with 15820 at 1,2
-Id : 34155, {_}: inverse (negative_part ?41304) =<= positive_part (inverse ?41304) [41304] by Demod 34109 with 2 at 2
-Id : 34195, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= inverse (negative_part ?7367) [7367] by Demod 4115 with 34155 at 3
-Id : 48045, {_}: inverse (inverse ?56723) =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Super 48018 with 34195 at 1,2,3
-Id : 48126, {_}: ?56723 =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Demod 48045 with 18 at 2
-Id : 48127, {_}: ?56723 =<= multiply (positive_part ?56723) (negative_part ?56723) [56723] by Demod 48126 with 18 at 2,3
-Id : 48357, {_}: a === a [] by Demod 1 with 48127 at 3
-Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
-% SZS output end CNFRefutation for GRP167-2.p
-22609: solved GRP167-2.p in 6.08038 using nrkbo
-22609: status Unsatisfiable for GRP167-2.p
-NO CLASH, using fixed ground order
-22621: Facts:
-NO CLASH, using fixed ground order
-22622: Facts:
-22622: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22622: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22622: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22622: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22622: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22622: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22622: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22622: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22622: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22622: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22622: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22622: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22622: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22622: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22622: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22622: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-22622: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-22622: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-22622: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-22622: Goal:
-22622: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-22622: Order:
-22622: kbo
-22622: Leaf order:
-22622: b 4 0 1 1,2,2
-22622: c 4 0 2 2,2,2
-22622: a 5 0 2 1,2
-22622: identity 6 0 0
-22622: inverse 1 1 0
-22622: least_upper_bound 16 2 0
-22622: greatest_lower_bound 16 2 2 0,2
-22622: multiply 19 2 1 0,2,2
-NO CLASH, using fixed ground order
-22623: Facts:
-22623: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22623: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22623: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22623: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22623: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22623: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22623: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22623: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22623: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22623: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22623: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22623: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22623: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22623: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22623: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22623: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-22623: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-22623: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-22623: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-22623: Goal:
-22623: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-22623: Order:
-22623: lpo
-22623: Leaf order:
-22623: b 4 0 1 1,2,2
-22623: c 4 0 2 2,2,2
-22623: a 5 0 2 1,2
-22623: identity 6 0 0
-22623: inverse 1 1 0
-22623: least_upper_bound 16 2 0
-22623: greatest_lower_bound 16 2 2 0,2
-22623: multiply 19 2 1 0,2,2
-22621: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22621: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22621: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22621: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22621: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22621: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22621: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22621: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22621: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22621: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22621: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22621: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22621: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22621: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22621: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22621: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
-22621: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
-22621: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
-22621: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
-22621: Goal:
-22621: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09a
-22621: Order:
-22621: nrkbo
-22621: Leaf order:
-22621: b 4 0 1 1,2,2
-22621: c 4 0 2 2,2,2
-22621: a 5 0 2 1,2
-22621: identity 6 0 0
-22621: inverse 1 1 0
-22621: least_upper_bound 16 2 0
-22621: greatest_lower_bound 16 2 2 0,2
-22621: multiply 19 2 1 0,2,2
-% SZS status Timeout for GRP178-1.p
-NO CLASH, using fixed ground order
-22657: Facts:
-22657: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22657: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22657: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22657: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22657: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22657: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22657: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22657: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22657: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22657: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22657: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22657: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22657: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22657: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22657: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22657: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-22657: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-22657: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-22657: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-22657: Goal:
-22657: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-22657: Order:
-22657: nrkbo
-22657: Leaf order:
-22657: b 3 0 1 1,2,2
-22657: c 3 0 2 2,2,2
-22657: a 4 0 2 1,2
-22657: identity 9 0 0
-22657: inverse 1 1 0
-22657: least_upper_bound 13 2 0
-22657: multiply 19 2 1 0,2,2
-22657: greatest_lower_bound 19 2 2 0,2
-NO CLASH, using fixed ground order
-22658: Facts:
-22658: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22658: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22658: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22658: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22658: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22658: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22658: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22658: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22658: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22658: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22658: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22658: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22658: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22658: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22658: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22658: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-22658: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-22658: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-22658: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-22658: Goal:
-22658: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-22658: Order:
-22658: kbo
-22658: Leaf order:
-22658: b 3 0 1 1,2,2
-22658: c 3 0 2 2,2,2
-22658: a 4 0 2 1,2
-22658: identity 9 0 0
-22658: inverse 1 1 0
-22658: least_upper_bound 13 2 0
-22658: multiply 19 2 1 0,2,2
-22658: greatest_lower_bound 19 2 2 0,2
-NO CLASH, using fixed ground order
-22659: Facts:
-22659: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22659: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22659: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22659: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22659: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22659: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22659: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22659: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22659: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22659: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22659: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22659: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22659: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22659: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22659: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22659: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
-22659: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
-22659: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
-22659: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
-22659: Goal:
-22659: Id : 1, {_}:
- greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
- [] by prove_p09b
-22659: Order:
-22659: lpo
-22659: Leaf order:
-22659: b 3 0 1 1,2,2
-22659: c 3 0 2 2,2,2
-22659: a 4 0 2 1,2
-22659: identity 9 0 0
-22659: inverse 1 1 0
-22659: least_upper_bound 13 2 0
-22659: multiply 19 2 1 0,2,2
-22659: greatest_lower_bound 19 2 2 0,2
-% SZS status Timeout for GRP178-2.p
-CLASH, statistics insufficient
-22685: Facts:
-22685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22685: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22685: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22685: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22685: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22685: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22685: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22685: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22685: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22685: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22685: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22685: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22685: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22685: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-22685: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-22685: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =<=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-22685: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =<=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-22685: Goal:
-22685: Id : 1, {_}: a =>= b [] by prove_p12x
-22685: Order:
-22685: nrkbo
-22685: Leaf order:
-22685: identity 2 0 0
-22685: a 3 0 1 2
-22685: b 3 0 1 3
-22685: c 4 0 0
-22685: inverse 7 1 0
-22685: greatest_lower_bound 17 2 0
-22685: least_upper_bound 17 2 0
-22685: multiply 18 2 0
-CLASH, statistics insufficient
-22686: Facts:
-22686: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22686: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22686: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22686: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22686: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-CLASH, statistics insufficient
-22687: Facts:
-22687: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22687: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22687: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22687: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22687: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22687: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22686: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22686: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22686: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22686: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22686: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22686: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22686: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22686: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22686: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22686: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22686: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-22686: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-22686: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =<=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-22686: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =<=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-22686: Goal:
-22686: Id : 1, {_}: a =>= b [] by prove_p12x
-22686: Order:
-22686: kbo
-22686: Leaf order:
-22686: identity 2 0 0
-22686: a 3 0 1 2
-22686: b 3 0 1 3
-22686: c 4 0 0
-22686: inverse 7 1 0
-22686: greatest_lower_bound 17 2 0
-22686: least_upper_bound 17 2 0
-22686: multiply 18 2 0
-22687: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22687: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22687: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22687: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22687: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22687: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22687: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22687: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22687: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22687: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_1
-22687: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
-22687: Id : 19, {_}:
- inverse (greatest_lower_bound ?52 ?53)
- =>=
- least_upper_bound (inverse ?52) (inverse ?53)
- [53, 52] by p12x_3 ?52 ?53
-22687: Id : 20, {_}:
- inverse (least_upper_bound ?55 ?56)
- =>=
- greatest_lower_bound (inverse ?55) (inverse ?56)
- [56, 55] by p12x_4 ?55 ?56
-22687: Goal:
-22687: Id : 1, {_}: a =>= b [] by prove_p12x
-22687: Order:
-22687: lpo
-22687: Leaf order:
-22687: identity 2 0 0
-22687: a 3 0 1 2
-22687: b 3 0 1 3
-22687: c 4 0 0
-22687: inverse 7 1 0
-22687: greatest_lower_bound 17 2 0
-22687: least_upper_bound 17 2 0
-22687: multiply 18 2 0
-% SZS status Timeout for GRP181-3.p
-NO CLASH, using fixed ground order
-22714: Facts:
-22714: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22714: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22714: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22714: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22714: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22714: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22714: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22714: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22714: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22714: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22714: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22714: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22714: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22714: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22714: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22714: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-22714: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-22714: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-22714: Goal:
-22714: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-22714: Order:
-22714: nrkbo
-22714: Leaf order:
-22714: a 4 0 4 1,1,2
-22714: identity 8 0 4 2,1,2
-22714: inverse 9 1 2 0,2,2
-22714: least_upper_bound 15 2 2 0,1,2
-22714: greatest_lower_bound 15 2 2 0,1,2,2
-22714: multiply 22 2 2 0,2
-NO CLASH, using fixed ground order
-22715: Facts:
-22715: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22715: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22715: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22715: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22715: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22715: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22715: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22715: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22715: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22715: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22715: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22715: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22715: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22715: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22715: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22715: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-22715: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-22715: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-22715: Goal:
-22715: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-22715: Order:
-22715: kbo
-22715: Leaf order:
-22715: a 4 0 4 1,1,2
-22715: identity 8 0 4 2,1,2
-22715: inverse 9 1 2 0,2,2
-22715: least_upper_bound 15 2 2 0,1,2
-22715: greatest_lower_bound 15 2 2 0,1,2,2
-22715: multiply 22 2 2 0,2
-NO CLASH, using fixed ground order
-22716: Facts:
-22716: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22716: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22716: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22716: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22716: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22716: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22716: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22716: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22716: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22716: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22716: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22716: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22716: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22716: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22716: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22716: Id : 17, {_}: inverse identity =>= identity [] by p21_1
-22716: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
-22716: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p21_3 ?53 ?54
-22716: Goal:
-22716: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-22716: Order:
-22716: lpo
-22716: Leaf order:
-22716: a 4 0 4 1,1,2
-22716: identity 8 0 4 2,1,2
-22716: inverse 9 1 2 0,2,2
-22716: least_upper_bound 15 2 2 0,1,2
-22716: greatest_lower_bound 15 2 2 0,1,2,2
-22716: multiply 22 2 2 0,2
-% SZS status Timeout for GRP184-2.p
-NO CLASH, using fixed ground order
-22807: Facts:
-22807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22807: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22807: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22807: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22807: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22807: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22807: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22807: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22807: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22807: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22807: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22807: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22807: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22807: Goal:
-22807: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22807: Order:
-22807: nrkbo
-22807: Leaf order:
-22807: a 3 0 3 1,1,1,2
-22807: b 3 0 3 2,1,1,2
-22807: identity 7 0 5 2,1,2
-22807: inverse 1 1 0
-22807: greatest_lower_bound 13 2 0
-22807: least_upper_bound 19 2 6 0,2
-22807: multiply 21 2 3 0,1,1,2
-NO CLASH, using fixed ground order
-22808: Facts:
-22808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22808: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22808: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22808: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22808: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22808: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22808: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22808: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22808: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22808: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22808: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22808: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22808: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22808: Goal:
-22808: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22808: Order:
-22808: kbo
-22808: Leaf order:
-22808: a 3 0 3 1,1,1,2
-22808: b 3 0 3 2,1,1,2
-22808: identity 7 0 5 2,1,2
-22808: inverse 1 1 0
-22808: greatest_lower_bound 13 2 0
-22808: least_upper_bound 19 2 6 0,2
-22808: multiply 21 2 3 0,1,1,2
-NO CLASH, using fixed ground order
-22809: Facts:
-22809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22809: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22809: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22809: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22809: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22809: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22809: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22809: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22809: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22809: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22809: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22809: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22809: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22809: Goal:
-22809: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22809: Order:
-22809: lpo
-22809: Leaf order:
-22809: a 3 0 3 1,1,1,2
-22809: b 3 0 3 2,1,1,2
-22809: identity 7 0 5 2,1,2
-22809: inverse 1 1 0
-22809: greatest_lower_bound 13 2 0
-22809: least_upper_bound 19 2 6 0,2
-22809: multiply 21 2 3 0,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 1.740382s
-% SZS status Unsatisfiable for GRP185-1.p
-% SZS output start CNFRefutation for GRP185-1.p
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
-Id : 482, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
-Id : 484, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 482 with 3 at 2,3
-Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
-Id : 490, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 482 with 27 at 2,3
-Id : 725, {_}: ?599 =<= multiply ?599 identity [599] by Demod 484 with 490 at 3
-Id : 73, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
-Id : 57, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
-Id : 3011, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) === least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3010 with 73 at 2,2,2
-Id : 3010, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (least_upper_bound identity (multiply a b)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3009 with 8 at 2,2
-Id : 3009, {_}: least_upper_bound b (least_upper_bound (least_upper_bound a identity) (least_upper_bound identity (multiply a b))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3008 with 8 at 2
-Id : 3008, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3007 with 8 at 2,3
-Id : 3007, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3006 with 57 at 2
-Id : 3006, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3005 with 8 at 3
-Id : 3005, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3004 with 2 at 2,2,2,2,2
-Id : 3004, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3003 with 725 at 1,2,2,2,2
-Id : 3003, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3002 with 2 at 1,2,2,2
-Id : 3002, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3001 with 6 at 3
-Id : 3001, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 3000 with 73 at 2,2
-Id : 3000, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 2999 with 2 at 2,2,2,3
-Id : 2999, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity))) [] by Demod 2998 with 725 at 1,2,2,3
-Id : 2998, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2997 with 2 at 1,2,3
-Id : 2997, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2996 with 8 at 2,2,2
-Id : 2996, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2995 with 8 at 3
-Id : 2995, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2994 with 15 at 2,2,2,2
-Id : 2994, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2993 with 15 at 1,2,2,2
-Id : 2993, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2992 with 15 at 2,3
-Id : 2992, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 2991 with 15 at 1,3
-Id : 2991, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2990 with 13 at 2,2,2
-Id : 2990, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2989 with 13 at 3
-Id : 2989, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 56 with 8 at 2
-Id : 56, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
-% SZS output end CNFRefutation for GRP185-1.p
-22809: solved GRP185-1.p in 0.852052 using lpo
-22809: status Unsatisfiable for GRP185-1.p
-NO CLASH, using fixed ground order
-22814: Facts:
-NO CLASH, using fixed ground order
-22815: Facts:
-22815: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22815: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22815: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22815: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22815: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22815: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22815: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-NO CLASH, using fixed ground order
-22816: Facts:
-22816: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22816: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22816: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22816: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22816: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22816: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22816: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22816: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22814: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22815: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22814: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-22815: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22815: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22815: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22814: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-22814: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-22814: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-22815: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22814: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-22815: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22814: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-22814: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-22814: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22814: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22814: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22814: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22814: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22814: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22814: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22814: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-22814: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-22814: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-22814: Goal:
-22814: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22814: Order:
-22814: nrkbo
-22814: Leaf order:
-22814: a 3 0 3 1,1,1,2
-22814: b 3 0 3 2,1,1,2
-22814: identity 9 0 5 2,1,2
-22814: inverse 7 1 0
-22814: greatest_lower_bound 13 2 0
-22814: least_upper_bound 19 2 6 0,2
-22814: multiply 23 2 3 0,1,1,2
-22816: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-22815: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22815: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22815: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-22815: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-22815: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-22815: Goal:
-22815: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22815: Order:
-22815: kbo
-22815: Leaf order:
-22815: a 3 0 3 1,1,1,2
-22815: b 3 0 3 2,1,1,2
-22815: identity 9 0 5 2,1,2
-22815: inverse 7 1 0
-22815: greatest_lower_bound 13 2 0
-22815: least_upper_bound 19 2 6 0,2
-22815: multiply 23 2 3 0,1,1,2
-22816: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-22816: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-22816: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-22816: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-22816: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-22816: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-22816: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-22816: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-22816: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22a_3 ?53 ?54
-22816: Goal:
-22816: Id : 1, {_}:
- least_upper_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- multiply (least_upper_bound a identity)
- (least_upper_bound b identity)
- [] by prove_p22a
-22816: Order:
-22816: lpo
-22816: Leaf order:
-22816: a 3 0 3 1,1,1,2
-22816: b 3 0 3 2,1,1,2
-22816: identity 9 0 5 2,1,2
-22816: inverse 7 1 0
-22816: greatest_lower_bound 13 2 0
-22816: least_upper_bound 19 2 6 0,2
-22816: multiply 23 2 3 0,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 4.698116s
-% SZS status Unsatisfiable for GRP185-2.p
-% SZS output start CNFRefutation for GRP185-2.p
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
-Id : 17, {_}: inverse identity =>= identity [] by p22a_1
-Id : 426, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
-Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-Id : 62, {_}: least_upper_bound ?157 (least_upper_bound ?158 ?159) =<= least_upper_bound (least_upper_bound ?157 ?158) ?159 [159, 158, 157] by associativity_of_lub ?157 ?158 ?159
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 63, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =<= least_upper_bound (least_upper_bound ?162 ?161) ?163 [163, 162, 161] by Super 62 with 6 at 1,3
-Id : 69, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =?= least_upper_bound ?162 (least_upper_bound ?161 ?163) [163, 162, 161] by Demod 63 with 8 at 3
-Id : 76, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3
-Id : 427, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 426 with 17 at 2,3
-Id : 481, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 427 with 2 at 1,2
-Id : 483, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 481 with 18 at 1,3
-Id : 491, {_}: ?572 =<= multiply ?572 identity [572] by Demod 483 with 18 at 2
-Id : 60, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3
-Id : 706, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3
-Id : 707, {_}: least_upper_bound ?670 (least_upper_bound ?671 ?670) =>= least_upper_bound ?670 ?671 [671, 670] by Super 706 with 6 at 2,2
-Id : 1184, {_}: least_upper_bound ?916 (least_upper_bound (least_upper_bound ?917 ?916) ?918) =?= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Super 8 with 707 at 1,3
-Id : 1214, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =<= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Demod 1184 with 8 at 2,2
-Id : 1215, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =>= least_upper_bound ?916 (least_upper_bound ?917 ?918) [918, 917, 916] by Demod 1214 with 8 at 3
-Id : 7862, {_}: least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) === least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7861 with 69 at 2
-Id : 7861, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7860 with 60 at 2,2
-Id : 7860, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7859 with 491 at 2,2,2,2
-Id : 7859, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7858 with 69 at 3
-Id : 7858, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7857 with 1215 at 2,2
-Id : 7857, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7856 with 60 at 2,3
-Id : 7856, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7855 with 69 at 2
-Id : 7855, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7854 with 491 at 2,2,2,3
-Id : 7854, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7853 with 69 at 2,2
-Id : 7853, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7852 with 69 at 2,3
-Id : 7852, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7851 with 76 at 2,2
-Id : 7851, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7850 with 69 at 3
-Id : 7850, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 509 with 69 at 2
-Id : 509, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 508 with 6 at 2,2,2,2,2
-Id : 508, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 507 with 6 at 2,2,3
-Id : 507, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 506 with 2 at 2,2,2,2,2,2
-Id : 506, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 505 with 2 at 1,2,2,2,2
-Id : 505, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 504 with 2 at 2,2,2,3
-Id : 504, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 503 with 2 at 1,2,3
-Id : 503, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 502 with 8 at 2,2,2
-Id : 502, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 501 with 8 at 3
-Id : 501, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 500 with 15 at 2,2,2,2
-Id : 500, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 499 with 15 at 1,2,2,2
-Id : 499, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 498 with 15 at 2,3
-Id : 498, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 497 with 15 at 1,3
-Id : 497, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 496 with 13 at 2,2,2
-Id : 496, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 495 with 13 at 3
-Id : 495, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2
-Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
-% SZS output end CNFRefutation for GRP185-2.p
-22816: solved GRP185-2.p in 2.292143 using lpo
-22816: status Unsatisfiable for GRP185-2.p
-CLASH, statistics insufficient
-22828: Facts:
-22828: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22828: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22828: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22828: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22828: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22828: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22828: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22828: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22828: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =?=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-22828: Goal:
-22828: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-22828: Order:
-22828: nrkbo
-22828: Leaf order:
-22828: a 2 0 2 1,1,1,2
-22828: c 2 0 2 2,1,2
-22828: identity 4 0 0
-22828: b 4 0 4 2,1,1,2
-22828: right_inverse 1 1 0
-22828: left_inverse 1 1 0
-22828: left_division 2 2 0
-22828: right_division 2 2 0
-22828: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-22829: Facts:
-22829: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22829: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22829: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22829: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22829: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22829: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22829: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22829: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22829: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =>=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-22829: Goal:
-22829: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-22829: Order:
-22829: kbo
-22829: Leaf order:
-22829: a 2 0 2 1,1,1,2
-22829: c 2 0 2 2,1,2
-22829: identity 4 0 0
-22829: b 4 0 4 2,1,1,2
-22829: right_inverse 1 1 0
-22829: left_inverse 1 1 0
-22829: left_division 2 2 0
-22829: right_division 2 2 0
-22829: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-22830: Facts:
-22830: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22830: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22830: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22830: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22830: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22830: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22830: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22830: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22830: Id : 10, {_}:
- multiply (multiply ?22 (multiply ?23 ?24)) ?22
- =>=
- multiply (multiply ?22 ?23) (multiply ?24 ?22)
- [24, 23, 22] by moufang1 ?22 ?23 ?24
-22830: Goal:
-22830: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-22830: Order:
-22830: lpo
-22830: Leaf order:
-22830: a 2 0 2 1,1,1,2
-22830: c 2 0 2 2,1,2
-22830: identity 4 0 0
-22830: b 4 0 4 2,1,1,2
-22830: right_inverse 1 1 0
-22830: left_inverse 1 1 0
-22830: left_division 2 2 0
-22830: right_division 2 2 0
-22830: multiply 20 2 6 0,2
-% SZS status Timeout for GRP200-1.p
-CLASH, statistics insufficient
-22867: Facts:
-22867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22867: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22867: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22867: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22867: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22867: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22867: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22867: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22867: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =?=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-22867: Goal:
-22867: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-22867: Order:
-22867: nrkbo
-22867: Leaf order:
-22867: b 2 0 2 2,1,1,2
-22867: c 2 0 2 2,2
-22867: identity 4 0 0
-22867: a 4 0 4 1,1,1,2
-22867: right_inverse 1 1 0
-22867: left_inverse 1 1 0
-22867: left_division 2 2 0
-22867: right_division 2 2 0
-22867: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-22868: Facts:
-22868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22868: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22868: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22868: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22868: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22868: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22868: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22868: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22868: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =>=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-22868: Goal:
-22868: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-22868: Order:
-22868: kbo
-22868: Leaf order:
-22868: b 2 0 2 2,1,1,2
-22868: c 2 0 2 2,2
-22868: identity 4 0 0
-22868: a 4 0 4 1,1,1,2
-22868: right_inverse 1 1 0
-22868: left_inverse 1 1 0
-22868: left_division 2 2 0
-22868: right_division 2 2 0
-22868: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-22869: Facts:
-22869: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22869: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22869: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22869: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22869: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22869: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22869: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22869: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22869: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?24) ?23
- =>=
- multiply ?22 (multiply ?23 (multiply ?24 ?23))
- [24, 23, 22] by moufang2 ?22 ?23 ?24
-22869: Goal:
-22869: Id : 1, {_}:
- multiply (multiply (multiply a b) a) c
- =>=
- multiply a (multiply b (multiply a c))
- [] by prove_moufang3
-22869: Order:
-22869: lpo
-22869: Leaf order:
-22869: b 2 0 2 2,1,1,2
-22869: c 2 0 2 2,2
-22869: identity 4 0 0
-22869: a 4 0 4 1,1,1,2
-22869: right_inverse 1 1 0
-22869: left_inverse 1 1 0
-22869: left_division 2 2 0
-22869: right_division 2 2 0
-22869: multiply 20 2 6 0,2
-Statistics :
-Max weight : 15
-Found proof, 24.434685s
-% SZS status Unsatisfiable for GRP201-1.p
-% SZS output start CNFRefutation for GRP201-1.p
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121
-Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2
-Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3
-Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2
-Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2
-Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2
-Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2
-Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2
-Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2
-Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2
-Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3
-Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2
-Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3
-Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2
-Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3
-Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2
-Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2
-Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2
-Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2
-Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3
-Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2
-Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2
-Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2
-Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2
-Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2
-Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2
-Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2
-Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3
-Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2
-Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2
-Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2
-Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3
-Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3
-Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3
-Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2
-Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2
-Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3
-Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2
-Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2
-Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2
-Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2
-Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3
-Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3
-Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2
-Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2
-Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2
-Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3
-Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2
-Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3
-Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3
-Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3
-Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2
-Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3
-Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2
-Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2
-Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3
-% SZS output end CNFRefutation for GRP201-1.p
-22868: solved GRP201-1.p in 12.232764 using kbo
-22868: status Unsatisfiable for GRP201-1.p
-CLASH, statistics insufficient
-22882: Facts:
-CLASH, statistics insufficient
-22883: Facts:
-22883: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22883: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22883: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22883: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22883: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22883: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22883: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22883: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22883: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-22883: Goal:
-22883: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-22883: Order:
-22883: kbo
-22883: Leaf order:
-22883: b 2 0 2 1,2,1,2
-22883: c 2 0 2 2,2,1,2
-22883: identity 4 0 0
-22883: a 4 0 4 1,1,2
-22883: right_inverse 1 1 0
-22883: left_inverse 1 1 0
-22883: left_division 2 2 0
-22883: right_division 2 2 0
-22883: multiply 20 2 6 0,2
-22882: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22882: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22882: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22882: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22882: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22882: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22882: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22882: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22882: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-22882: Goal:
-22882: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-22882: Order:
-22882: nrkbo
-22882: Leaf order:
-22882: b 2 0 2 1,2,1,2
-22882: c 2 0 2 2,2,1,2
-22882: identity 4 0 0
-22882: a 4 0 4 1,1,2
-22882: right_inverse 1 1 0
-22882: left_inverse 1 1 0
-22882: left_division 2 2 0
-22882: right_division 2 2 0
-22882: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-22884: Facts:
-22884: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-22884: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-22884: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-22884: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-22884: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-22884: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-22884: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-22884: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-22884: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-22884: Goal:
-22884: Id : 1, {_}:
- multiply (multiply a (multiply b c)) a
- =>=
- multiply (multiply a b) (multiply c a)
- [] by prove_moufang1
-22884: Order:
-22884: lpo
-22884: Leaf order:
-22884: b 2 0 2 1,2,1,2
-22884: c 2 0 2 2,2,1,2
-22884: identity 4 0 0
-22884: a 4 0 4 1,1,2
-22884: right_inverse 1 1 0
-22884: left_inverse 1 1 0
-22884: left_division 2 2 0
-22884: right_division 2 2 0
-22884: multiply 20 2 6 0,2
-Statistics :
-Max weight : 20
-Found proof, 29.906330s
-% SZS status Unsatisfiable for GRP202-1.p
-% SZS output start CNFRefutation for GRP202-1.p
-Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
-Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
-Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
-Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2
-Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
-Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
-Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
-Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
-Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
-Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2
-Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2
-Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2
-Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2
-Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2
-Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3
-Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
-Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
-Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2
-Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2
-Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2
-Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2
-Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2
-Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3
-Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2
-Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3
-Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2
-Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
-Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2
-Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
-Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3
-Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3
-Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2
-Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2
-Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3
-Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2
-Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2
-Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3
-Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3
-Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3
-Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3
-Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3
-Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2
-Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2
-Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2
-Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3
-Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3
-Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2
-Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2
-Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3
-Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2
-Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3
-Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2
-Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2
-Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3
-Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2
-Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3
-Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2
-Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3
-Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2
-Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3
-Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3
-Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2
-Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2
-Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3
-Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2
-Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3
-Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2
-Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3
-Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3
-Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3
-Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2
-Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3
-Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3
-Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2
-Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3
-Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2
-Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2
-Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3
-Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3
-Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
-Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
-Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3
-Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2
-Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2
-Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2
-Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2
-Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2
-Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3
-Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2
-Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3
-Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2
-Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3
-Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2
-Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3
-Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3
-Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2
-Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2
-Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3
-Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2
-Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
-Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2
-Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3
-Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2
-Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3
-Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2
-Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3
-Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2
-Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2
-Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3
-Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2
-Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3
-Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2
-Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3
-Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2
-Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2
-Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3
-Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3
-Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2
-Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2
-Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2
-Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3
-Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2
-Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2
-Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3
-Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2
-Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3
-Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3
-Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2
-Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2
-Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2
-Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3
-Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2
-Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3
-Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3
-Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3
-Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3
-Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2
-Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
-% SZS output end CNFRefutation for GRP202-1.p
-22883: solved GRP202-1.p in 14.88493 using kbo
-22883: status Unsatisfiable for GRP202-1.p
-NO CLASH, using fixed ground order
-22932: Facts:
-22932: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-22932: Goal:
-22932: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-22932: Order:
-22932: nrkbo
-22932: Leaf order:
-22932: b2 2 0 2 1,1,1,2
-22932: a2 2 0 2 2,2
-22932: inverse 6 1 1 0,1,1,2
-22932: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-22933: Facts:
-22933: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-22933: Goal:
-22933: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-22933: Order:
-22933: kbo
-22933: Leaf order:
-22933: b2 2 0 2 1,1,1,2
-22933: a2 2 0 2 2,2
-22933: inverse 6 1 1 0,1,1,2
-22933: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-22934: Facts:
-22934: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-22934: Goal:
-22934: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-22934: Order:
-22934: lpo
-22934: Leaf order:
-22934: b2 2 0 2 1,1,1,2
-22934: a2 2 0 2 2,2
-22934: inverse 6 1 1 0,1,1,2
-22934: multiply 8 2 2 0,2
-% SZS status Timeout for GRP404-1.p
-NO CLASH, using fixed ground order
-23295: Facts:
-23295: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23295: Goal:
-23295: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23295: Order:
-23295: nrkbo
-23295: Leaf order:
-23295: a3 2 0 2 1,1,2
-23295: b3 2 0 2 2,1,2
-23295: c3 2 0 2 2,2
-23295: inverse 5 1 0
-23295: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23296: Facts:
-23296: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23296: Goal:
-23296: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23296: Order:
-23296: kbo
-23296: Leaf order:
-23296: a3 2 0 2 1,1,2
-23296: b3 2 0 2 2,1,2
-23296: c3 2 0 2 2,2
-23296: inverse 5 1 0
-23296: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23297: Facts:
-23297: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
- (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
- =>=
- ?4
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23297: Goal:
-23297: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23297: Order:
-23297: lpo
-23297: Leaf order:
-23297: a3 2 0 2 1,1,2
-23297: b3 2 0 2 2,1,2
-23297: c3 2 0 2 2,2
-23297: inverse 5 1 0
-23297: multiply 10 2 4 0,2
-% SZS status Timeout for GRP405-1.p
-NO CLASH, using fixed ground order
-23512: Facts:
-NO CLASH, using fixed ground order
-23513: Facts:
-23513: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23513: Goal:
-23513: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23513: Order:
-23513: kbo
-23513: Leaf order:
-23513: b2 2 0 2 1,1,1,2
-23513: a2 2 0 2 2,2
-23513: inverse 6 1 1 0,1,1,2
-23513: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-23514: Facts:
-23514: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23514: Goal:
-23514: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23514: Order:
-23514: lpo
-23514: Leaf order:
-23514: b2 2 0 2 1,1,1,2
-23514: a2 2 0 2 2,2
-23514: inverse 6 1 1 0,1,1,2
-23514: multiply 8 2 2 0,2
-23512: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23512: Goal:
-23512: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23512: Order:
-23512: nrkbo
-23512: Leaf order:
-23512: b2 2 0 2 1,1,1,2
-23512: a2 2 0 2 2,2
-23512: inverse 6 1 1 0,1,1,2
-23512: multiply 8 2 2 0,2
-Statistics :
-Max weight : 71
-Found proof, 51.580663s
-% SZS status Unsatisfiable for GRP410-1.p
-% SZS output start CNFRefutation for GRP410-1.p
-Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2
-Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2
-Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2
-Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2
-Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2
-Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2
-Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3
-Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2
-Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3
-Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2
-Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2
-Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2
-Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2
-Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3
-Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3
-Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2
-Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2
-Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2
-Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3
-Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2
-Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2
-Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2
-Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2
-Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2
-Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2
-Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2
-Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2
-Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2
-Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3
-Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3
-Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2
-Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2
-Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3
-Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3
-Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3
-Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3
-Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2
-Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3
-Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2
-Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2
-Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2
-Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2
-Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2
-Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2
-Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2
-Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2
-Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2
-Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2
-Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2
-Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2
-Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2
-Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3
-Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3
-Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2
-Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2
-Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3
-Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2
-Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3
-Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2
-Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2
-Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2
-Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2
-Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2
-Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3
-Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2
-Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2
-Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2
-Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2
-Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3
-Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2
-Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2
-Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2
-Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2
-Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2
-Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2
-Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2
-Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2
-Id : 32788, {_}: multiply (multiply (inverse ?68177) ?68177) ?68178 =>= ?68178 [68178, 68177] by Demod 28698 with 29399 at 1,2
-Id : 32852, {_}: a2 === a2 [] by Demod 1 with 32788 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP410-1.p
-23512: solved GRP410-1.p in 25.797611 using nrkbo
-23512: status Unsatisfiable for GRP410-1.p
-NO CLASH, using fixed ground order
-23552: Facts:
-23552: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23552: Goal:
-23552: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23552: Order:
-23552: nrkbo
-23552: Leaf order:
-23552: a3 2 0 2 1,1,2
-23552: b3 2 0 2 2,1,2
-23552: c3 2 0 2 2,2
-23552: inverse 5 1 0
-23552: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23553: Facts:
-23553: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23553: Goal:
-23553: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23553: Order:
-23553: kbo
-23553: Leaf order:
-23553: a3 2 0 2 1,1,2
-23553: b3 2 0 2 2,1,2
-23553: c3 2 0 2 2,2
-23553: inverse 5 1 0
-23553: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23554: Facts:
-23554: Id : 2, {_}:
- multiply
- (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
- (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23554: Goal:
-23554: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23554: Order:
-23554: lpo
-23554: Leaf order:
-23554: a3 2 0 2 1,1,2
-23554: b3 2 0 2 2,1,2
-23554: c3 2 0 2 2,2
-23554: inverse 5 1 0
-23554: multiply 10 2 4 0,2
-Statistics :
-Max weight : 83
-Found proof, 26.764346s
-% SZS status Unsatisfiable for GRP411-1.p
-% SZS output start CNFRefutation for GRP411-1.p
-Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2
-Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2
-Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2
-Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2
-Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2
-Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2
-Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3
-Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2
-Id : 1238, {_}: multiply (inverse (multiply ?5362 (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365)))) (multiply ?5362 ?5366) =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363, 5362] by Super 1213 with 210 at 1,3
-Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3
-Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2
-Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2
-Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2
-Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2
-Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3
-Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3
-Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2
-Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2
-Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2
-Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3
-Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2
-Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2
-Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2
-Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2
-Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2
-Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2
-Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2
-Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2
-Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2
-Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3
-Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3
-Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2
-Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2
-Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3
-Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3
-Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3
-Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3
-Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2
-Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3
-Id : 23367, {_}: multiply (inverse (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 1238 with 23108 at 2
-Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2
-Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2
-Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3
-Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2
-Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2
-Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2
-Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2
-Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3
-Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2
-Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2
-Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2
-Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2
-Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2
-Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2
-Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2
-Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2
-Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2
-Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2
-Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2
-Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2
-Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2
-Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3
-Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3
-Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2
-Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2
-Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3
-Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2
-Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3
-Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2
-Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2
-Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2
-Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2
-Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2
-Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2
-Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2
-Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2
-Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2
-Id : 29266, {_}: multiply (inverse (inverse (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 23367 with 29259 at 1,1,1,1,2
-Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2
-Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2
-Id : 32787, {_}: multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 29266 with 29399 at 1,2
-Id : 32817, {_}: multiply (multiply (multiply ?69480 (multiply ?69481 ?69482)) (inverse ?69482)) ?69483 =>= multiply ?69480 (multiply ?69481 ?69483) [69483, 69482, 69481, 69480] by Super 32787 with 29399 at 2,2,1,1,2
-Id : 27049, {_}: multiply (inverse (inverse (multiply ?65328 (multiply (inverse ?65329) ?65329)))) (inverse (multiply (inverse ?65330) ?65330)) =>= multiply (inverse (inverse (multiply ?65328 ?65329))) (inverse ?65329) [65330, 65329, 65328] by Super 3510 with 23545 at 3
-Id : 27102, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =?= multiply (inverse (inverse (multiply (inverse (multiply (inverse ?65602) ?65602)) ?65600))) (inverse ?65600) [65602, 65601, 65600] by Super 27049 with 22724 at 1,1,1,2
-Id : 27480, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =>= multiply (inverse (inverse ?65600)) (inverse ?65600) [65601, 65600] by Demod 27102 with 14495 at 1,3
-Id : 27499, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse ?17)) (inverse ?17))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23376 with 27480 at 1,2,2
-Id : 28687, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?68131)) (inverse ?68131))) (inverse (inverse (multiply (inverse ?68132) ?68132)))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132, 68131] by Super 27499 with 28438 at 1,1,1,2
-Id : 28770, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132] by Demod 28687 with 28218 at 1,2
-Id : 9, {_}: multiply (multiply (inverse (multiply ?31 (inverse (inverse ?32)))) (multiply ?31 (inverse (inverse (multiply (inverse ?32) ?32))))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32, 31] by Super 2 with 6 at 1,2,1,1,1,2
-Id : 23370, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32] by Demod 9 with 23108 at 1,2
-Id : 23371, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23370 with 23108 at 1,2,3
-Id : 23387, {_}: multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse ?32) =<= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23371 with 23376 at 2
-Id : 25785, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (inverse (multiply (inverse ?63179) ?63179)) (multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178)) [63180, 63179, 63178] by Super 23387 with 23801 at 1,3
-Id : 25940, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178) [63180, 63178] by Demod 25785 with 22724 at 3
-Id : 26391, {_}: multiply (inverse (inverse (multiply (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074))) ?64075))) (inverse ?64075) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64075, 64074] by Super 23366 with 25940 at 1,1,1,1,2
-Id : 26476, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64074] by Demod 26391 with 23366 at 2
-Id : 26477, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26476 with 23545 at 3
-Id : 26478, {_}: inverse (inverse (multiply (inverse ?64074) ?64074)) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26477 with 14495 at 2
-Id : 28771, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28770 with 26478 at 3
-Id : 28772, {_}: multiply (inverse (inverse ?68132)) (inverse ?68132) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28771 with 27480 at 2
-Id : 28931, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 4844 with 28772 at 1,3
-Id : 29275, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 28931 with 29259 at 1,1,2,1,2
-Id : 32786, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (multiply (inverse ?21769) ?21769) [21769, 21768] by Demod 29275 with 29399 at 3
-Id : 32802, {_}: inverse (multiply ?69432 (inverse (multiply (multiply ?69432 ?69433) (inverse ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Super 32786 with 29399 at 2,1,1,2,1,2
-Id : 21975, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996, 5995] by Demod 1364 with 21784 at 1,2,2
-Id : 23386, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 21975 with 23108 at 1,2
-Id : 28932, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 23386 with 28772 at 1,2,2
-Id : 29265, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 28932 with 29259 at 1,1,2,1,3
-Id : 32767, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 29265 with 29399 at 1,1,2
-Id : 32768, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse ?5998) ?5998)) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32767 with 29399 at 2,2
-Id : 32797, {_}: multiply ?5996 (inverse (multiply ?5997 (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32768 with 29259 at 2
-Id : 32841, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Demod 32802 with 32797 at 1,2
-Id : 32842, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32841 with 29399 at 1,1,3
-Id : 32843, {_}: multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32842 with 29399 at 2
-Id : 10, {_}: multiply (multiply (inverse (inverse ?36)) (multiply (multiply (inverse ?37) (multiply (multiply (inverse (multiply ?38 (inverse (multiply ?37 ?36)))) (multiply ?38 (inverse ?36))) (inverse ?36))) (inverse ?36))) (inverse (multiply (inverse ?36) ?36)) =>= inverse ?36 [38, 37, 36] by Super 2 with 6 at 1,1,1,2
-Id : 37, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (multiply ?176 (inverse (multiply ?175 ?174)))) (multiply ?176 (inverse ?174))) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 176, 175, 174] by Super 6 with 10 at 1,2,1,1,1,2,1,2
-Id : 23364, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 175, 174] by Demod 37 with 23108 at 1,2,1,2,1,1,1,2
-Id : 23365, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [175, 174] by Demod 23364 with 23108 at 1,2,1,2
-Id : 23401, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174)) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23365 with 23387 at 1,2,1,1,1,2
-Id : 23402, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23401 with 23387 at 1,1,1,2
-Id : 27500, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse ?174)) (inverse ?174))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23402 with 27480 at 1,2,2
-Id : 28930, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 27500 with 28772 at 1,2,2
-Id : 29247, {_}: multiply (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 28930 with 28698 at 1,1,1,2
-Id : 32772, {_}: multiply (multiply ?174 (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 29247 with 29399 at 1,1,2
-Id : 32773, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32772 with 29399 at 1,1,2,1,2
-Id : 32774, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32773 with 29399 at 2,1,2,1,2
-Id : 32775, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32774 with 29399 at 2,2,1,2
-Id : 32776, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32775 with 29399 at 2,2
-Id : 32777, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32776 with 29399 at 3
-Id : 32792, {_}: multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32777 with 29259 at 2
-Id : 28933, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 27499 with 28772 at 1,2,2
-Id : 29256, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= inverse (inverse (multiply ?16 (multiply (inverse ?17) ?17))) [17, 16] by Demod 28933 with 29249 at 3
-Id : 29262, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29256 with 29258 at 3
-Id : 32782, {_}: multiply (multiply ?16 (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29262 with 29399 at 1,1,2
-Id : 32783, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 32782 with 29399 at 2,1,2
-Id : 32784, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (multiply (inverse ?17) ?17)) =>= ?16 [17, 16] by Demod 32783 with 29399 at 2,2
-Id : 32789, {_}: multiply ?16 (multiply (inverse ?17) ?17) =>= ?16 [17, 16] by Demod 32784 with 29259 at 2
-Id : 32793, {_}: multiply ?174 (multiply (inverse ?174) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32792 with 32789 at 2,2
-Id : 32794, {_}: multiply ?174 (inverse ?174) =?= multiply (inverse ?174) ?174 [174] by Demod 32793 with 32789 at 2,2
-Id : 32844, {_}: multiply (inverse (multiply ?69432 ?69433)) (multiply ?69432 ?69433) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32843 with 32794 at 2
-Id : 32845, {_}: multiply (inverse ?69433) ?69433 =<= inverse (multiply ?69433 (inverse ?69433)) [69433] by Demod 32844 with 23108 at 2
-Id : 32878, {_}: inverse (multiply (inverse ?69602) ?69602) =>= multiply ?69602 (inverse ?69602) [69602] by Super 29399 with 32845 at 1,2
-Id : 32984, {_}: multiply ?16894 (multiply ?16895 (inverse ?16895)) =>= ?16894 [16895, 16894] by Demod 29259 with 32878 at 2,2
-Id : 38023, {_}: multiply ?72734 (multiply ?72735 (multiply ?72736 (inverse ?72736))) =?= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72736, 72735, 72734] by Super 32984 with 32817 at 2
-Id : 38122, {_}: multiply ?72734 ?72735 =<= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72735, 72734] by Demod 38023 with 32984 at 2,2
-Id : 40272, {_}: multiply (multiply ?69480 ?69481) ?69483 =?= multiply ?69480 (multiply ?69481 ?69483) [69483, 69481, 69480] by Demod 32817 with 38122 at 1,2
-Id : 40468, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 40272 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP411-1.p
-23552: solved GRP411-1.p in 26.617662 using nrkbo
-23552: status Unsatisfiable for GRP411-1.p
-NO CLASH, using fixed ground order
-23570: Facts:
-23570: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23570: Goal:
-23570: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23570: Order:
-23570: nrkbo
-23570: Leaf order:
-23570: b2 2 0 2 1,1,1,2
-23570: a2 2 0 2 2,2
-23570: inverse 8 1 1 0,1,1,2
-23570: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-23571: Facts:
-23571: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23571: Goal:
-23571: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23571: Order:
-23571: kbo
-23571: Leaf order:
-23571: b2 2 0 2 1,1,1,2
-23571: a2 2 0 2 2,2
-23571: inverse 8 1 1 0,1,1,2
-23571: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-23572: Facts:
-23572: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23572: Goal:
-23572: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23572: Order:
-23572: lpo
-23572: Leaf order:
-23572: b2 2 0 2 1,1,1,2
-23572: a2 2 0 2 2,2
-23572: inverse 8 1 1 0,1,1,2
-23572: multiply 8 2 2 0,2
-Statistics :
-Max weight : 117
-Found proof, 75.766748s
-% SZS status Unsatisfiable for GRP419-1.p
-% SZS output start CNFRefutation for GRP419-1.p
-Id : 3, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (inverse (multiply ?8 (inverse (multiply (inverse ?8) ?8)))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
-Id : 2, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (inverse (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 31, {_}: inverse (multiply (inverse (multiply ?219 (inverse (multiply (inverse ?220) (inverse (multiply (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)) (inverse (multiply ?222 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))))))))) (multiply ?219 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))) =>= ?220 [223, 222, 221, 220, 219] by Super 3 with 2 at 1,1,2,1,2,1,2,1,1,1,2
-Id : 5, {_}: inverse (multiply (inverse (multiply ?16 (inverse (multiply ?17 (inverse (multiply ?18 (inverse (multiply (inverse ?18) ?18)))))))) (multiply ?16 ?18)) =?= multiply (inverse (multiply ?19 (inverse (multiply (inverse ?17) (inverse (multiply ?20 (inverse (multiply (inverse ?20) ?20)))))))) (multiply ?19 ?20) [20, 19, 18, 17, 16] by Super 3 with 2 at 1,1,2,1,1,1,2
-Id : 39, {_}: inverse (multiply (inverse (multiply ?290 (inverse (multiply (inverse ?291) (inverse (multiply (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)) (inverse (multiply ?293 (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)))))))))) (multiply ?290 (inverse (multiply (inverse (multiply ?295 (inverse (multiply ?293 (inverse (multiply ?296 (inverse (multiply (inverse ?296) ?296)))))))) (multiply ?295 ?296))))) =>= ?291 [296, 295, 294, 293, 292, 291, 290] by Super 31 with 5 at 2,2,1,2
-Id : 11, {_}: multiply (inverse (multiply ?51 (inverse (multiply (inverse (inverse ?52)) (inverse (multiply ?53 (inverse (multiply (inverse ?53) ?53)))))))) (multiply ?51 ?53) =>= ?52 [53, 52, 51] by Super 2 with 5 at 2
-Id : 131, {_}: inverse (multiply (inverse (multiply (inverse (multiply ?678 (inverse (multiply (inverse (inverse ?679)) (inverse (multiply ?680 (inverse (multiply (inverse ?680) ?680)))))))) (inverse (multiply (inverse ?681) (inverse (multiply (multiply ?678 ?680) (inverse (multiply (inverse (multiply ?678 ?680)) (multiply ?678 ?680))))))))) ?679) =>= ?681 [681, 680, 679, 678] by Super 2 with 11 at 2,1,2
-Id : 592, {_}: inverse (multiply (inverse (multiply ?3887 ?3888)) (multiply ?3887 ?3889)) =?= multiply (inverse (multiply ?3890 (inverse (multiply (inverse (inverse (inverse (multiply ?3889 (inverse (multiply (inverse ?3889) ?3889)))))) (inverse (multiply ?3891 (inverse (multiply (inverse ?3891) ?3891)))))))) (inverse (multiply (inverse ?3888) (inverse (multiply (multiply ?3890 ?3891) (inverse (multiply (inverse (multiply ?3890 ?3891)) (multiply ?3890 ?3891))))))) [3891, 3890, 3889, 3888, 3887] by Super 2 with 131 at 2,1,1,1,2
-Id : 1723, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?12104 ?12105)) (multiply ?12104 ?12106)))) (inverse (multiply ?12106 (inverse (multiply (inverse ?12106) ?12106))))) =>= ?12105 [12106, 12105, 12104] by Super 131 with 592 at 1,1,1,2
-Id : 139, {_}: multiply (inverse (multiply ?714 (inverse (multiply (inverse (inverse ?715)) (inverse (multiply ?716 (inverse (multiply (inverse ?716) ?716)))))))) (multiply ?714 ?716) =>= ?715 [716, 715, 714] by Super 2 with 5 at 2
-Id : 140, {_}: multiply (inverse (multiply (inverse (multiply ?718 (inverse (multiply (inverse (inverse ?719)) (inverse (multiply ?720 (inverse (multiply (inverse ?720) ?720)))))))) (inverse (multiply (inverse (inverse ?721)) (inverse (multiply (multiply ?718 ?720) (inverse (multiply (inverse (multiply ?718 ?720)) (multiply ?718 ?720))))))))) ?719 =>= ?721 [721, 720, 719, 718] by Super 139 with 11 at 2,2
-Id : 1734, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?12189 (inverse ?12190))) (multiply ?12189 ?12191)))) (inverse (multiply ?12191 (inverse (multiply (inverse ?12191) ?12191)))) =>= ?12190 [12191, 12190, 12189] by Super 140 with 592 at 1,1,2
-Id : 10, {_}: inverse (inverse (multiply (inverse (multiply ?47 (inverse (multiply ?48 (inverse (multiply ?49 (inverse (multiply (inverse ?49) ?49)))))))) (multiply ?47 ?49))) =>= ?48 [49, 48, 47] by Super 2 with 5 at 1,2
-Id : 1746, {_}: inverse (multiply (inverse (multiply ?12293 ?12294)) (multiply ?12293 ?12295)) =?= multiply (inverse (multiply ?12296 (inverse (multiply (inverse (inverse (inverse (multiply ?12295 (inverse (multiply (inverse ?12295) ?12295)))))) (inverse (multiply ?12297 (inverse (multiply (inverse ?12297) ?12297)))))))) (inverse (multiply (inverse ?12294) (inverse (multiply (multiply ?12296 ?12297) (inverse (multiply (inverse (multiply ?12296 ?12297)) (multiply ?12296 ?12297))))))) [12297, 12296, 12295, 12294, 12293] by Super 2 with 131 at 2,1,1,1,2
-Id : 1828, {_}: inverse (multiply (inverse (multiply ?13070 ?13071)) (multiply ?13070 ?13072)) =?= inverse (multiply (inverse (multiply ?13073 ?13071)) (multiply ?13073 ?13072)) [13073, 13072, 13071, 13070] by Super 1746 with 592 at 3
-Id : 6984, {_}: inverse (inverse (multiply (inverse (multiply ?54958 (inverse (multiply ?54959 (inverse (multiply (multiply ?54960 ?54961) (inverse (multiply (inverse (multiply ?54962 ?54961)) (multiply ?54962 ?54961))))))))) (multiply ?54958 (multiply ?54960 ?54961)))) =>= ?54959 [54962, 54961, 54960, 54959, 54958] by Super 10 with 1828 at 2,1,2,1,2,1,1,1,1,2
-Id : 6987, {_}: inverse (inverse (multiply (inverse (multiply ?54980 (inverse (multiply ?54981 (inverse (multiply (multiply (inverse (multiply (inverse (multiply ?54982 (inverse (multiply (inverse (inverse ?54983)) (inverse (multiply ?54984 (inverse (multiply (inverse ?54984) ?54984)))))))) (inverse (multiply (inverse (inverse ?54985)) (inverse (multiply (multiply ?54982 ?54984) (inverse (multiply (inverse (multiply ?54982 ?54984)) (multiply ?54982 ?54984))))))))) ?54983) (inverse (multiply (inverse (multiply ?54986 ?54983)) (multiply ?54986 ?54983))))))))) (multiply ?54980 ?54985))) =>= ?54981 [54986, 54985, 54984, 54983, 54982, 54981, 54980] by Super 6984 with 140 at 2,2,1,1,2
-Id : 7283, {_}: inverse (inverse (multiply (inverse (multiply ?56997 (inverse (multiply ?56998 (inverse (multiply ?56999 (inverse (multiply (inverse (multiply ?57000 ?57001)) (multiply ?57000 ?57001))))))))) (multiply ?56997 ?56999))) =>= ?56998 [57001, 57000, 56999, 56998, 56997] by Demod 6987 with 140 at 1,1,2,1,2,1,1,1,1,2
-Id : 7302, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse (multiply (inverse (multiply ?57176 (inverse (multiply (inverse (inverse ?57177)) (inverse (multiply ?57178 (inverse (multiply (inverse ?57178) ?57178)))))))) (multiply ?57176 ?57178))) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57178, 57177, 57176, 57175, 57174, 57173] by Super 7283 with 11 at 2,1,2,1,2,1,2,1,1,1,1,2
-Id : 7433, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse ?57177) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57177, 57175, 57174, 57173] by Demod 7302 with 2 at 1,1,2,1,2,1,2,1,1,1,1,2
-Id : 7485, {_}: multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58077) ?58077)))) =?= multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58078) ?58078)))) [58078, 58077, 58076] by Super 1734 with 7433 at 1,2
-Id : 8374, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?64683 (inverse (multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)))))) (multiply ?64683 ?64686)))) (inverse (multiply ?64686 (inverse (multiply (inverse ?64686) ?64686)))) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64686, 64685, 64684, 64683] by Super 1734 with 7485 at 1,1,1,1,1,2
-Id : 8749, {_}: multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64685, 64684] by Demod 8374 with 1734 at 2
-Id : 8815, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?67872 (inverse (multiply (inverse ?67872) ?67872)))) (multiply ?67872 ?67873)))) (inverse (multiply ?67873 (inverse (multiply (inverse ?67873) ?67873))))) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67873, 67872] by Super 1723 with 8749 at 1,1,1,1,1,1,2
-Id : 9225, {_}: inverse (multiply (inverse ?67872) ?67872) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67872] by Demod 8815 with 1723 at 2
-Id : 9030, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?69262 (inverse (multiply (inverse ?69262) ?69262)))) (multiply ?69262 ?69263)))) (inverse (multiply ?69263 (inverse (multiply (inverse ?69263) ?69263)))) =?= multiply (inverse ?69264) ?69264 [69264, 69263, 69262] by Super 1734 with 8749 at 1,1,1,1,1,2
-Id : 9183, {_}: multiply (inverse ?69262) ?69262 =?= multiply (inverse ?69264) ?69264 [69264, 69262] by Demod 9030 with 1734 at 2
-Id : 12179, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88672) ?88672))) (inverse (multiply ?88673 (inverse (multiply (inverse ?88673) ?88673))))) =>= ?88673 [88673, 88672] by Super 1723 with 9183 at 1,1,1,1,2
-Id : 12213, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88894) ?88894))) (inverse (multiply ?88895 (inverse (multiply (inverse ?88896) ?88896))))) =>= ?88895 [88896, 88895, 88894] by Super 12179 with 9183 at 1,2,1,2,1,2
-Id : 13701, {_}: inverse (multiply (inverse ?97964) ?97964) =?= inverse (inverse (multiply (inverse ?97965) ?97965)) [97965, 97964] by Super 9225 with 12213 at 3
-Id : 34411, {_}: inverse (multiply (inverse (multiply (inverse ?202408) ?202408)) (inverse (multiply ?202409 (inverse (multiply (inverse ?202409) ?202409))))) =>= ?202409 [202409, 202408] by Super 1723 with 13701 at 1,1,2
-Id : 9086, {_}: multiply ?69615 (inverse (multiply (inverse ?69616) ?69616)) =?= multiply ?69615 (inverse (multiply (inverse ?69615) ?69615)) [69616, 69615] by Demod 8374 with 1734 at 2
-Id : 9126, {_}: multiply ?69879 (inverse (multiply (inverse ?69880) ?69880)) =?= multiply ?69879 (inverse (multiply (inverse ?69881) ?69881)) [69881, 69880, 69879] by Super 9086 with 8749 at 3
-Id : 56, {_}: inverse (multiply (inverse (multiply ?444 (inverse (multiply (inverse ?445) (inverse (multiply (inverse (multiply (inverse (multiply ?446 (inverse (multiply ?447 (inverse (multiply ?448 (inverse (multiply (inverse ?448) ?448)))))))) (multiply ?446 ?448))) (inverse (multiply ?447 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))))))))) (multiply ?444 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))) =>= ?445 [450, 449, 448, 447, 446, 445, 444] by Super 31 with 5 at 1,1,2,1,2,1,1,1,2
-Id : 14563, {_}: inverse (multiply (inverse (multiply ?103053 (inverse (multiply (inverse (inverse (multiply (inverse ?103054) ?103054))) (inverse (multiply (inverse (multiply (inverse (multiply ?103055 (inverse (multiply ?103056 (inverse (multiply ?103057 (inverse (multiply (inverse ?103057) ?103057)))))))) (multiply ?103055 ?103057))) (inverse (multiply ?103056 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))))))))) (multiply ?103053 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))) =?= multiply (inverse ?103060) ?103060 [103060, 103059, 103058, 103057, 103056, 103055, 103054, 103053] by Super 56 with 13701 at 1,1,2,1,1,1,2
-Id : 14713, {_}: inverse (multiply (inverse ?103054) ?103054) =?= multiply (inverse ?103060) ?103060 [103060, 103054] by Demod 14563 with 56 at 2
-Id : 15410, {_}: multiply ?107836 (inverse (multiply (inverse ?107837) ?107837)) =?= multiply ?107836 (multiply (inverse ?107838) ?107838) [107838, 107837, 107836] by Super 9126 with 14713 at 2,3
-Id : 34485, {_}: inverse (multiply (inverse (multiply (inverse ?202808) ?202808)) (inverse (multiply (inverse (multiply (inverse ?202809) ?202809)) (inverse (multiply (inverse (inverse (multiply (inverse ?202809) ?202809))) (multiply (inverse ?202810) ?202810)))))) =>= inverse (multiply (inverse ?202809) ?202809) [202810, 202809, 202808] by Super 34411 with 15410 at 1,2,1,2,1,2
-Id : 14824, {_}: multiply (inverse ?103830) ?103830 =?= inverse (inverse (multiply (inverse ?103831) ?103831)) [103831, 103830] by Super 12213 with 14713 at 2
-Id : 24848, {_}: inverse (multiply (multiply (inverse ?160661) ?160661) (inverse (multiply ?160662 (inverse (multiply (inverse ?160662) ?160662))))) =>= ?160662 [160662, 160661] by Super 1723 with 14824 at 1,1,2
-Id : 25277, {_}: inverse (multiply (multiply (inverse ?163120) ?163120) (inverse (multiply ?163121 (multiply (inverse ?163122) ?163122)))) =>= ?163121 [163122, 163121, 163120] by Super 24848 with 14713 at 2,1,2,1,2
-Id : 25479, {_}: inverse (multiply (inverse (multiply (inverse ?164337) ?164337)) (inverse (multiply ?164338 (multiply (inverse ?164339) ?164339)))) =>= ?164338 [164339, 164338, 164337] by Super 25277 with 14713 at 1,1,2
-Id : 35006, {_}: inverse (multiply (inverse (multiply (inverse ?204646) ?204646)) (inverse (inverse (multiply (inverse ?204647) ?204647)))) =>= inverse (multiply (inverse ?204647) ?204647) [204647, 204646] by Demod 34485 with 25479 at 2,1,2
-Id : 35218, {_}: inverse (multiply (multiply (inverse ?205705) ?205705) (inverse (inverse (multiply (inverse ?205706) ?205706)))) =>= inverse (multiply (inverse ?205706) ?205706) [205706, 205705] by Super 35006 with 14713 at 1,1,2
-Id : 35602, {_}: inverse (multiply (inverse (multiply ?206697 (inverse (multiply (inverse (multiply (inverse ?206698) ?206698)) (inverse (multiply (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)) (inverse (multiply ?206700 (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)))))))))) (multiply ?206697 (inverse (multiply (inverse (multiply ?206702 (inverse (multiply ?206700 (inverse (multiply ?206703 (inverse (multiply (inverse ?206703) ?206703)))))))) (multiply ?206702 ?206703))))) =?= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206703, 206702, 206701, 206700, 206699, 206698, 206697] by Super 39 with 35218 at 1,1,2,1,1,1,2
-Id : 35866, {_}: multiply (inverse ?206698) ?206698 =<= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206698] by Demod 35602 with 39 at 2
-Id : 36115, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (inverse (multiply (inverse (inverse (multiply (inverse ?208197) ?208197))) (inverse (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197))))))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Super 2 with 35866 at 2,1,2
-Id : 15929, {_}: inverse (multiply (multiply (inverse ?110579) ?110579) (inverse (multiply ?110580 (inverse (multiply (inverse ?110580) ?110580))))) =>= ?110580 [110580, 110579] by Super 1723 with 14824 at 1,1,2
-Id : 24931, {_}: inverse (multiply (multiply (inverse ?161104) ?161104) (inverse (multiply ?161105 (multiply (inverse ?161106) ?161106)))) =>= ?161105 [161106, 161105, 161104] by Super 24848 with 14713 at 2,1,2,1,2
-Id : 25816, {_}: inverse (multiply (multiply (inverse ?166039) ?166039) (inverse (multiply (inverse ?166040) ?166040))) =>= multiply (inverse ?166040) ?166040 [166040, 166039] by Super 15929 with 24931 at 2,1,2
-Id : 25967, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?166851) ?166851))) (inverse (multiply (inverse ?166852) ?166852))) =>= multiply (inverse ?166852) ?166852 [166852, 166851] by Super 25816 with 14824 at 1,1,2
-Id : 36557, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197)))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Demod 36115 with 25967 at 2,1,2,1,1,1,2
-Id : 36558, {_}: inverse (multiply (inverse ?208196) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196] by Demod 36557 with 24931 at 1,1,2
-Id : 37252, {_}: inverse (multiply (multiply (inverse ?211410) ?211410) ?211411) =>= inverse ?211411 [211411, 211410] by Super 24931 with 36558 at 2,1,2
-Id : 40835, {_}: inverse (multiply (inverse ?231064) (multiply (inverse ?231065) ?231065)) =?= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231065, 231064] by Super 36558 with 37252 at 1,1,2
-Id : 40960, {_}: ?231064 =<= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231064] by Demod 40835 with 36558 at 2
-Id : 42184, {_}: a2 === a2 [] by Demod 1 with 40960 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP419-1.p
-23570: solved GRP419-1.p in 75.644727 using nrkbo
-23570: status Unsatisfiable for GRP419-1.p
-NO CLASH, using fixed ground order
-23595: Facts:
-23595: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23595: Goal:
-23595: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23595: Order:
-23595: nrkbo
-23595: Leaf order:
-23595: b2 2 0 2 1,1,1,2
-23595: a2 2 0 2 2,2
-23595: inverse 8 1 1 0,1,1,2
-23595: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-23596: Facts:
-23596: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23596: Goal:
-23596: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23596: Order:
-23596: kbo
-23596: Leaf order:
-23596: b2 2 0 2 1,1,1,2
-23596: a2 2 0 2 2,2
-23596: inverse 8 1 1 0,1,1,2
-23596: multiply 8 2 2 0,2
-NO CLASH, using fixed ground order
-23597: Facts:
-23597: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23597: Goal:
-23597: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23597: Order:
-23597: lpo
-23597: Leaf order:
-23597: b2 2 0 2 1,1,1,2
-23597: a2 2 0 2 2,2
-23597: inverse 8 1 1 0,1,1,2
-23597: multiply 8 2 2 0,2
-% SZS status Timeout for GRP422-1.p
-NO CLASH, using fixed ground order
-23629: Facts:
-23629: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23629: Goal:
-23629: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23629: Order:
-23629: nrkbo
-23629: Leaf order:
-23629: a3 2 0 2 1,1,2
-23629: b3 2 0 2 2,1,2
-23629: c3 2 0 2 2,2
-23629: inverse 7 1 0
-23629: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23630: Facts:
-23630: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23630: Goal:
-23630: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23630: Order:
-23630: kbo
-23630: Leaf order:
-23630: a3 2 0 2 1,1,2
-23630: b3 2 0 2 2,1,2
-23630: c3 2 0 2 2,2
-23630: inverse 7 1 0
-23630: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23631: Facts:
-23631: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (multiply (inverse ?4)
- (inverse (multiply (inverse ?4) ?4)))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23631: Goal:
-23631: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23631: Order:
-23631: lpo
-23631: Leaf order:
-23631: a3 2 0 2 1,1,2
-23631: b3 2 0 2 2,1,2
-23631: c3 2 0 2 2,2
-23631: inverse 7 1 0
-23631: multiply 10 2 4 0,2
-% SZS status Timeout for GRP423-1.p
-NO CLASH, using fixed ground order
-23653: Facts:
-23653: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23653: Goal:
-23653: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23653: Order:
-23653: nrkbo
-23653: Leaf order:
-23653: a3 2 0 2 1,1,2
-23653: b3 2 0 2 2,1,2
-23653: c3 2 0 2 2,2
-23653: inverse 5 1 0
-23653: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23654: Facts:
-23654: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23654: Goal:
-23654: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23654: Order:
-23654: kbo
-23654: Leaf order:
-23654: a3 2 0 2 1,1,2
-23654: b3 2 0 2 2,1,2
-23654: c3 2 0 2 2,2
-23654: inverse 5 1 0
-23654: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23655: Facts:
-23655: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply
- (multiply
- (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
- ?5) (inverse (multiply ?3 ?5))))
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23655: Goal:
-23655: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23655: Order:
-23655: lpo
-23655: Leaf order:
-23655: a3 2 0 2 1,1,2
-23655: b3 2 0 2 2,1,2
-23655: c3 2 0 2 2,2
-23655: inverse 5 1 0
-23655: multiply 10 2 4 0,2
-Statistics :
-Max weight : 62
-Found proof, 11.852538s
-% SZS status Unsatisfiable for GRP429-1.p
-% SZS output start CNFRefutation for GRP429-1.p
-Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
-Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
-Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
-Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
-Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
-Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
-Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
-Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
-Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
-Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
-Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
-Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
-Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
-Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
-Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
-Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
-Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
-Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
-Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
-Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
-Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
-Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
-Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
-Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
-Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
-Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
-Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
-Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
-Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
-Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
-Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
-Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
-Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
-Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
-Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
-Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
-Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
-Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
-Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
-Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
-Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
-Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
-Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
-Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
-Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
-Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
-Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
-Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
-Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
-Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
-Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
-Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
-Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
-Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
-Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
-Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
-Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
-Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
-Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
-Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
-Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
-Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
-Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
-Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
-Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
-Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
-Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
-Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
-Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
-Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
-Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
-Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
-Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
-Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
-Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
-Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
-Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
-Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
-Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
-Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
-Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
-Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
-Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
-Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
-Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
-Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
-Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
-Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
-Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
-Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
-Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
-Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
-Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
-Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
-Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
-Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
-Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
-Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
-Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
-Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
-Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
-Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
-Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
-Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
-Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
-Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
-Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
-Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
-Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
-Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
-Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
-Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
-Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
-Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
-Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
-Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
-Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
-Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
-Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
-Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
-Id : 33337, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 32860 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP429-1.p
-23653: solved GRP429-1.p in 11.596724 using nrkbo
-23653: status Unsatisfiable for GRP429-1.p
-NO CLASH, using fixed ground order
-23669: Facts:
-23669: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23669: Goal:
-23669: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23669: Order:
-23669: nrkbo
-23669: Leaf order:
-23669: a3 2 0 2 1,1,2
-23669: b3 2 0 2 2,1,2
-23669: c3 2 0 2 2,2
-23669: inverse 3 1 0
-23669: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23670: Facts:
-23670: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23670: Goal:
-23670: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23670: Order:
-23670: kbo
-23670: Leaf order:
-23670: a3 2 0 2 1,1,2
-23670: b3 2 0 2 2,1,2
-23670: c3 2 0 2 2,2
-23670: inverse 3 1 0
-23670: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-23671: Facts:
-23671: Id : 2, {_}:
- inverse
- (multiply ?2
- (multiply ?3
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?5 (multiply ?2 ?3))))))
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23671: Goal:
-23671: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23671: Order:
-23671: lpo
-23671: Leaf order:
-23671: a3 2 0 2 1,1,2
-23671: b3 2 0 2 2,1,2
-23671: c3 2 0 2 2,2
-23671: inverse 3 1 0
-23671: multiply 10 2 4 0,2
-Statistics :
-Max weight : 52
-Found proof, 56.465480s
-% SZS status Unsatisfiable for GRP444-1.p
-% SZS output start CNFRefutation for GRP444-1.p
-Id : 3, {_}: inverse (multiply ?7 (multiply ?8 (multiply (multiply ?9 (inverse ?9)) (inverse (multiply ?10 (multiply ?7 ?8)))))) =>= ?10 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
-Id : 2, {_}: inverse (multiply ?2 (multiply ?3 (multiply (multiply ?4 (inverse ?4)) (inverse (multiply ?5 (multiply ?2 ?3)))))) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 5, {_}: inverse (multiply ?18 (multiply ?19 (multiply (multiply (multiply ?20 (multiply ?21 (multiply (multiply ?22 (inverse ?22)) (inverse (multiply ?23 (multiply ?20 ?21)))))) ?23) (inverse (multiply ?24 (multiply ?18 ?19)))))) =>= ?24 [24, 23, 22, 21, 20, 19, 18] by Super 3 with 2 at 2,1,2,2,1,2
-Id : 4, {_}: inverse (multiply ?12 (multiply (multiply (multiply ?13 (inverse ?13)) (inverse (multiply ?14 (multiply ?15 ?12)))) (multiply (multiply ?16 (inverse ?16)) ?14))) =>= ?15 [16, 15, 14, 13, 12] by Super 3 with 2 at 2,2,2,1,2
-Id : 7, {_}: inverse (multiply (multiply (multiply ?28 (inverse ?28)) (inverse (multiply ?29 (multiply ?30 ?31)))) (multiply (multiply (multiply ?32 (inverse ?32)) ?29) (multiply (multiply ?33 (inverse ?33)) ?30))) =>= ?31 [33, 32, 31, 30, 29, 28] by Super 2 with 4 at 2,2,2,1,2
-Id : 9, {_}: inverse (multiply ?44 (multiply (multiply (multiply ?45 (inverse ?45)) (inverse (multiply ?46 (multiply ?47 ?44)))) (multiply (multiply ?48 (inverse ?48)) ?46))) =>= ?47 [48, 47, 46, 45, 44] by Super 3 with 2 at 2,2,2,1,2
-Id : 13, {_}: inverse (multiply (multiply (multiply ?76 (inverse ?76)) ?77) (multiply (multiply (multiply ?78 (inverse ?78)) ?79) (multiply (multiply ?80 (inverse ?80)) ?81))) =?= multiply (multiply ?82 (inverse ?82)) (inverse (multiply ?77 (multiply ?79 ?81))) [82, 81, 80, 79, 78, 77, 76] by Super 9 with 4 at 2,1,2,1,2
-Id : 178, {_}: multiply (multiply ?1864 (inverse ?1864)) (inverse (multiply (inverse (multiply ?1865 (multiply ?1866 ?1867))) (multiply ?1865 ?1866))) =>= ?1867 [1867, 1866, 1865, 1864] by Super 7 with 13 at 2
-Id : 184, {_}: multiply (multiply ?1909 (inverse ?1909)) (inverse (multiply ?1910 (multiply ?1911 (multiply (multiply ?1912 (inverse ?1912)) (inverse (multiply ?1913 (multiply ?1910 ?1911))))))) =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1912, 1911, 1910, 1909] by Super 178 with 4 at 1,1,2,2
-Id : 205, {_}: multiply (multiply ?1909 (inverse ?1909)) ?1913 =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1909] by Demod 184 with 2 at 2,2
-Id : 277, {_}: inverse (multiply ?2556 (multiply ?2557 (multiply (multiply (multiply ?2558 (multiply ?2559 (multiply (multiply ?2560 (inverse ?2560)) (inverse (multiply ?2561 (multiply ?2558 ?2559)))))) ?2561) (inverse (multiply (multiply ?2562 (inverse ?2562)) (multiply ?2556 ?2557)))))) =?= multiply ?2563 (inverse ?2563) [2563, 2562, 2561, 2560, 2559, 2558, 2557, 2556] by Super 5 with 205 at 1,2,2,2,1,2
-Id : 348, {_}: multiply ?2562 (inverse ?2562) =?= multiply ?2563 (inverse ?2563) [2563, 2562] by Demod 277 with 5 at 2
-Id : 1129, {_}: inverse (multiply ?9239 (multiply (inverse ?9239) (multiply (multiply ?9240 (inverse ?9240)) (inverse (multiply ?9241 (multiply ?9242 (inverse ?9242))))))) =>= ?9241 [9242, 9241, 9240, 9239] by Super 2 with 348 at 2,1,2,2,2,1,2
-Id : 86, {_}: multiply (multiply ?817 (inverse ?817)) (inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819))) =>= ?820 [820, 819, 818, 817] by Super 7 with 13 at 2
-Id : 1168, {_}: inverse (multiply ?9548 (multiply (inverse ?9548) ?9549)) =?= inverse (multiply ?9550 (multiply (inverse ?9550) ?9549)) [9550, 9549, 9548] by Super 1129 with 86 at 2,2,1,2
-Id : 3826, {_}: inverse (multiply (inverse ?28880) (multiply ?28881 (multiply (multiply ?28882 (inverse ?28882)) (inverse (multiply ?28883 (multiply (inverse ?28883) ?28881)))))) =>= ?28880 [28883, 28882, 28881, 28880] by Super 2 with 1168 at 2,2,2,1,2
-Id : 529, {_}: multiply (multiply ?4511 (inverse ?4511)) (inverse (multiply (inverse (multiply ?4512 (multiply (inverse ?4512) ?4513))) (multiply ?4514 (inverse ?4514)))) =>= ?4513 [4514, 4513, 4512, 4511] by Super 86 with 348 at 2,1,2,2
-Id : 3910, {_}: inverse (multiply (inverse ?29502) (multiply (inverse (inverse (inverse (multiply ?29503 (multiply (inverse ?29503) ?29504))))) ?29504)) =>= ?29502 [29504, 29503, 29502] by Super 3826 with 529 at 2,2,1,2
-Id : 5137, {_}: inverse (multiply (inverse (inverse (inverse (multiply ?39280 (multiply (inverse ?39280) ?39281))))) (multiply ?39281 (multiply (multiply ?39282 (inverse ?39282)) ?39283))) =>= inverse ?39283 [39283, 39282, 39281, 39280] by Super 2 with 3910 at 2,2,2,1,2
-Id : 17340, {_}: inverse (inverse (multiply ?127629 (multiply (inverse (inverse (inverse (multiply ?127630 (multiply (inverse ?127630) ?127631))))) ?127631))) =>= ?127629 [127631, 127630, 127629] by Super 2 with 5137 at 2
-Id : 5128, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (inverse (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Super 86 with 3910 at 2,2
-Id : 3928, {_}: inverse (multiply (inverse (multiply ?29660 (multiply (inverse ?29660) ?29661))) (multiply ?29662 (multiply (multiply ?29663 (inverse ?29663)) (inverse (multiply ?29664 (multiply (inverse ?29664) ?29662)))))) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29664, 29663, 29662, 29661, 29660] by Super 3826 with 1168 at 1,1,2
-Id : 1246, {_}: inverse (multiply (inverse ?10029) (multiply ?10030 (multiply (multiply ?10031 (inverse ?10031)) (inverse (multiply ?10032 (multiply (inverse ?10032) ?10030)))))) =>= ?10029 [10032, 10031, 10030, 10029] by Super 2 with 1168 at 2,2,2,1,2
-Id : 3958, {_}: multiply ?29660 (multiply (inverse ?29660) ?29661) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29661, 29660] by Demod 3928 with 1246 at 2
-Id : 531, {_}: multiply (multiply ?4521 (inverse ?4521)) (inverse (multiply (inverse (multiply ?4522 (multiply ?4523 (inverse ?4523)))) (multiply ?4522 ?4524))) =>= inverse ?4524 [4524, 4523, 4522, 4521] by Super 86 with 348 at 2,1,1,1,2,2
-Id : 737, {_}: multiply (multiply ?5774 (inverse ?5774)) (inverse (multiply (inverse (multiply ?5775 (multiply ?5776 (inverse ?5776)))) (multiply ?5775 ?5777))) =>= inverse ?5777 [5777, 5776, 5775, 5774] by Super 86 with 348 at 2,1,1,1,2,2
-Id : 1911, {_}: multiply (multiply ?15350 (inverse ?15350)) (inverse (multiply (inverse (multiply ?15351 (multiply ?15352 (inverse ?15352)))) (multiply ?15353 (inverse ?15353)))) =>= inverse (inverse ?15351) [15353, 15352, 15351, 15350] by Super 737 with 348 at 2,1,2,2
-Id : 1956, {_}: multiply (multiply ?15717 (inverse ?15717)) (inverse (multiply (inverse (multiply (multiply ?15718 (inverse ?15718)) (multiply ?15719 (inverse ?15719)))) (multiply ?15720 (inverse ?15720)))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15720, 15719, 15718, 15717] by Super 1911 with 205 at 1,1,1,2,2
-Id : 740, {_}: multiply (multiply ?5792 (inverse ?5792)) (inverse (multiply (inverse (multiply ?5793 (multiply ?5794 (inverse ?5794)))) (multiply ?5795 (inverse ?5795)))) =>= inverse (inverse ?5793) [5795, 5794, 5793, 5792] by Super 737 with 348 at 2,1,2,2
-Id : 2009, {_}: inverse (inverse (multiply ?15718 (inverse ?15718))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15718] by Demod 1956 with 740 at 2
-Id : 2083, {_}: multiply ?16427 (inverse ?16427) =?= multiply (inverse (multiply ?16428 (inverse ?16428))) (inverse (inverse (multiply ?16429 (inverse ?16429)))) [16429, 16428, 16427] by Super 348 with 2009 at 2,3
-Id : 2187, {_}: multiply (multiply ?17062 (inverse ?17062)) (inverse (multiply (inverse (multiply (inverse (multiply ?17063 (inverse ?17063))) (multiply ?17064 (inverse ?17064)))) (multiply ?17065 (inverse ?17065)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17065, 17064, 17063, 17062] by Super 531 with 2083 at 2,1,2,2
-Id : 2437, {_}: inverse (inverse (inverse (multiply ?17063 (inverse ?17063)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17063] by Demod 2187 with 740 at 2
-Id : 2507, {_}: multiply ?19079 (inverse ?19079) =?= multiply (inverse (inverse (multiply ?19080 (inverse ?19080)))) (inverse (inverse (inverse (multiply ?19081 (inverse ?19081))))) [19081, 19080, 19079] by Super 348 with 2437 at 2,3
-Id : 5155, {_}: multiply (multiply ?39417 (inverse ?39417)) (multiply (inverse (inverse (inverse (multiply ?39418 (multiply (inverse ?39418) ?39419))))) (multiply ?39420 (inverse ?39420))) =>= inverse ?39419 [39420, 39419, 39418, 39417] by Super 531 with 3910 at 2,2
-Id : 21348, {_}: inverse (inverse (inverse (multiply ?158881 (inverse ?158881)))) =?= multiply ?158882 (inverse ?158882) [158882, 158881] by Super 17340 with 5155 at 1,1,2
-Id : 21903, {_}: multiply ?162370 (inverse ?162370) =?= multiply (inverse (inverse (multiply ?162371 (inverse ?162371)))) (multiply ?162372 (inverse ?162372)) [162372, 162371, 162370] by Super 2507 with 21348 at 2,3
-Id : 27319, {_}: multiply ?194055 (multiply (inverse ?194055) (inverse (inverse (inverse (inverse (multiply ?194056 (inverse ?194056))))))) =?= multiply ?194057 (inverse ?194057) [194057, 194056, 194055] by Super 3958 with 21903 at 3
-Id : 38543, {_}: multiply (multiply ?266891 (inverse ?266891)) (multiply (inverse (inverse (inverse (multiply ?266892 (multiply (inverse ?266892) ?266893))))) (multiply ?266894 (inverse ?266894))) =?= multiply (inverse ?266893) (inverse (inverse (inverse (inverse (multiply ?266895 (inverse ?266895)))))) [266895, 266894, 266893, 266892, 266891] by Super 5128 with 27319 at 2,2,2
-Id : 39135, {_}: inverse ?270165 =<= multiply (inverse ?270165) (inverse (inverse (inverse (inverse (multiply ?270166 (inverse ?270166)))))) [270166, 270165] by Demod 38543 with 5155 at 2
-Id : 39578, {_}: inverse ?271815 =<= multiply (inverse ?271815) (inverse (multiply ?271816 (inverse ?271816))) [271816, 271815] by Super 39135 with 21348 at 1,2,3
-Id : 39704, {_}: inverse (multiply ?272432 (multiply ?272433 (multiply (multiply ?272434 (inverse ?272434)) (inverse (multiply ?272435 (multiply ?272432 ?272433)))))) =?= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435, 272434, 272433, 272432] by Super 39578 with 2 at 1,3
-Id : 39842, {_}: ?272435 =<= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435] by Demod 39704 with 2 at 2
-Id : 40136, {_}: inverse (inverse (multiply ?274147 (multiply (inverse (inverse (inverse (multiply ?274148 (inverse ?274148))))) (inverse (multiply ?274149 (inverse ?274149)))))) =>= ?274147 [274149, 274148, 274147] by Super 17340 with 39842 at 2,1,1,1,1,2,1,1,2
-Id : 42233, {_}: inverse (inverse (multiply ?290970 (inverse (inverse (inverse (multiply ?290971 (inverse ?290971))))))) =>= ?290970 [290971, 290970] by Demod 40136 with 39842 at 2,1,1,2
-Id : 42325, {_}: inverse (inverse (multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))))) =>= ?291465 [291466, 291465] by Super 42233 with 21348 at 1,1,1,2,1,1,2
-Id : 3911, {_}: inverse (multiply (inverse ?29506) (multiply (inverse (inverse (inverse (multiply ?29507 (multiply ?29508 (inverse ?29508)))))) (inverse (inverse ?29507)))) =>= ?29506 [29508, 29507, 29506] by Super 3826 with 740 at 2,2,1,2
-Id : 42355, {_}: inverse (inverse (multiply ?291566 (multiply ?291567 (inverse ?291567)))) =>= ?291566 [291567, 291566] by Super 42233 with 21348 at 2,1,1,2
-Id : 42465, {_}: inverse (multiply (inverse ?29506) (multiply (inverse ?29507) (inverse (inverse ?29507)))) =>= ?29506 [29507, 29506] by Demod 3911 with 42355 at 1,1,2,1,2
-Id : 42659, {_}: inverse (multiply (inverse ?292844) (multiply (inverse (inverse (multiply ?292845 (multiply ?292846 (inverse ?292846))))) (inverse ?292845))) =>= ?292844 [292846, 292845, 292844] by Super 42465 with 42355 at 1,2,2,1,2
-Id : 42797, {_}: inverse (multiply (inverse ?292844) (multiply ?292845 (inverse ?292845))) =>= ?292844 [292845, 292844] by Demod 42659 with 42355 at 1,2,1,2
-Id : 42874, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= inverse (inverse ?5793) [5794, 5793, 5792] by Demod 740 with 42797 at 2,2
-Id : 46254, {_}: ?309013 =<= multiply ?309013 (inverse (multiply (inverse (multiply ?309014 (multiply ?309015 (inverse ?309015)))) ?309014)) [309015, 309014, 309013] by Super 39842 with 42355 at 2,1,2,3
-Id : 46402, {_}: ?309842 =<= multiply ?309842 (multiply (multiply ?309843 (inverse ?309843)) (multiply ?309844 (inverse ?309844))) [309844, 309843, 309842] by Super 46254 with 42797 at 2,3
-Id : 46563, {_}: multiply ?309963 (inverse ?309963) =?= inverse (inverse (multiply ?309964 (inverse ?309964))) [309964, 309963] by Super 42874 with 46402 at 2
-Id : 47597, {_}: inverse (inverse (multiply ?315584 (inverse (inverse (inverse (inverse (multiply ?315585 (inverse ?315585)))))))) =>= ?315584 [315585, 315584] by Super 42325 with 46563 at 1,1,1,1,2,1,1,2
-Id : 39281, {_}: inverse (multiply ?270847 (multiply ?270848 (multiply (multiply ?270849 (inverse ?270849)) (inverse (multiply ?270850 (multiply ?270847 ?270848)))))) =?= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850, 270849, 270848, 270847] by Super 39135 with 2 at 1,3
-Id : 39433, {_}: ?270850 =<= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850] by Demod 39281 with 2 at 2
-Id : 47849, {_}: inverse (inverse ?315584) =>= ?315584 [315584] by Demod 47597 with 39433 at 1,1,2
-Id : 48100, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= ?5793 [5794, 5793, 5792] by Demod 42874 with 47849 at 3
-Id : 48103, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))) =>= ?291465 [291466, 291465] by Demod 42325 with 47849 at 2
-Id : 48104, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))) =>= ?291465 [291466, 291465] by Demod 48103 with 47849 at 2,2
-Id : 48105, {_}: multiply ?291465 (inverse (inverse (multiply ?291466 (inverse ?291466)))) =>= ?291465 [291466, 291465] by Demod 48104 with 47849 at 2,2
-Id : 48106, {_}: multiply ?291465 (multiply ?291466 (inverse ?291466)) =>= ?291465 [291466, 291465] by Demod 48105 with 47849 at 2,2
-Id : 48126, {_}: multiply (multiply ?5792 (inverse ?5792)) ?5793 =>= ?5793 [5793, 5792] by Demod 48100 with 48106 at 2,2
-Id : 48146, {_}: inverse (multiply ?2 (multiply ?3 (inverse (multiply ?5 (multiply ?2 ?3))))) =>= ?5 [5, 3, 2] by Demod 2 with 48126 at 2,2,1,2
-Id : 48243, {_}: multiply (multiply (inverse ?316807) ?316807) ?316808 =>= ?316808 [316808, 316807] by Super 48126 with 47849 at 2,1,2
-Id : 48369, {_}: inverse (multiply (multiply (inverse ?317633) ?317633) (multiply ?317634 (inverse (multiply ?317635 ?317634)))) =>= ?317635 [317635, 317634, 317633] by Super 48146 with 48243 at 2,1,2,2,1,2
-Id : 48458, {_}: inverse (multiply ?317634 (inverse (multiply ?317635 ?317634))) =>= ?317635 [317635, 317634] by Demod 48369 with 48243 at 1,2
-Id : 49027, {_}: inverse ?319864 =<= multiply ?319865 (inverse (multiply ?319864 ?319865)) [319865, 319864] by Super 47849 with 48458 at 1,2
-Id : 48054, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Demod 5128 with 47849 at 1,2,2
-Id : 48214, {_}: multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208, 39207] by Demod 48054 with 48126 at 2
-Id : 42875, {_}: multiply (multiply ?4511 (inverse ?4511)) (multiply ?4512 (multiply (inverse ?4512) ?4513)) =>= ?4513 [4513, 4512, 4511] by Demod 529 with 42797 at 2,2
-Id : 48128, {_}: multiply ?4512 (multiply (inverse ?4512) ?4513) =>= ?4513 [4513, 4512] by Demod 42875 with 48126 at 2
-Id : 48215, {_}: multiply (inverse ?39208) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208] by Demod 48214 with 48128 at 1,1,2
-Id : 49034, {_}: inverse (inverse ?319885) =<= multiply (multiply ?319885 ?319886) (inverse ?319886) [319886, 319885] by Super 49027 with 48215 at 1,2,3
-Id : 49824, {_}: ?323338 =<= multiply (multiply ?323338 ?323339) (inverse ?323339) [323339, 323338] by Demod 49034 with 47849 at 2
-Id : 48152, {_}: inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819)) =>= ?820 [820, 819, 818] by Demod 86 with 48126 at 2
-Id : 48896, {_}: inverse ?319286 =<= multiply ?319287 (inverse (multiply ?319286 ?319287)) [319287, 319286] by Super 47849 with 48458 at 1,2
-Id : 49169, {_}: multiply (inverse ?320479) (inverse ?320480) =>= inverse (multiply ?320480 ?320479) [320480, 320479] by Super 48215 with 48896 at 2,2
-Id : 49171, {_}: multiply (inverse ?320486) ?320487 =<= inverse (multiply (inverse ?320487) ?320486) [320487, 320486] by Super 49169 with 47849 at 2,2
-Id : 49369, {_}: multiply (inverse (multiply ?818 ?819)) (multiply ?818 (multiply ?819 ?820)) =>= ?820 [820, 819, 818] by Demod 48152 with 49171 at 2
-Id : 49850, {_}: inverse (multiply ?323494 ?323495) =<= multiply ?323496 (inverse (multiply ?323494 (multiply ?323495 ?323496))) [323496, 323495, 323494] by Super 49824 with 49369 at 1,3
-Id : 49041, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) (inverse (inverse ?319907)) [319907, 319906] by Super 49027 with 48896 at 1,2,3
-Id : 49999, {_}: inverse ?323996 =<= multiply (inverse (multiply ?323997 ?323996)) ?323997 [323997, 323996] by Demod 49041 with 47849 at 2,3
-Id : 50016, {_}: inverse (multiply ?324063 (inverse (multiply ?324064 (multiply ?324065 ?324063)))) =>= multiply ?324064 ?324065 [324065, 324064, 324063] by Super 49999 with 48146 at 1,3
-Id : 49025, {_}: multiply ?319858 (inverse ?319859) =<= inverse (multiply ?319859 (inverse ?319858)) [319859, 319858] by Super 48128 with 48896 at 2,2
-Id : 53578, {_}: multiply (multiply ?332164 (multiply ?332165 ?332166)) (inverse ?332166) =>= multiply ?332164 ?332165 [332166, 332165, 332164] by Demod 50016 with 49025 at 2
-Id : 49088, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) ?319907 [319907, 319906] by Demod 49041 with 47849 at 2,3
-Id : 53621, {_}: multiply (inverse ?332348) (inverse ?332349) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332349, 332348] by Super 53578 with 49088 at 1,2
-Id : 48971, {_}: multiply (inverse ?319476) (inverse ?319477) =>= inverse (multiply ?319477 ?319476) [319477, 319476] by Super 48215 with 48896 at 2,2
-Id : 53698, {_}: inverse (multiply ?332349 ?332348) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332348, 332349] by Demod 53621 with 48971 at 2
-Id : 55617, {_}: inverse (multiply (inverse (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719)) ?335716) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Super 49850 with 53698 at 1,2,3
-Id : 55728, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Demod 55617 with 49171 at 2
-Id : 55729, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717, 335716] by Demod 55728 with 47849 at 2,3
-Id : 53403, {_}: inverse (multiply ?331872 ?331873) =<= multiply ?331874 (inverse (multiply ?331872 (multiply ?331873 ?331874))) [331874, 331873, 331872] by Super 49824 with 49369 at 1,3
-Id : 49375, {_}: multiply (inverse ?321009) (multiply (inverse ?321010) ?321011) =>= inverse (multiply (multiply (inverse ?321011) ?321010) ?321009) [321011, 321010, 321009] by Super 48971 with 49171 at 2,2
-Id : 53436, {_}: inverse (multiply (inverse ?332006) (inverse ?332007)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332007, 332006] by Super 53403 with 49375 at 1,2,3
-Id : 53542, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332006, 332007] by Demod 53436 with 49025 at 2
-Id : 53543, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53542 with 47849 at 2,3
-Id : 53544, {_}: multiply ?332007 ?332006 =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53543 with 47849 at 2,2
-Id : 54357, {_}: multiply (inverse ?333550) (multiply ?333551 ?333552) =<= multiply (multiply (inverse ?333550) ?333551) ?333552 [333552, 333551, 333550] by Super 48215 with 53544 at 2,2
-Id : 53440, {_}: inverse (multiply (inverse (multiply (multiply ?332022 ?332023) ?332024)) ?332022) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Super 53403 with 49088 at 1,2,3
-Id : 53553, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Demod 53440 with 49171 at 2
-Id : 53554, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 ?332024 [332024, 332023, 332022] by Demod 53553 with 47849 at 2,3
-Id : 54857, {_}: multiply (inverse ?334428) (multiply (multiply (multiply ?334428 ?334429) ?334430) ?334431) =>= multiply (multiply ?334429 ?334430) ?334431 [334431, 334430, 334429, 334428] by Super 54357 with 53554 at 1,3
-Id : 81835, {_}: multiply (multiply ?335717 ?335718) ?335719 =?= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717] by Demod 55729 with 54857 at 2
-Id : 82672, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 81835 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP444-1.p
-23669: solved GRP444-1.p in 49.195074 using nrkbo
-23669: status Unsatisfiable for GRP444-1.p
-NO CLASH, using fixed ground order
-23734: Facts:
-23734: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23734: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-23734: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-23734: Goal:
-23734: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23734: Order:
-23734: nrkbo
-23734: Leaf order:
-23734: b2 2 0 2 1,1,1,2
-23734: a2 2 0 2 2,2
-23734: inverse 2 1 1 0,1,1,2
-23734: multiply 3 2 2 0,2
-23734: divide 13 2 0
-NO CLASH, using fixed ground order
-23735: Facts:
-23735: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23735: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-23735: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-23735: Goal:
-23735: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23735: Order:
-23735: kbo
-23735: Leaf order:
-23735: b2 2 0 2 1,1,1,2
-23735: a2 2 0 2 2,2
-23735: inverse 2 1 1 0,1,1,2
-23735: multiply 3 2 2 0,2
-23735: divide 13 2 0
-NO CLASH, using fixed ground order
-23736: Facts:
-23736: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-23736: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-23736: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-23736: Goal:
-23736: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23736: Order:
-23736: lpo
-23736: Leaf order:
-23736: b2 2 0 2 1,1,1,2
-23736: a2 2 0 2 2,2
-23736: inverse 2 1 1 0,1,1,2
-23736: multiply 3 2 2 0,2
-23736: divide 13 2 0
-Statistics :
-Max weight : 38
-Found proof, 0.373646s
-% SZS status Unsatisfiable for GRP452-1.p
-% SZS output start CNFRefutation for GRP452-1.p
-Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
-Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
-Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
-Id : 41, {_}: multiply (divide ?104 ?104) ?105 =>= inverse (inverse ?105) [105, 104] by Super 29 with 4 at 3
-Id : 43, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= inverse (inverse ?111) [111, 110] by Super 41 with 29 at 1,2
-Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
-Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
-Id : 205, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
-Id : 206, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 205 with 4 at 1,2,1,1,1,2
-Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
-Id : 207, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 206 with 36 at 2,1,1,1,2
-Id : 208, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 207 with 29 at 1,1,1,2
-Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
-Id : 61, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
-Id : 62, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 61 with 4 at 3
-Id : 63, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 62 with 4 at 1,2,2,1,3
-Id : 68, {_}: divide (inverse (divide ?170 ?171)) ?172 =<= inverse (divide ?173 (divide ?171 (divide (inverse ?173) (divide (inverse ?170) ?172)))) [173, 172, 171, 170] by Demod 63 with 4 at 1,2,2,2,1,3
-Id : 75, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (divide (divide ?216 ?216) (divide ?214 (inverse (divide (inverse ?213) ?215)))) [216, 215, 214, 213] by Super 68 with 36 at 2,2,1,3
-Id : 85, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (divide ?214 (inverse (divide (inverse ?213) ?215)))) [215, 214, 213] by Demod 75 with 4 at 1,3
-Id : 329, {_}: divide (inverse (divide ?884 ?885)) ?886 =<= inverse (inverse (multiply ?885 (divide (inverse ?884) ?886))) [886, 885, 884] by Demod 85 with 29 at 1,1,3
-Id : 336, {_}: divide (inverse (divide (divide ?919 ?919) ?920)) ?921 =>= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920, 919] by Super 329 with 36 at 2,1,1,3
-Id : 348, {_}: divide (inverse (inverse ?920)) ?921 =<= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920] by Demod 336 with 4 at 1,1,2
-Id : 435, {_}: divide (inverse (inverse ?1126)) ?1127 =<= inverse (inverse (multiply ?1126 (inverse ?1127))) [1127, 1126] by Demod 336 with 4 at 1,1,2
-Id : 439, {_}: divide (inverse (inverse (divide ?1144 ?1144))) ?1145 =>= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145, 1144] by Super 435 with 32 at 1,1,3
-Id : 46, {_}: inverse ?115 =<= divide (inverse (inverse (divide ?116 ?116))) ?115 [116, 115] by Super 4 with 36 at 1,3
-Id : 452, {_}: inverse ?1145 =<= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145] by Demod 439 with 46 at 2
-Id : 461, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= divide ?1187 (inverse ?1188) [1188, 1187] by Super 29 with 452 at 2,3
-Id : 480, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= multiply ?1187 ?1188 [1188, 1187] by Demod 461 with 29 at 3
-Id : 490, {_}: divide (inverse (inverse ?1237)) (inverse (inverse (inverse ?1238))) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Super 348 with 480 at 1,1,3
-Id : 543, {_}: multiply (inverse (inverse ?1237)) (inverse (inverse ?1238)) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Demod 490 with 29 at 2
-Id : 564, {_}: divide (inverse (inverse (inverse (inverse ?1361)))) (inverse ?1362) =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Super 348 with 543 at 1,1,3
-Id : 586, {_}: multiply (inverse (inverse (inverse (inverse ?1361)))) ?1362 =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Demod 564 with 29 at 2
-Id : 608, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1454 ?1455))))))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Super 208 with 586 at 1,1,1,2
-Id : 633, {_}: divide (inverse (inverse (multiply ?1454 ?1455))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Demod 608 with 452 at 1,2
-Id : 634, {_}: ?1454 =<= inverse (inverse (inverse (inverse ?1454))) [1454] by Demod 633 with 208 at 2
-Id : 755, {_}: multiply ?1763 (inverse (inverse (inverse ?1764))) =>= divide ?1763 ?1764 [1764, 1763] by Super 29 with 634 at 2,3
-Id : 797, {_}: divide (inverse (inverse ?1873)) (inverse (inverse ?1874)) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Super 348 with 755 at 1,1,3
-Id : 816, {_}: multiply (inverse (inverse ?1873)) (inverse ?1874) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Demod 797 with 29 at 2
-Id : 868, {_}: divide (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) (inverse ?1958) =>= inverse (inverse ?1957) [1958, 1957] by Super 208 with 816 at 1,1,1,2
-Id : 892, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 868 with 29 at 2
-Id : 915, {_}: multiply (divide ?2055 ?2056) ?2056 =>= inverse (inverse ?2055) [2056, 2055] by Demod 892 with 634 at 1,2
-Id : 921, {_}: multiply (multiply ?2076 ?2077) (inverse ?2077) =>= inverse (inverse ?2076) [2077, 2076] by Super 915 with 29 at 1,2
-Id : 872, {_}: multiply (inverse (inverse ?1970)) (inverse ?1971) =>= inverse (inverse (divide ?1970 ?1971)) [1971, 1970] by Demod 797 with 29 at 2
-Id : 885, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (divide (inverse (inverse ?2028)) ?2029)) [2029, 2028] by Super 872 with 634 at 1,2
-Id : 86, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (multiply ?214 (divide (inverse ?213) ?215))) [215, 214, 213] by Demod 85 with 29 at 1,1,3
-Id : 64, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 63 with 4 at 1,2,2,2,1,3
-Id : 893, {_}: multiply (divide ?1957 ?1958) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 892 with 634 at 1,2
-Id : 910, {_}: inverse (inverse ?2040) =<= divide (divide ?2040 (inverse (inverse (inverse ?2041)))) ?2041 [2041, 2040] by Super 755 with 893 at 2
-Id : 1447, {_}: inverse (inverse ?3326) =<= divide (multiply ?3326 (inverse (inverse ?3327))) ?3327 [3327, 3326] by Demod 910 with 29 at 1,3
-Id : 51, {_}: multiply (inverse (inverse (divide ?133 ?133))) ?134 =>= inverse (inverse ?134) [134, 133] by Super 32 with 36 at 1,2
-Id : 1463, {_}: inverse (inverse (inverse (inverse (divide ?3389 ?3389)))) =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Super 1447 with 51 at 1,3
-Id : 1498, {_}: divide ?3389 ?3389 =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Demod 1463 with 634 at 2
-Id : 1499, {_}: divide ?3389 ?3389 =?= divide ?3390 ?3390 [3390, 3389] by Demod 1498 with 634 at 1,3
-Id : 1548, {_}: divide (inverse (divide ?3530 (divide (inverse ?3531) (divide (inverse ?3530) ?3532)))) ?3532 =?= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3532, 3531, 3530] by Super 64 with 1499 at 2,1,3
-Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
-Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
-Id : 1619, {_}: inverse ?3531 =<= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3531] by Demod 1548 with 31 at 2
-Id : 1667, {_}: divide ?3815 (divide ?3816 ?3816) =>= inverse (inverse (inverse (inverse ?3815))) [3816, 3815] by Super 634 with 1619 at 1,1,1,3
-Id : 1711, {_}: divide ?3815 (divide ?3816 ?3816) =>= ?3815 [3816, 3815] by Demod 1667 with 634 at 3
-Id : 1774, {_}: divide (inverse (divide ?4058 ?4059)) (divide ?4060 ?4060) =>= inverse (inverse (multiply ?4059 (inverse ?4058))) [4060, 4059, 4058] by Super 86 with 1711 at 2,1,1,3
-Id : 1809, {_}: inverse (divide ?4058 ?4059) =<= inverse (inverse (multiply ?4059 (inverse ?4058))) [4059, 4058] by Demod 1774 with 1711 at 2
-Id : 1810, {_}: inverse (divide ?4058 ?4059) =<= divide (inverse (inverse ?4059)) ?4058 [4059, 4058] by Demod 1809 with 348 at 3
-Id : 1856, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (inverse (divide ?2029 ?2028))) [2029, 2028] by Demod 885 with 1810 at 1,1,3
-Id : 52, {_}: inverse ?136 =<= divide (inverse (divide ?137 ?137)) ?136 [137, 136] by Super 35 with 4 at 1,3
-Id : 55, {_}: inverse ?145 =<= divide (inverse (inverse (inverse (divide ?146 ?146)))) ?145 [146, 145] by Super 52 with 36 at 1,1,3
-Id : 1858, {_}: inverse ?145 =<= inverse (divide ?145 (inverse (divide ?146 ?146))) [146, 145] by Demod 55 with 1810 at 3
-Id : 1862, {_}: inverse ?145 =<= inverse (multiply ?145 (divide ?146 ?146)) [146, 145] by Demod 1858 with 29 at 1,3
-Id : 1778, {_}: multiply ?4073 (divide ?4074 ?4074) =>= inverse (inverse ?4073) [4074, 4073] by Super 893 with 1711 at 1,2
-Id : 2425, {_}: inverse ?145 =<= inverse (inverse (inverse ?145)) [145] by Demod 1862 with 1778 at 1,3
-Id : 2428, {_}: multiply ?2028 (inverse ?2029) =>= inverse (divide ?2029 ?2028) [2029, 2028] by Demod 1856 with 2425 at 3
-Id : 2431, {_}: inverse (divide ?2077 (multiply ?2076 ?2077)) =>= inverse (inverse ?2076) [2076, 2077] by Demod 921 with 2428 at 2
-Id : 1860, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 208 with 1810 at 2
-Id : 2432, {_}: ?2076 =<= inverse (inverse ?2076) [2076] by Demod 2431 with 1860 at 2
-Id : 2437, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= ?111 [111, 110] by Demod 43 with 2432 at 3
-Id : 2539, {_}: a2 === a2 [] by Demod 1 with 2437 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP452-1.p
-23734: solved GRP452-1.p in 0.388023 using nrkbo
-23734: status Unsatisfiable for GRP452-1.p
-NO CLASH, using fixed ground order
-23741: Facts:
-23741: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-NO CLASH, using fixed ground order
-23742: Facts:
-23742: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23742: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23742: Goal:
-23742: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23742: Order:
-23742: kbo
-23742: Leaf order:
-23742: a1 2 0 2 1,1,2
-23742: b1 2 0 2 1,1,3
-23742: inverse 4 1 2 0,1,2
-23742: multiply 3 2 2 0,2
-23742: divide 7 2 0
-NO CLASH, using fixed ground order
-23743: Facts:
-23743: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23743: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23743: Goal:
-23743: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23743: Order:
-23743: lpo
-23743: Leaf order:
-23743: a1 2 0 2 1,1,2
-23743: b1 2 0 2 1,1,3
-23743: inverse 4 1 2 0,1,2
-23743: multiply 3 2 2 0,2
-23743: divide 7 2 0
-23741: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23741: Goal:
-23741: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23741: Order:
-23741: nrkbo
-23741: Leaf order:
-23741: a1 2 0 2 1,1,2
-23741: b1 2 0 2 1,1,3
-23741: inverse 4 1 2 0,1,2
-23741: multiply 3 2 2 0,2
-23741: divide 7 2 0
-% SZS status Timeout for GRP469-1.p
-NO CLASH, using fixed ground order
-23763: Facts:
-23763: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23763: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23763: Goal:
-23763: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23763: Order:
-23763: nrkbo
-23763: Leaf order:
-23763: b2 2 0 2 1,1,1,2
-23763: a2 2 0 2 2,2
-23763: inverse 3 1 1 0,1,1,2
-23763: multiply 3 2 2 0,2
-23763: divide 7 2 0
-NO CLASH, using fixed ground order
-23764: Facts:
-23764: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23764: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23764: Goal:
-23764: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23764: Order:
-23764: kbo
-23764: Leaf order:
-23764: b2 2 0 2 1,1,1,2
-23764: a2 2 0 2 2,2
-23764: inverse 3 1 1 0,1,1,2
-23764: multiply 3 2 2 0,2
-23764: divide 7 2 0
-NO CLASH, using fixed ground order
-23765: Facts:
-23765: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23765: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23765: Goal:
-23765: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23765: Order:
-23765: lpo
-23765: Leaf order:
-23765: b2 2 0 2 1,1,1,2
-23765: a2 2 0 2 2,2
-23765: inverse 3 1 1 0,1,1,2
-23765: multiply 3 2 2 0,2
-23765: divide 7 2 0
-% SZS status Timeout for GRP470-1.p
-NO CLASH, using fixed ground order
-23801: Facts:
-23801: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23801: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23801: Goal:
-23801: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23801: Order:
-23801: nrkbo
-23801: Leaf order:
-23801: a3 2 0 2 1,1,2
-23801: b3 2 0 2 2,1,2
-23801: c3 2 0 2 2,2
-23801: inverse 2 1 0
-23801: multiply 5 2 4 0,2
-23801: divide 7 2 0
-NO CLASH, using fixed ground order
-23802: Facts:
-23802: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23802: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23802: Goal:
-23802: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23802: Order:
-23802: kbo
-23802: Leaf order:
-23802: a3 2 0 2 1,1,2
-23802: b3 2 0 2 2,1,2
-23802: c3 2 0 2 2,2
-23802: inverse 2 1 0
-23802: multiply 5 2 4 0,2
-23802: divide 7 2 0
-NO CLASH, using fixed ground order
-23803: Facts:
-23803: Id : 2, {_}:
- divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
- (divide (divide ?5 ?4) ?2)
- =>=
- ?3
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23803: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23803: Goal:
-23803: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23803: Order:
-23803: lpo
-23803: Leaf order:
-23803: a3 2 0 2 1,1,2
-23803: b3 2 0 2 2,1,2
-23803: c3 2 0 2 2,2
-23803: inverse 2 1 0
-23803: multiply 5 2 4 0,2
-23803: divide 7 2 0
-% SZS status Timeout for GRP471-1.p
-NO CLASH, using fixed ground order
-23910: Facts:
-23910: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23910: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23910: Goal:
-23910: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23910: Order:
-23910: nrkbo
-23910: Leaf order:
-23910: a1 2 0 2 1,1,2
-23910: b1 2 0 2 1,1,3
-23910: inverse 4 1 2 0,1,2
-23910: multiply 3 2 2 0,2
-23910: divide 7 2 0
-NO CLASH, using fixed ground order
-23911: Facts:
-23911: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23911: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23911: Goal:
-23911: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23911: Order:
-23911: kbo
-23911: Leaf order:
-23911: a1 2 0 2 1,1,2
-23911: b1 2 0 2 1,1,3
-23911: inverse 4 1 2 0,1,2
-23911: multiply 3 2 2 0,2
-23911: divide 7 2 0
-NO CLASH, using fixed ground order
-23912: Facts:
-23912: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23912: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23912: Goal:
-23912: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23912: Order:
-23912: lpo
-23912: Leaf order:
-23912: a1 2 0 2 1,1,2
-23912: b1 2 0 2 1,1,3
-23912: inverse 4 1 2 0,1,2
-23912: multiply 3 2 2 0,2
-23912: divide 7 2 0
-% SZS status Timeout for GRP475-1.p
-NO CLASH, using fixed ground order
-23945: Facts:
-23945: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23945: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23945: Goal:
-23945: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23945: Order:
-23945: nrkbo
-23945: Leaf order:
-23945: b2 2 0 2 1,1,1,2
-23945: a2 2 0 2 2,2
-23945: inverse 3 1 1 0,1,1,2
-23945: multiply 3 2 2 0,2
-23945: divide 7 2 0
-NO CLASH, using fixed ground order
-23946: Facts:
-23946: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23946: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23946: Goal:
-23946: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23946: Order:
-23946: kbo
-23946: Leaf order:
-23946: b2 2 0 2 1,1,1,2
-23946: a2 2 0 2 2,2
-23946: inverse 3 1 1 0,1,1,2
-23946: multiply 3 2 2 0,2
-23946: divide 7 2 0
-NO CLASH, using fixed ground order
-23947: Facts:
-23947: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23947: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23947: Goal:
-23947: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23947: Order:
-23947: lpo
-23947: Leaf order:
-23947: b2 2 0 2 1,1,1,2
-23947: a2 2 0 2 2,2
-23947: inverse 3 1 1 0,1,1,2
-23947: multiply 3 2 2 0,2
-23947: divide 7 2 0
-Statistics :
-Max weight : 50
-Found proof, 11.024829s
-% SZS status Unsatisfiable for GRP476-1.p
-% SZS output start CNFRefutation for GRP476-1.p
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
-Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
-Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
-Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
-Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2
-Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2
-Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2
-Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2
-Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2
-Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
-Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2
-Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2
-Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2
-Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2
-Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2
-Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2
-Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2
-Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3
-Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3
-Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3
-Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2
-Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2
-Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2
-Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2
-Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3
-Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2
-Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2
-Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
-Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2
-Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2
-Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2
-Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2
-Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3
-Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2
-Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2
-Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2
-Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2
-Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2
-Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2
-Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2
-Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3
-Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2
-Id : 26641, {_}: divide ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 25208 with 26405 at 2
-Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2
-Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2
-Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2
-Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2
-Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3
-Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2
-Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3
-Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2
-Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2
-Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3
-Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3
-Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2
-Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3
-Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2
-Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2
-Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2
-Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2
-Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2
-Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2
-Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3
-Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2
-Id : 27507, {_}: multiply ?127752 (divide (divide ?127753 ?127754) (divide ?127753 ?127754)) =>= ?127752 [127754, 127753, 127752] by Demod 26641 with 27506 at 2
-Id : 27516, {_}: multiply ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 27507 with 25599 at 2,2
-Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2
-Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3
-Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3
-Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3
-Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2
-Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2
-Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2
-Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3
-Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3
-Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3
-Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2
-Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2
-Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2
-Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2
-Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2
-Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2
-Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2
-Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2
-Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2
-Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2
-Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2
-Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2
-Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2
-Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2
-Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3
-Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3
-Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2
-Id : 33479, {_}: multiply ?154885 (multiply (divide (multiply ?154886 ?154887) ?154887) (inverse ?154886)) =>= ?154885 [154887, 154886, 154885] by Super 27516 with 33094 at 2,2,2
-Id : 33980, {_}: multiply ?154885 (divide (divide (multiply ?154886 ?154887) ?154887) ?154886) =>= ?154885 [154887, 154886, 154885] by Demod 33479 with 27734 at 2,2
-Id : 33981, {_}: multiply ?154885 (divide ?154886 ?154886) =>= ?154885 [154886, 154885] by Demod 33980 with 32203 at 1,2,2
-Id : 34313, {_}: multiply (inverse (divide ?156478 ?156478)) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Super 26966 with 33981 at 1,3
-Id : 34773, {_}: multiply (divide ?156478 ?156478) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Demod 34313 with 26405 at 1,2
-Id : 36051, {_}: multiply (divide ?160644 ?160644) ?160645 =>= ?160645 [160645, 160644] by Demod 34773 with 27632 at 3
-Id : 36066, {_}: multiply (multiply (inverse ?160721) ?160721) ?160722 =>= ?160722 [160722, 160721] by Super 36051 with 3 at 1,2
-Id : 39894, {_}: a2 === a2 [] by Demod 1 with 36066 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP476-1.p
-23945: solved GRP476-1.p in 11.032689 using nrkbo
-23945: status Unsatisfiable for GRP476-1.p
-NO CLASH, using fixed ground order
-23952: Facts:
-23952: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23952: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23952: Goal:
-23952: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23952: Order:
-23952: nrkbo
-23952: Leaf order:
-23952: a3 2 0 2 1,1,2
-23952: b3 2 0 2 2,1,2
-23952: c3 2 0 2 2,2
-23952: inverse 2 1 0
-23952: multiply 5 2 4 0,2
-23952: divide 7 2 0
-NO CLASH, using fixed ground order
-23953: Facts:
-23953: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23953: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23953: Goal:
-23953: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23953: Order:
-23953: kbo
-23953: Leaf order:
-23953: a3 2 0 2 1,1,2
-23953: b3 2 0 2 2,1,2
-23953: c3 2 0 2 2,2
-23953: inverse 2 1 0
-23953: multiply 5 2 4 0,2
-23953: divide 7 2 0
-NO CLASH, using fixed ground order
-23954: Facts:
-23954: Id : 2, {_}:
- divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
- (divide ?3 ?2)
- =>=
- ?5
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23954: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23954: Goal:
-23954: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-23954: Order:
-23954: lpo
-23954: Leaf order:
-23954: a3 2 0 2 1,1,2
-23954: b3 2 0 2 2,1,2
-23954: c3 2 0 2 2,2
-23954: inverse 2 1 0
-23954: multiply 5 2 4 0,2
-23954: divide 7 2 0
-Statistics :
-Max weight : 50
-Found proof, 32.327095s
-% SZS status Unsatisfiable for GRP477-1.p
-% SZS output start CNFRefutation for GRP477-1.p
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
-Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
-Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
-Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2
-Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2
-Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2
-Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
-Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2
-Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2
-Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2
-Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2
-Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2
-Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2
-Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2
-Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3
-Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3
-Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3
-Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2
-Id : 22444, {_}: ?116047 =<= multiply (multiply ?116047 (divide (inverse ?116048) ?116049)) (multiply ?116049 ?116048) [116049, 116048, 116047] by Super 22416 with 3 at 2,3
-Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
-Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2
-Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2
-Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2
-Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2
-Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2
-Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2
-Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3
-Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2
-Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2
-Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
-Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2
-Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2
-Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2
-Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2
-Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3
-Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2
-Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2
-Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2
-Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2
-Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2
-Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2
-Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2
-Id : 26849, {_}: ?116047 =<= multiply (multiply ?116047 (inverse (multiply ?116049 ?116048))) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 22444 with 26764 at 2,1,3
-Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2
-Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2
-Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3
-Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2
-Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2
-Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2
-Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3
-Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3
-Id : 27821, {_}: ?116047 =<= multiply (divide ?116047 (multiply ?116049 ?116048)) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 26849 with 27734 at 1,3
-Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2
-Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2
-Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2
-Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2
-Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2
-Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2
-Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2
-Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2
-Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2
-Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2
-Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2
-Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2
-Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2
-Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2
-Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3
-Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2
-Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3
-Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2
-Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2
-Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3
-Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3
-Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2
-Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3
-Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2
-Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2
-Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3
-Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2
-Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2
-Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2
-Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3
-Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2
-Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2
-Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2
-Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2
-Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2
-Id : 31835, {_}: ?147320 =<= multiply (divide ?147320 (multiply (multiply (divide ?147321 ?147322) (multiply ?147322 (multiply (multiply ?147323 (multiply (divide ?147324 ?147325) (divide ?147326 ?147327))) (divide ?147327 ?147326)))) (multiply (divide (divide ?147325 ?147324) ?147328) (divide ?147328 ?147323)))) ?147321 [147328, 147327, 147326, 147325, 147324, 147323, 147322, 147321, 147320] by Super 27821 with 31744 at 2,3
-Id : 32201, {_}: ?147320 =<= multiply (divide ?147320 ?147321) ?147321 [147321, 147320] by Demod 31835 with 31744 at 2,1,3
-Id : 835, {_}: divide (divide (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4528 ?4527)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Super 17 with 20 at 1,2
-Id : 25994, {_}: divide (multiply (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Demod 835 with 25599 at 1,2
-Id : 26651, {_}: divide (multiply (divide ?4530 (divide (divide ?4527 ?4528) ?4529)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4529, 4528, 4527, 4530] by Demod 25994 with 26405 at 1,1,2
-Id : 26667, {_}: divide (multiply (multiply ?4530 (divide ?4529 (divide ?4527 ?4528))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4528, 4527, 4529, 4530] by Demod 26651 with 25599 at 1,1,2
-Id : 26668, {_}: divide (multiply (multiply ?4530 (multiply ?4529 (divide ?4528 ?4527))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4527, 4528, 4529, 4530] by Demod 26667 with 25599 at 2,1,1,2
-Id : 32718, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =?= divide ?151970 (multiply ?151973 (divide ?151972 ?151971)) [151973, 151972, 151971, 151970] by Super 26668 with 32201 at 1,1,2
-Id : 42767, {_}: divide (multiply ?174190 (divide ?174191 ?174192)) ?174193 =>= multiply ?174190 (divide (divide ?174191 ?174192) ?174193) [174193, 174192, 174191, 174190] by Demod 32718 with 27506 at 3
-Id : 25986, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 232 with 25599 at 1,2,1,2
-Id : 26619, {_}: divide (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026) (multiply (divide ?1024 ?1025) ?1026) =>= ?1027 [1026, 1025, 1024, 1027] by Demod 25986 with 26405 at 2
-Id : 42770, {_}: divide (multiply ?174208 ?174209) ?174210 =<= multiply ?174208 (divide (divide (multiply (multiply ?174209 (divide ?174211 ?174212)) ?174213) (multiply (divide ?174211 ?174212) ?174213)) ?174210) [174213, 174212, 174211, 174210, 174209, 174208] by Super 42767 with 26619 at 2,1,2
-Id : 43287, {_}: divide (multiply ?174208 ?174209) ?174210 =>= multiply ?174208 (divide ?174209 ?174210) [174210, 174209, 174208] by Demod 42770 with 26619 at 1,2,3
-Id : 45294, {_}: multiply ?177592 ?177593 =<= multiply (multiply ?177592 (divide ?177593 ?177594)) ?177594 [177594, 177593, 177592] by Super 32201 with 43287 at 1,3
-Id : 25967, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 20 with 25599 at 2
-Id : 25968, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25967 with 25599 at 1,3
-Id : 25969, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25968 with 25599 at 2,1,1,1,3
-Id : 26616, {_}: multiply (divide ?83 (divide (divide ?80 ?81) ?82)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 82, 81, 80, 83] by Demod 25969 with 26405 at 1,2
-Id : 26679, {_}: multiply (multiply ?83 (divide ?82 (divide ?80 ?81))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 81, 80, 82, 83] by Demod 26616 with 25599 at 1,2
-Id : 26680, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 80, 81, 82, 83] by Demod 26679 with 25599 at 2,1,2
-Id : 28666, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= divide (divide ?83 ?87) (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 26680 with 26724 at 3
-Id : 28715, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82)))) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 28666 with 25599 at 3
-Id : 28664, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (divide ?31561 (divide ?31557 ?31556)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27299 with 26724 at 3
-Id : 28717, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (multiply ?31561 (divide ?31556 ?31557)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28664 with 25599 at 1,3
-Id : 32902, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =>= multiply ?151970 (divide (divide ?151971 ?151972) ?151973) [151973, 151972, 151971, 151970] by Demod 32718 with 27506 at 3
-Id : 42552, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28717 with 32902 at 3
-Id : 10, {_}: divide (inverse (divide (divide (divide ?43 ?44) (inverse ?45)) (multiply ?46 ?45))) (divide ?44 ?43) =>= ?46 [46, 45, 44, 43] by Super 2 with 3 at 2,1,1,2
-Id : 58, {_}: divide (inverse (divide (multiply (divide ?293 ?294) ?295) (multiply ?296 ?295))) (divide ?294 ?293) =>= ?296 [296, 295, 294, 293] by Demod 10 with 3 at 1,1,1,2
-Id : 66, {_}: divide (inverse (divide (multiply (multiply ?349 ?350) ?351) (multiply ?352 ?351))) (divide (inverse ?350) ?349) =>= ?352 [352, 351, 350, 349] by Super 58 with 3 at 1,1,1,1,2
-Id : 5845, {_}: inverse (divide (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31658 ?31657)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Super 5809 with 66 at 1,1,3
-Id : 25939, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 5845 with 25599 at 1,2
-Id : 25940, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 25939 with 25599 at 1,3
-Id : 26656, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 25940 with 26405 at 1,1,1,2
-Id : 26874, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (inverse (multiply ?31653 ?31654)) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26656 with 26764 at 1,2,1,3
-Id : 26875, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (inverse (multiply ?31658 (multiply ?31653 ?31654)))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26874 with 26764 at 2,1,3
-Id : 11, {_}: divide (inverse (divide (divide (multiply ?48 ?49) ?50) (divide ?51 ?50))) (divide (inverse ?49) ?48) =>= ?51 [51, 50, 49, 48] by Super 2 with 3 at 1,1,1,1,2
-Id : 5813, {_}: inverse (divide (divide ?31391 ?31392) (divide (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))) ?31392)) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Super 5809 with 11 at 2,1,3
-Id : 26012, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 5813 with 25599 at 1,2
-Id : 26013, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26012 with 25599 at 1,1,3
-Id : 26014, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26013 with 25599 at 1,2,2,1,2
-Id : 26060, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26014 with 3 at 2,1,2
-Id : 26061, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (multiply ?31393 ?31394)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26060 with 3 at 2,1,1,3
-Id : 26649, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26061 with 26405 at 3
-Id : 5837, {_}: inverse (divide (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31584 ?31583)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Super 5809 with 11 at 1,1,3
-Id : 26017, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 5837 with 25599 at 1,2
-Id : 26018, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26017 with 25599 at 1,3
-Id : 26019, {_}: inverse (multiply (divide (inverse (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26018 with 25599 at 1,1,1,1,2
-Id : 26844, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26019 with 26764 at 1,1,2
-Id : 26845, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (inverse (multiply ?31579 ?31580)) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26844 with 26764 at 1,2,1,3
-Id : 26846, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26845 with 26764 at 2,1,3
-Id : 27296, {_}: multiply (inverse (divide ?31583 ?31584)) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31584, 31583] by Demod 26846 with 26966 at 2
-Id : 27301, {_}: multiply (divide ?31584 ?31583) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31583, 31584] by Demod 27296 with 26405 at 1,2
-Id : 27302, {_}: inverse (inverse (multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 26649 with 27301 at 1,2
-Id : 27505, {_}: multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 27302 with 27254 at 2
-Id : 27520, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (multiply ?31658 (multiply ?31653 ?31654))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26875 with 27505 at 1,3
-Id : 27523, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31658, 31657, 31654, 31653, 31655, 31656] by Demod 27520 with 26405 at 3
-Id : 28682, {_}: divide (divide ?31658 ?31657) (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 27523 with 26724 at 2
-Id : 28683, {_}: multiply (divide ?31658 ?31657) (divide ?31657 (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 28682 with 25599 at 2
-Id : 28684, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28683 with 25599 at 2,2
-Id : 43520, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28684 with 43287 at 2,2,2
-Id : 43521, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (divide (multiply ?31653 ?31654) ?31656) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43520 with 43287 at 3
-Id : 43522, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43521 with 43287 at 2,3
-Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3
-Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3
-Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3
-Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3
-Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3
-Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2
-Id : 43571, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (inverse ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43522 with 33094 at 2,2,2,2
-Id : 43572, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply ?31653 ?31654) ?31656)) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43571 with 27734 at 2,2,2
-Id : 43573, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply ?31653 (divide ?31654 ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43572 with 43287 at 2,2,2
-Id : 43575, {_}: multiply ?31561 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31561] by Demod 42552 with 43573 at 2
-Id : 43578, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (divide (divide ?85 ?84) ?82))) [85, 84, 87, 80, 81, 82, 83] by Demod 28715 with 43575 at 2,2,3
-Id : 43604, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (multiply ?87 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85))) [84, 85, 87, 80, 81, 82, 83] by Demod 43578 with 27506 at 2,3
-Id : 243, {_}: inverse (divide (multiply (divide ?1104 ?1105) ?1106) (multiply (divide ?1107 (divide ?1105 ?1104)) ?1106)) =>= ?1107 [1107, 1106, 1105, 1104] by Demod 213 with 3 at 1,1,2
-Id : 748, {_}: inverse (divide (multiply (divide (inverse ?3864) ?3865) ?3866) (multiply (divide ?3867 (multiply ?3865 ?3864)) ?3866)) =>= ?3867 [3867, 3866, 3865, 3864] by Super 243 with 3 at 2,1,2,1,2
-Id : 753, {_}: inverse (divide (multiply (divide (inverse (divide (divide (divide ?3899 ?3900) ?3901) (divide ?3902 ?3901))) (divide ?3900 ?3899)) ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902, 3901, 3900, 3899] by Super 748 with 272 at 1,2,1,2
-Id : 773, {_}: inverse (divide (multiply ?3902 ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902] by Demod 753 with 2 at 1,1,1,2
-Id : 15665, {_}: inverse (divide (multiply (divide ?84988 (divide ?84989 ?84990)) ?84991) (multiply (divide ?84992 ?84993) ?84991)) =>= divide (divide (inverse (divide ?84993 ?84992)) (divide ?84990 ?84989)) ?84988 [84993, 84992, 84991, 84990, 84989, 84988] by Super 773 with 14284 at 3
-Id : 15692, {_}: inverse (divide (multiply (divide ?85261 (divide ?85262 ?85263)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85263, 85262, 85261] by Super 15665 with 3 at 1,2,1,2
-Id : 25923, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 15692 with 25599 at 1,1,1,2
-Id : 25924, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 25923 with 25599 at 1,3
-Id : 26606, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 25924 with 26405 at 2
-Id : 26607, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (divide ?85265 (inverse ?85266)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26606 with 26405 at 1,1,3
-Id : 26682, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (multiply ?85265 ?85266) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26607 with 3 at 1,1,3
-Id : 42547, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26682 with 32902 at 3
-Id : 43537, {_}: multiply (multiply ?85265 ?85266) (divide ?85264 (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 42547 with 43287 at 2
-Id : 43538, {_}: multiply (multiply ?85265 ?85266) (inverse (multiply ?85261 (divide ?85263 ?85262))) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43537 with 33094 at 2,2
-Id : 43539, {_}: divide (multiply ?85265 ?85266) (multiply ?85261 (divide ?85263 ?85262)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43538 with 27734 at 2
-Id : 43540, {_}: multiply ?85265 (divide ?85266 (multiply ?85261 (divide ?85263 ?85262))) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43539 with 43287 at 2
-Id : 43541, {_}: multiply ?85265 (multiply ?85266 (divide (divide ?85262 ?85263) ?85261)) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85261, 85263, 85262, 85266, 85265] by Demod 43540 with 27506 at 2,2
-Id : 43605, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (multiply (divide ?83 ?87) ?87) (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 87, 80, 81, 82, 83] by Demod 43604 with 43541 at 3
-Id : 43606, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 80, 81, 82, 83] by Demod 43605 with 32201 at 1,3
-Id : 43607, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (multiply (divide ?82 (divide ?85 ?84)) (divide ?85 ?84)) [84, 85, 80, 81, 82, 83] by Demod 43606 with 25599 at 2,3
-Id : 43608, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =>= multiply ?83 ?82 [80, 81, 82, 83] by Demod 43607 with 32201 at 2,3
-Id : 45322, {_}: multiply (multiply ?177731 (multiply ?177732 (divide ?177733 ?177734))) ?177734 =>= multiply (multiply ?177731 ?177732) ?177733 [177734, 177733, 177732, 177731] by Super 45294 with 43608 at 1,3
-Id : 45299, {_}: multiply ?177614 (multiply ?177615 ?177616) =<= multiply (multiply ?177614 (multiply ?177615 (divide ?177616 ?177617))) ?177617 [177617, 177616, 177615, 177614] by Super 45294 with 43287 at 2,1,3
-Id : 64505, {_}: multiply ?177731 (multiply ?177732 ?177733) =?= multiply (multiply ?177731 ?177732) ?177733 [177733, 177732, 177731] by Demod 45322 with 45299 at 2
-Id : 64928, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 64505 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP477-1.p
-23952: solved GRP477-1.p in 16.221013 using nrkbo
-23952: status Unsatisfiable for GRP477-1.p
-NO CLASH, using fixed ground order
-23966: Facts:
-23966: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23966: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23966: Goal:
-23966: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23966: Order:
-23966: nrkbo
-23966: Leaf order:
-23966: a1 2 0 2 1,1,2
-23966: b1 2 0 2 1,1,3
-23966: inverse 4 1 2 0,1,2
-23966: multiply 3 2 2 0,2
-23966: divide 7 2 0
-NO CLASH, using fixed ground order
-23967: Facts:
-23967: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23967: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23967: Goal:
-23967: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23967: Order:
-23967: kbo
-23967: Leaf order:
-23967: a1 2 0 2 1,1,2
-23967: b1 2 0 2 1,1,3
-23967: inverse 4 1 2 0,1,2
-23967: multiply 3 2 2 0,2
-23967: divide 7 2 0
-NO CLASH, using fixed ground order
-23968: Facts:
-23968: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23968: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23968: Goal:
-23968: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-23968: Order:
-23968: lpo
-23968: Leaf order:
-23968: a1 2 0 2 1,1,2
-23968: b1 2 0 2 1,1,3
-23968: inverse 4 1 2 0,1,2
-23968: multiply 3 2 2 0,2
-23968: divide 7 2 0
-% SZS status Timeout for GRP478-1.p
-NO CLASH, using fixed ground order
-23995: Facts:
-23995: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23995: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23995: Goal:
-23995: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23995: Order:
-23995: nrkbo
-23995: Leaf order:
-23995: b2 2 0 2 1,1,1,2
-23995: a2 2 0 2 2,2
-23995: inverse 3 1 1 0,1,1,2
-23995: multiply 3 2 2 0,2
-23995: divide 7 2 0
-NO CLASH, using fixed ground order
-23996: Facts:
-23996: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23996: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23996: Goal:
-23996: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23996: Order:
-23996: kbo
-23996: Leaf order:
-23996: b2 2 0 2 1,1,1,2
-23996: a2 2 0 2 2,2
-23996: inverse 3 1 1 0,1,1,2
-23996: multiply 3 2 2 0,2
-23996: divide 7 2 0
-NO CLASH, using fixed ground order
-23997: Facts:
-23997: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-23997: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-23997: Goal:
-23997: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-23997: Order:
-23997: lpo
-23997: Leaf order:
-23997: b2 2 0 2 1,1,1,2
-23997: a2 2 0 2 2,2
-23997: inverse 3 1 1 0,1,1,2
-23997: multiply 3 2 2 0,2
-23997: divide 7 2 0
-Statistics :
-Max weight : 78
-Found proof, 37.151334s
-% SZS status Unsatisfiable for GRP479-1.p
-% SZS output start CNFRefutation for GRP479-1.p
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
-Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
-Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
-Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
-Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
-Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
-Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
-Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
-Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
-Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
-Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
-Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
-Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
-Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
-Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
-Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
-Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
-Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
-Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
-Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
-Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
-Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
-Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
-Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
-Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
-Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
-Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
-Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
-Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
-Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
-Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
-Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
-Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
-Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
-Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
-Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
-Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
-Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
-Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
-Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
-Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
-Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
-Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
-Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
-Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
-Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
-Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
-Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
-Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
-Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
-Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
-Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
-Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
-Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
-Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
-Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
-Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
-Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
-Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
-Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
-Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
-Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
-Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
-Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
-Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
-Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
-Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
-Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
-Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
-Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
-Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
-Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
-Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
-Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
-Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
-Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
-Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
-Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
-Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
-Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2
-Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3
-Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3
-Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2
-Id : 102959, {_}: inverse (divide ?539857 ?539858) =>= divide ?539858 ?539857 [539858, 539857] by Demod 102787 with 102471 at 3
-Id : 102980, {_}: inverse (multiply ?539955 ?539956) =<= divide (inverse ?539956) ?539955 [539956, 539955] by Super 102959 with 3 at 1,2
-Id : 103330, {_}: multiply (inverse ?540510) ?540511 =<= inverse (multiply (inverse ?540511) ?540510) [540511, 540510] by Super 3 with 102980 at 3
-Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2
-Id : 96346, {_}: multiply ?522565 (divide ?522566 ?522566) =>= ?522565 [522566, 522565] by Super 93587 with 93886 at 1,2
-Id : 96425, {_}: multiply ?523023 (multiply (inverse ?523024) ?523024) =>= ?523023 [523024, 523023] by Super 96346 with 3 at 2,2
-Id : 103339, {_}: multiply (inverse (multiply (inverse ?540545) ?540545)) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Super 103330 with 96425 at 1,3
-Id : 103110, {_}: multiply (inverse ?540161) ?540162 =<= inverse (multiply (inverse ?540162) ?540161) [540162, 540161] by Super 3 with 102980 at 3
-Id : 103424, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Demod 103339 with 103110 at 1,2
-Id : 103425, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= ?540546 [540546, 540545] by Demod 103424 with 101328 at 3
-Id : 104863, {_}: a2 === a2 [] by Demod 1 with 103425 at 2
-Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
-% SZS output end CNFRefutation for GRP479-1.p
-23995: solved GRP479-1.p in 37.162321 using nrkbo
-23995: status Unsatisfiable for GRP479-1.p
-NO CLASH, using fixed ground order
-24007: Facts:
-24007: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-24007: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-24007: Goal:
-24007: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-24007: Order:
-24007: nrkbo
-24007: Leaf order:
-24007: a3 2 0 2 1,1,2
-24007: b3 2 0 2 2,1,2
-24007: c3 2 0 2 2,2
-24007: inverse 2 1 0
-24007: multiply 5 2 4 0,2
-24007: divide 7 2 0
-NO CLASH, using fixed ground order
-24008: Facts:
-24008: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-24008: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-24008: Goal:
-24008: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-24008: Order:
-24008: kbo
-24008: Leaf order:
-24008: a3 2 0 2 1,1,2
-24008: b3 2 0 2 2,1,2
-24008: c3 2 0 2 2,2
-24008: inverse 2 1 0
-24008: multiply 5 2 4 0,2
-24008: divide 7 2 0
-NO CLASH, using fixed ground order
-24009: Facts:
-24009: Id : 2, {_}:
- divide
- (inverse
- (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
- ?5
- =>=
- ?4
- [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-24009: Id : 3, {_}:
- multiply ?7 ?8 =<= divide ?7 (inverse ?8)
- [8, 7] by multiply ?7 ?8
-24009: Goal:
-24009: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-24009: Order:
-24009: lpo
-24009: Leaf order:
-24009: a3 2 0 2 1,1,2
-24009: b3 2 0 2 2,1,2
-24009: c3 2 0 2 2,2
-24009: inverse 2 1 0
-24009: multiply 5 2 4 0,2
-24009: divide 7 2 0
-Statistics :
-Max weight : 78
-Found proof, 40.781292s
-% SZS status Unsatisfiable for GRP480-1.p
-% SZS output start CNFRefutation for GRP480-1.p
-Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
-Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
-Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
-Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
-Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
-Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
-Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
-Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
-Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
-Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
-Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
-Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
-Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
-Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
-Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
-Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
-Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
-Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
-Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
-Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
-Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
-Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
-Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
-Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
-Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
-Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
-Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
-Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
-Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
-Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
-Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
-Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
-Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
-Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
-Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
-Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
-Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
-Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
-Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
-Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
-Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
-Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
-Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
-Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
-Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
-Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
-Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
-Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
-Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
-Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
-Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
-Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
-Id : 100522, {_}: divide (inverse (divide (inverse (inverse (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95] by Demod 23 with 100489 at 1,1,1,2
-Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
-Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
-Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
-Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
-Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
-Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
-Id : 101259, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96] by Demod 100522 with 100849 at 1,1,1,1,1,1,2
-Id : 101260, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101259 with 100849 at 1,1,3
-Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
-Id : 101498, {_}: divide (inverse (divide (divide (inverse ?96) (divide ?97 (divide ?96 ?98))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101260 with 101328 at 1,1,1,2
-Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
-Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
-Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
-Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
-Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
-Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
-Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
-Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
-Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
-Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
-Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
-Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
-Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
-Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
-Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
-Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
-Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
-Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
-Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
-Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
-Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
-Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
-Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
-Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
-Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
-Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
-Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
-Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2
-Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3
-Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3
-Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2
-Id : 102788, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102787 with 102471 at 3
-Id : 102815, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 98, 97, 96, 99] by Demod 101498 with 102788 at 1,2
-Id : 102816, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 98, 97, 96, 99] by Demod 102815 with 102788 at 3
-Id : 2390, {_}: divide (divide ?13180 ?13181) (divide ?13182 ?13181) =?= divide (divide ?13180 ?13183) (divide ?13182 ?13183) [13183, 13182, 13181, 13180] by Super 86 with 1057 at 1,1,2
-Id : 212, {_}: divide (divide (inverse (divide (multiply (divide ?1043 ?1043) ?1044) ?1045)) ?1046) (divide (inverse ?1044) ?1046) =>= ?1045 [1046, 1045, 1044, 1043] by Super 202 with 3 at 1,1,1,1,2
-Id : 2401, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (multiply (divide ?13275 ?13275) ?13276) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13275, 13274, 13273] by Super 2390 with 212 at 2,3
-Id : 100530, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (inverse (inverse ?13276)) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 2401 with 100489 at 1,1,1,1,2,2
-Id : 101375, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide ?13276 ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 100530 with 101328 at 1,1,1,1,2,2
-Id : 102446, {_}: divide ?13273 (divide (inverse (divide ?13276 ?13277)) ?13278) =?= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13273] by Demod 101375 with 102436 at 2
-Id : 102862, {_}: divide ?13273 (divide (divide ?13277 ?13276) ?13278) =<= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13276, 13277, 13273] by Demod 102446 with 102788 at 1,2,2
-Id : 102906, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 97, 96, 98, 99] by Demod 102816 with 102862 at 2
-Id : 102907, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 97, 96, 98, 99] by Demod 102906 with 3 at 3
-Id : 102924, {_}: multiply ?539666 (divide ?539667 ?539668) =<= divide ?539666 (divide ?539668 ?539667) [539668, 539667, 539666] by Super 102471 with 102788 at 2,2
-Id : 103472, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 98, 96, 97, 99] by Demod 102907 with 102924 at 2
-Id : 103473, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103472 with 102924 at 1,3
-Id : 103474, {_}: multiply ?99 (multiply (divide ?97 (divide ?96 ?98)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103473 with 102924 at 2,2
-Id : 103475, {_}: multiply ?99 (multiply (multiply ?97 (divide ?98 ?96)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 96, 98, 97, 99] by Demod 103474 with 102924 at 1,2,2
-Id : 9, {_}: divide (inverse (divide (divide (multiply (inverse ?36) ?36) ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37, 36] by Super 2 with 3 at 1,1,1,1,2
-Id : 101427, {_}: divide (inverse (divide (inverse ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37] by Demod 9 with 101312 at 1,2
-Id : 102819, {_}: divide (divide (divide ?38 (divide ?37 ?39)) (inverse ?37)) ?39 =>= ?38 [39, 37, 38] by Demod 101427 with 102788 at 1,2
-Id : 102903, {_}: divide (multiply (divide ?38 (divide ?37 ?39)) ?37) ?39 =>= ?38 [39, 37, 38] by Demod 102819 with 3 at 1,2
-Id : 103476, {_}: divide (multiply (multiply ?38 (divide ?39 ?37)) ?37) ?39 =>= ?38 [37, 39, 38] by Demod 102903 with 102924 at 1,1,2
-Id : 2408, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (multiply (divide ?13324 ?13324) ?13325) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13324, 13323, 13322] by Super 2390 with 378 at 2,3
-Id : 100531, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (inverse (inverse ?13325)) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 2408 with 100489 at 1,1,1,1,2,2
-Id : 101355, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide ?13325 ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 100531 with 101328 at 1,1,1,1,2,2
-Id : 102440, {_}: divide ?13322 (multiply (inverse (divide ?13325 ?13326)) ?13327) =?= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13322] by Demod 101355 with 102436 at 2
-Id : 102864, {_}: divide ?13322 (multiply (divide ?13326 ?13325) ?13327) =<= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13325, 13326, 13322] by Demod 102440 with 102788 at 1,2,2
-Id : 102611, {_}: divide ?539467 (multiply ?539468 ?539467) =>= inverse ?539468 [539468, 539467] by Super 101429 with 101594 at 1,2
-Id : 102625, {_}: divide (inverse ?539525) (divide ?539526 ?539525) =>= inverse ?539526 [539526, 539525] by Super 102611 with 102471 at 2,2
-Id : 103817, {_}: multiply (inverse ?539525) (divide ?539525 ?539526) =>= inverse ?539526 [539526, 539525] by Demod 102625 with 102924 at 2
-Id : 103831, {_}: divide ?541233 (multiply (divide ?541234 ?541235) (divide ?541235 ?541236)) =>= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541235, 541234, 541233] by Super 102864 with 103817 at 2,1,3
-Id : 103478, {_}: multiply (divide ?11774 ?11775) (divide ?11775 ?11776) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 102436 with 102924 at 2
-Id : 103925, {_}: divide ?541233 (divide ?541234 ?541236) =<= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541234, 541233] by Demod 103831 with 103478 at 2,2
-Id : 103926, {_}: divide ?541233 (divide ?541234 ?541236) =?= divide (multiply ?541233 ?541236) ?541234 [541236, 541234, 541233] by Demod 103925 with 3 at 1,3
-Id : 103927, {_}: multiply ?541233 (divide ?541236 ?541234) =<= divide (multiply ?541233 ?541236) ?541234 [541234, 541236, 541233] by Demod 103926 with 102924 at 2
-Id : 103998, {_}: multiply (multiply ?38 (divide ?39 ?37)) (divide ?37 ?39) =>= ?38 [37, 39, 38] by Demod 103476 with 103927 at 2
-Id : 104001, {_}: multiply ?99 ?97 =<= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 97, 99] by Demod 103475 with 103998 at 2,2
-Id : 104034, {_}: multiply ?541526 (multiply ?541527 ?541528) =<= multiply (multiply ?541526 (multiply ?541527 (divide ?541528 ?541529))) ?541529 [541529, 541528, 541527, 541526] by Super 104001 with 103927 at 2,1,3
-Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2
-Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2
-Id : 104145, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102788 at 1,2
-Id : 104146, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104145 with 102788 at 3
-Id : 104147, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 210, 211, 212] by Demod 104146 with 102924 at 1,2
-Id : 104148, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104147 with 102924 at 3
-Id : 104149, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104148 with 102924 at 2,1,2
-Id : 104150, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104149 with 102924 at 1,3
-Id : 104151, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104150 with 102924 at 2,3
-Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2
-Id : 95434, {_}: multiply ?517965 (divide ?517966 ?517966) =>= ?517965 [517966, 517965] by Super 93587 with 93886 at 1,2
-Id : 104152, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104151 with 95434 at 2,1,2
-Id : 104153, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104152 with 103927 at 2,1,3
-Id : 104154, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) ?215 [215, 213, 211, 212] by Demod 104153 with 95434 at 2,3
-Id : 115019, {_}: multiply ?541526 (multiply ?541527 ?541528) =?= multiply (multiply ?541526 ?541527) ?541528 [541528, 541527, 541526] by Demod 104034 with 104154 at 3
-Id : 115288, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 115019 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP480-1.p
-24007: solved GRP480-1.p in 40.758547 using nrkbo
-24007: status Unsatisfiable for GRP480-1.p
-NO CLASH, using fixed ground order
-24021: Facts:
-24021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24021: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24021: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24021: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24021: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24021: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-24021: Goal:
-24021: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24021: Order:
-24021: nrkbo
-24021: Leaf order:
-24021: c 2 0 2 2,2,2
-24021: a 4 0 4 1,2
-24021: b 4 0 4 1,2,2
-24021: meet 17 2 4 0,2
-24021: join 19 2 4 0,2,2
-NO CLASH, using fixed ground order
-24022: Facts:
-24022: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24022: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24022: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24022: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24022: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24022: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24022: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24022: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24022: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-24022: Goal:
-24022: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24022: Order:
-24022: kbo
-24022: Leaf order:
-24022: c 2 0 2 2,2,2
-24022: a 4 0 4 1,2
-24022: b 4 0 4 1,2,2
-24022: meet 17 2 4 0,2
-24022: join 19 2 4 0,2,2
-NO CLASH, using fixed ground order
-24023: Facts:
-24023: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-24023: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-24023: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-24023: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-24023: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-24023: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-24023: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-24023: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-24023: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-24023: Goal:
-24023: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-24023: Order:
-24023: lpo
-24023: Leaf order:
-24023: c 2 0 2 2,2,2
-24023: a 4 0 4 1,2
-24023: b 4 0 4 1,2,2
-24023: meet 17 2 4 0,2
-24023: join 19 2 4 0,2,2
-% SZS status Timeout for LAT168-1.p
-NO CLASH, using fixed ground order
-24053: Facts:
-24053: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24053: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24053: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24053: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24053: Goal:
-24053: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-24053: Order:
-24053: kbo
-24053: Leaf order:
-24053: a 3 0 3 1,1,1,2
-24053: b 3 0 3 2,1,1,2
-24053: truth 4 0 1 3
-24053: not 2 1 0
-24053: implies 18 2 5 0,2
-NO CLASH, using fixed ground order
-24054: Facts:
-24054: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24054: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24054: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24054: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24054: Goal:
-24054: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-24054: Order:
-24054: lpo
-24054: Leaf order:
-24054: a 3 0 3 1,1,1,2
-24054: b 3 0 3 2,1,1,2
-24054: truth 4 0 1 3
-24054: not 2 1 0
-24054: implies 18 2 5 0,2
-NO CLASH, using fixed ground order
-24052: Facts:
-24052: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24052: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24052: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24052: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24052: Goal:
-24052: Id : 1, {_}:
- implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
- [] by prove_wajsberg_mv_4
-24052: Order:
-24052: nrkbo
-24052: Leaf order:
-24052: a 3 0 3 1,1,1,2
-24052: b 3 0 3 2,1,1,2
-24052: truth 4 0 1 3
-24052: not 2 1 0
-24052: implies 18 2 5 0,2
-% SZS status Timeout for LCL109-2.p
-NO CLASH, using fixed ground order
-24075: Facts:
-24075: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24075: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24075: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24075: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24075: Goal:
-24075: Id : 1, {_}:
- implies x (implies y z) =<= implies y (implies x z)
- [] by prove_wajsberg_lemma
-24075: Order:
-24075: nrkbo
-24075: Leaf order:
-24075: x 2 0 2 1,2
-24075: y 2 0 2 1,2,2
-24075: z 2 0 2 2,2,2
-24075: truth 3 0 0
-24075: not 2 1 0
-24075: implies 17 2 4 0,2
-NO CLASH, using fixed ground order
-24076: Facts:
-24076: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24076: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24076: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24076: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24076: Goal:
-24076: Id : 1, {_}:
- implies x (implies y z) =<= implies y (implies x z)
- [] by prove_wajsberg_lemma
-24076: Order:
-24076: kbo
-24076: Leaf order:
-24076: x 2 0 2 1,2
-24076: y 2 0 2 1,2,2
-24076: z 2 0 2 2,2,2
-24076: truth 3 0 0
-24076: not 2 1 0
-24076: implies 17 2 4 0,2
-NO CLASH, using fixed ground order
-24077: Facts:
-24077: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24077: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24077: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24077: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24077: Goal:
-24077: Id : 1, {_}:
- implies x (implies y z) =<= implies y (implies x z)
- [] by prove_wajsberg_lemma
-24077: Order:
-24077: lpo
-24077: Leaf order:
-24077: x 2 0 2 1,2
-24077: y 2 0 2 1,2,2
-24077: z 2 0 2 2,2,2
-24077: truth 3 0 0
-24077: not 2 1 0
-24077: implies 17 2 4 0,2
-% SZS status Timeout for LCL138-1.p
-NO CLASH, using fixed ground order
-24160: Facts:
-24160: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24160: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24160: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24160: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24160: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-24160: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-24160: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-24160: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-24160: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-24160: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-24160: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-24160: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-24160: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-24160: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-24160: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-24160: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-24160: Goal:
-24160: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-24160: Order:
-24160: nrkbo
-24160: Leaf order:
-24160: falsehood 1 0 0
-24160: x 2 0 2 1,2
-24160: y 2 0 2 2,2,2
-24160: truth 6 0 2 1,2,2
-24160: not 12 1 0
-24160: and_star 7 2 0
-24160: xor 7 2 4 0,2
-24160: and 9 2 0
-24160: or 10 2 0
-24160: implies 14 2 0
-NO CLASH, using fixed ground order
-24161: Facts:
-24161: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24161: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24161: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24161: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24161: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-24161: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-24161: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-24161: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-24161: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-24161: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-24161: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-24161: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-24161: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-24161: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-24161: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-24161: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-24161: Goal:
-24161: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-24161: Order:
-24161: kbo
-24161: Leaf order:
-24161: falsehood 1 0 0
-24161: x 2 0 2 1,2
-24161: y 2 0 2 2,2,2
-24161: truth 6 0 2 1,2,2
-24161: not 12 1 0
-24161: and_star 7 2 0
-24161: xor 7 2 4 0,2
-24161: and 9 2 0
-24161: or 10 2 0
-24161: implies 14 2 0
-NO CLASH, using fixed ground order
-24162: Facts:
-24162: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-24162: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-24162: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-24162: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-24162: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-24162: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-24162: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-24162: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-24162: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-24162: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-24162: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-24162: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-24162: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-24162: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-24162: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-24162: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-24162: Goal:
-24162: Id : 1, {_}:
- xor x (xor truth y) =<= xor (xor x truth) y
- [] by prove_alternative_wajsberg_axiom
-24162: Order:
-24162: lpo
-24162: Leaf order:
-24162: falsehood 1 0 0
-24162: x 2 0 2 1,2
-24162: y 2 0 2 2,2,2
-24162: truth 6 0 2 1,2,2
-24162: not 12 1 0
-24162: and_star 7 2 0
-24162: xor 7 2 4 0,2
-24162: and 9 2 0
-24162: or 10 2 0
-24162: implies 14 2 0
-Statistics :
-Max weight : 32
-Found proof, 8.845379s
-% SZS status Unsatisfiable for LCL159-1.p
-% SZS output start CNFRefutation for LCL159-1.p
-Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
-Id : 10, {_}: and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) [29, 28, 27] by and_associativity ?27 ?28 ?29
-Id : 13, {_}: xor ?37 ?38 =?= xor ?38 ?37 [38, 37] by xor_commutativity ?37 ?38
-Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
-Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
-Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112
-Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
-Id : 17, {_}: not truth =>= falsehood [] by false_definition
-Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
-Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
-Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
-Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
-Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
-Id : 154, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
-Id : 162, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 154 at 1,3
-Id : 163, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 162 with 154 at 2,3
-Id : 173, {_}: or truth ?418 =<= implies falsehood ?418 [418] by Super 6 with 17 at 1,3
-Id : 183, {_}: implies (implies ?424 falsehood) falsehood =>= implies (or truth ?424) ?424 [424] by Super 4 with 173 at 1,3
-Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
-Id : 437, {_}: implies (implies ?923 truth) (implies ?924 (implies ?923 ?924)) =>= truth [924, 923] by Super 20 with 2 at 1,2,2
-Id : 438, {_}: implies (implies truth truth) (implies ?926 ?926) =>= truth [926] by Super 437 with 2 at 2,2,2
-Id : 471, {_}: implies truth (implies ?926 ?926) =>= truth [926] by Demod 438 with 2 at 1,2
-Id : 472, {_}: implies ?926 ?926 =>= truth [926] by Demod 471 with 2 at 2
-Id : 501, {_}: implies (implies (implies ?1003 ?1003) ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004, 1003] by Super 22 with 472 at 2,1,2,2
-Id : 529, {_}: implies (implies truth ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004] by Demod 501 with 472 at 1,1,2
-Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3
-Id : 495, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 472 at 3
-Id : 530, {_}: implies (implies truth ?1004) truth =>= truth [1004] by Demod 529 with 495 at 2,2
-Id : 531, {_}: implies ?1004 truth =>= truth [1004] by Demod 530 with 2 at 1,2
-Id : 567, {_}: or ?1050 truth =>= truth [1050] by Super 6 with 531 at 3
-Id : 621, {_}: or truth ?1090 =>= truth [1090] by Super 8 with 567 at 3
-Id : 637, {_}: implies (implies ?424 falsehood) falsehood =>= implies truth ?424 [424] by Demod 183 with 621 at 1,3
-Id : 638, {_}: implies (implies ?424 falsehood) falsehood =>= ?424 [424] by Demod 637 with 2 at 3
-Id : 157, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 154 at 2
-Id : 327, {_}: and_star truth ?755 =<= not (or falsehood (not ?755)) [755] by Super 157 with 17 at 1,1,3
-Id : 328, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 327 with 17 at 2,1,3
-Id : 341, {_}: or (or falsehood falsehood) ?773 =<= implies (and_star truth truth) ?773 [773] by Super 6 with 328 at 1,3
-Id : 346, {_}: or falsehood (or falsehood ?773) =<= implies (and_star truth truth) ?773 [773] by Demod 341 with 7 at 2
-Id : 750, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 638 with 346 at 1,2
-Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
-Id : 174, {_}: implies (or ?420 falsehood) (implies truth ?420) =>= truth [420] by Super 69 with 17 at 2,1,2
-Id : 177, {_}: implies (or ?420 falsehood) ?420 =>= truth [420] by Demod 174 with 2 at 2,2
-Id : 777, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 638 with 177 at 1,2
-Id : 799, {_}: falsehood =<= or falsehood falsehood [] by Demod 777 with 2 at 2
-Id : 805, {_}: and_star truth truth =>= not falsehood [] by Demod 328 with 799 at 1,3
-Id : 809, {_}: or falsehood (or falsehood ?773) =<= implies (not falsehood) ?773 [773] by Demod 346 with 805 at 1,3
-Id : 810, {_}: or falsehood (or falsehood ?773) =>= or falsehood ?773 [773] by Demod 809 with 6 at 3
-Id : 898, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 750 with 810 at 1,2
-Id : 899, {_}: implies (or falsehood falsehood) falsehood =>= not falsehood [] by Demod 898 with 805 at 3
-Id : 900, {_}: truth =<= not falsehood [] by Demod 899 with 177 at 2
-Id : 904, {_}: or falsehood ?1384 =<= implies truth ?1384 [1384] by Super 6 with 900 at 1,3
-Id : 919, {_}: or falsehood ?1384 =>= ?1384 [1384] by Demod 904 with 2 at 3
-Id : 1209, {_}: or ?1836 falsehood =>= ?1836 [1836] by Super 8 with 919 at 3
-Id : 908, {_}: and_star falsehood ?1392 =<= not (or truth (not ?1392)) [1392] by Super 157 with 900 at 1,1,3
-Id : 916, {_}: and_star falsehood ?1392 =>= not truth [1392] by Demod 908 with 621 at 1,3
-Id : 917, {_}: and_star falsehood ?1392 =>= falsehood [1392] by Demod 916 with 17 at 3
-Id : 1175, {_}: xor falsehood ?1822 =<= or falsehood (and_star (not falsehood) ?1822) [1822] by Super 163 with 917 at 1,3
-Id : 1182, {_}: xor falsehood ?1822 =<= or falsehood (and_star truth ?1822) [1822] by Demod 1175 with 900 at 1,2,3
-Id : 907, {_}: and_star ?1390 falsehood =<= not (or (not ?1390) truth) [1390] by Super 157 with 900 at 2,1,3
-Id : 913, {_}: and_star ?1390 falsehood =<= not (or truth (not ?1390)) [1390] by Demod 907 with 8 at 1,3
-Id : 914, {_}: and_star ?1390 falsehood =>= not truth [1390] by Demod 913 with 621 at 1,3
-Id : 915, {_}: and_star ?1390 falsehood =>= falsehood [1390] by Demod 914 with 17 at 3
-Id : 1144, {_}: xor ?1792 falsehood =<= or (and_star ?1792 (not falsehood)) falsehood [1792] by Super 163 with 915 at 2,3
-Id : 1161, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 (not falsehood)) [1792] by Demod 1144 with 8 at 3
-Id : 1162, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 truth) [1792] by Demod 1161 with 900 at 2,2,3
-Id : 1257, {_}: xor ?1792 falsehood =>= and_star ?1792 truth [1792] by Demod 1162 with 919 at 3
-Id : 1258, {_}: xor falsehood ?1880 =>= and_star ?1880 truth [1880] by Super 13 with 1257 at 3
-Id : 1283, {_}: and_star ?1822 truth =<= or falsehood (and_star truth ?1822) [1822] by Demod 1182 with 1258 at 2
-Id : 1284, {_}: and_star ?1822 truth =?= and_star truth ?1822 [1822] by Demod 1283 with 919 at 3
-Id : 170, {_}: and_star truth ?412 =<= not (or falsehood (not ?412)) [412] by Super 157 with 17 at 1,1,3
-Id : 1193, {_}: and_star truth ?412 =>= not (not ?412) [412] by Demod 170 with 919 at 1,3
-Id : 1285, {_}: and_star ?1822 truth =>= not (not ?1822) [1822] by Demod 1284 with 1193 at 3
-Id : 158, {_}: and_star (and ?27 ?28) ?29 =<= and ?27 (and ?28 ?29) [29, 28, 27] by Demod 10 with 154 at 2
-Id : 159, {_}: and_star (and ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 158 with 154 at 3
-Id : 160, {_}: and_star (and_star ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 159 with 154 at 1,2
-Id : 161, {_}: and_star (and_star ?27 ?28) ?29 =>= and_star ?27 (and_star ?28 ?29) [29, 28, 27] by Demod 160 with 154 at 2,3
-Id : 1290, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (and_star truth ?1910) [1910, 1909] by Super 161 with 1285 at 1,2
-Id : 1306, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (not (not ?1910)) [1910, 1909] by Demod 1290 with 1193 at 2,3
-Id : 1659, {_}: and_star ?2411 (not (not truth)) =>= not (not (not (not ?2411))) [2411] by Super 1285 with 1306 at 2
-Id : 1669, {_}: and_star ?2411 (not falsehood) =>= not (not (not (not ?2411))) [2411] by Demod 1659 with 17 at 1,2,2
-Id : 1670, {_}: and_star ?2411 truth =>= not (not (not (not ?2411))) [2411] by Demod 1669 with 900 at 2,2
-Id : 1671, {_}: not (not ?2411) =<= not (not (not (not ?2411))) [2411] by Demod 1670 with 1285 at 2
-Id : 1703, {_}: or (not (not (not ?2451))) ?2452 =<= implies (not (not ?2451)) ?2452 [2452, 2451] by Super 6 with 1671 at 1,3
-Id : 1722, {_}: or (not (not (not ?2451))) ?2452 =>= or (not ?2451) ?2452 [2452, 2451] by Demod 1703 with 6 at 3
-Id : 1999, {_}: or (not ?2759) falsehood =>= not (not (not ?2759)) [2759] by Super 1209 with 1722 at 2
-Id : 2014, {_}: or falsehood (not ?2759) =>= not (not (not ?2759)) [2759] by Demod 1999 with 8 at 2
-Id : 2015, {_}: not ?2759 =<= not (not (not ?2759)) [2759] by Demod 2014 with 919 at 2
-Id : 2063, {_}: or (not (not ?2816)) ?2817 =<= implies (not ?2816) ?2817 [2817, 2816] by Super 6 with 2015 at 1,3
-Id : 2088, {_}: or (not (not ?2816)) ?2817 =>= or ?2816 ?2817 [2817, 2816] by Demod 2063 with 6 at 3
-Id : 2169, {_}: or ?2929 falsehood =>= not (not ?2929) [2929] by Super 1209 with 2088 at 2
-Id : 2202, {_}: ?2929 =<= not (not ?2929) [2929] by Demod 2169 with 1209 at 2
-Id : 2232, {_}: and_star ?2997 (not ?2998) =<= not (or (not ?2997) ?2998) [2998, 2997] by Super 157 with 2202 at 2,1,3
-Id : 2716, {_}: or (not ?3623) ?3624 =>= not (and_star ?3623 (not ?3624)) [3624, 3623] by Super 2202 with 2232 at 1,3
-Id : 2722, {_}: or ?3642 ?3643 =>= not (and_star (not ?3642) (not ?3643)) [3643, 3642] by Super 2716 with 2202 at 1,2
-Id : 2787, {_}: xor ?34 ?35 =>= not (and_star (not (and_star ?34 (not ?35))) (not (and_star (not ?34) ?35))) [35, 34] by Demod 163 with 2722 at 3
-Id : 2819, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =<= xor ?38 ?37 [38, 37] by Demod 13 with 2787 at 2
-Id : 2820, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =?= not (and_star (not (and_star ?38 (not ?37))) (not (and_star (not ?38) ?37))) [38, 37] by Demod 2819 with 2787 at 3
-Id : 2785, {_}: not (and_star (not ?21) (not ?22)) =<= or ?22 ?21 [22, 21] by Demod 8 with 2722 at 2
-Id : 2786, {_}: not (and_star (not ?21) (not ?22)) =?= not (and_star (not ?22) (not ?21)) [22, 21] by Demod 2785 with 2722 at 3
-Id : 155, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 154 at 2
-Id : 156, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 155 with 154 at 3
-Id : 2226, {_}: and_star truth ?412 =>= ?412 [412] by Demod 1193 with 2202 at 3
-Id : 2228, {_}: and_star ?1822 truth =>= ?1822 [1822] by Demod 1285 with 2202 at 3
-Id : 2921, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) === not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) [] by Demod 2920 with 156 at 1,1,1,3
-Id : 2920, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not x) (not y)))) [] by Demod 2919 with 2786 at 2,1,3
-Id : 2919, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not y) (not x)))) [] by Demod 2918 with 2228 at 2,1,1,1,3
-Id : 2918, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not x)))) [] by Demod 2917 with 2228 at 1,2,1,2,1,3
-Id : 2917, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2916 with 900 at 2,2,1,1,1,3
-Id : 2916, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2915 with 2228 at 1,2,1,2,1,2
-Id : 2915, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2914 with 2228 at 2,1,1,1,2
-Id : 2914, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2913 with 2786 at 3
-Id : 2913, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2912 with 900 at 2,1,2,1,2,1,2
-Id : 2912, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2911 with 900 at 2,2,1,1,1,2
-Id : 2911, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2910 with 917 at 1,2,2,1,2,1,3
-Id : 2910, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not (and_star falsehood x)))))) [] by Demod 2909 with 2202 at 1,2,1,2,1,3
-Id : 2909, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2908 with 900 at 2,1,2,1,1,1,3
-Id : 2908, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2907 with 917 at 1,2,1,2,1,2,1,2
-Id : 2907, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2906 with 2202 at 1,1,2,1,2,1,2
-Id : 2906, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2905 with 917 at 1,2,2,1,1,1,2
-Id : 2905, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2904 with 156 at 2,1,2,1,3
-Id : 2904, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2903 with 917 at 1,2,1,2,1,1,1,3
-Id : 2903, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2902 with 2202 at 1,1,2,1,1,1,3
-Id : 2902, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2901 with 2786 at 2,1,2,1,2
-Id : 2901, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2900 with 156 at 1,2,2,1,1,1,2
-Id : 2900, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2899 with 2226 at 1,2,2,1,2,1,3
-Id : 2899, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) [] by Demod 2898 with 156 at 1,1,2,1,2,1,3
-Id : 2898, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2897 with 2786 at 2,1,1,1,3
-Id : 2897, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2896 with 2226 at 1,2,1,2,1,2,1,2
-Id : 2896, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2895 with 156 at 1,1,1,2,1,2,1,2
-Id : 2895, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2894 with 17 at 2,1,2,2,1,1,1,2
-Id : 2894, {_}: not (and_star (not (and_star x (and_star y (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2893 with 2202 at 1,2,1,1,1,2
-Id : 2893, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2892 with 156 at 1,2,2,1,2,1,3
-Id : 2892, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star (not x) truth)))))) [] by Demod 2891 with 17 at 2,1,1,2,1,2,1,3
-Id : 2891, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2890 with 2226 at 1,2,1,2,1,1,1,3
-Id : 2890, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2889 with 156 at 1,1,1,2,1,1,1,3
-Id : 2889, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2888 with 2786 at 2
-Id : 2888, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2887 with 2786 at 3
-Id : 2887, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2886 with 156 at 1,2,2,1,2,1,2
-Id : 2886, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2885 with 2226 at 1,1,2,1,2,1,2
-Id : 2885, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2884 with 156 at 1,2,1,2,1,1,1,2
-Id : 2884, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2883 with 17 at 2,1,1,1,2,1,1,1,2
-Id : 2883, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2882 with 156 at 1,2,1,2,1,2,1,3
-Id : 2882, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star (not x) truth))))))) [] by Demod 2881 with 17 at 2,1,1,1,2,1,2,1,3
-Id : 2881, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2880 with 2202 at 2,1,1,1,3
-Id : 2880, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2879 with 2786 at 2
-Id : 2879, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2878 with 2787 at 2,1,2,1,3
-Id : 2878, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (xor x truth)))) [] by Demod 2877 with 2787 at 1,2,1,1,1,3
-Id : 2877, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2876 with 2820 at 2,1,2,1,2
-Id : 2876, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2875 with 2202 at 2,1,1,1,2
-Id : 2875, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2874 with 2820 at 3
-Id : 2874, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2873 with 2787 at 2,1,2,1,2
-Id : 2873, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2872 with 2787 at 1,2,1,1,1,2
-Id : 2872, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2871 with 2787 at 3
-Id : 2871, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =<= xor (xor x truth) y [] by Demod 1 with 2787 at 2
-Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
-% SZS output end CNFRefutation for LCL159-1.p
-24162: solved LCL159-1.p in 4.49628 using lpo
-24162: status Unsatisfiable for LCL159-1.p
-NO CLASH, using fixed ground order
-24168: Facts:
-24168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24168: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24168: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24168: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24168: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24168: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24168: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24168: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24168: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24168: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24168: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24168: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-NO CLASH, using fixed ground order
-24169: Facts:
-24169: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24169: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24169: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24169: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24169: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24169: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24169: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24169: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24169: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24169: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24169: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24169: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24169: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24169: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24169: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24169: Goal:
-24169: Id : 1, {_}:
- associator x y (add u v)
- =>=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-24169: Order:
-24169: lpo
-24169: Leaf order:
-24169: u 2 0 2 1,3,2
-24169: v 2 0 2 2,3,2
-24169: x 3 0 3 1,2
-24169: y 3 0 3 2,2
-24169: additive_identity 8 0 0
-24169: additive_inverse 6 1 0
-24169: commutator 1 2 0
-24169: add 18 2 2 0,3,2
-24169: multiply 22 2 0
-24169: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-24167: Facts:
-24167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24167: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24167: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24167: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24167: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24167: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24167: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24167: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24167: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24167: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24167: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24167: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24167: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24167: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24167: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24167: Goal:
-24167: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-24167: Order:
-24167: nrkbo
-24167: Leaf order:
-24167: u 2 0 2 1,3,2
-24167: v 2 0 2 2,3,2
-24167: x 3 0 3 1,2
-24167: y 3 0 3 2,2
-24167: additive_identity 8 0 0
-24167: additive_inverse 6 1 0
-24167: commutator 1 2 0
-24167: add 18 2 2 0,3,2
-24167: multiply 22 2 0
-24167: associator 4 3 3 0,2
-24168: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24168: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24168: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24168: Goal:
-24168: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-24168: Order:
-24168: kbo
-24168: Leaf order:
-24168: u 2 0 2 1,3,2
-24168: v 2 0 2 2,3,2
-24168: x 3 0 3 1,2
-24168: y 3 0 3 2,2
-24168: additive_identity 8 0 0
-24168: additive_inverse 6 1 0
-24168: commutator 1 2 0
-24168: add 18 2 2 0,3,2
-24168: multiply 22 2 0
-24168: associator 4 3 3 0,2
-% SZS status Timeout for RNG019-6.p
-NO CLASH, using fixed ground order
-24186: Facts:
-24186: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24186: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24186: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24186: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24186: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24186: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24186: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24186: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24186: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24186: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24186: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24186: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24186: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24186: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24186: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24186: Goal:
-24186: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-24186: Order:
-24186: kbo
-24186: Leaf order:
-24186: u 2 0 2 1,1,2
-24186: v 2 0 2 2,1,2
-24186: x 3 0 3 2,2
-24186: y 3 0 3 3,2
-24186: additive_identity 8 0 0
-24186: additive_inverse 6 1 0
-24186: commutator 1 2 0
-24186: add 18 2 2 0,1,2
-24186: multiply 22 2 0
-24186: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-24185: Facts:
-24185: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24185: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24185: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24185: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24185: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24185: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24185: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24185: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24185: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24185: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24185: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24185: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24185: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24185: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24185: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24185: Goal:
-24185: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-24185: Order:
-24185: nrkbo
-24185: Leaf order:
-24185: u 2 0 2 1,1,2
-24185: v 2 0 2 2,1,2
-24185: x 3 0 3 2,2
-24185: y 3 0 3 3,2
-24185: additive_identity 8 0 0
-24185: additive_inverse 6 1 0
-24185: commutator 1 2 0
-24185: add 18 2 2 0,1,2
-24185: multiply 22 2 0
-24185: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-24187: Facts:
-24187: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24187: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24187: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24187: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24187: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24187: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24187: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24187: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24187: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24187: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24187: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24187: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24187: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24187: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24187: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24187: Goal:
-24187: Id : 1, {_}:
- associator (add u v) x y
- =>=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-24187: Order:
-24187: lpo
-24187: Leaf order:
-24187: u 2 0 2 1,1,2
-24187: v 2 0 2 2,1,2
-24187: x 3 0 3 2,2
-24187: y 3 0 3 3,2
-24187: additive_identity 8 0 0
-24187: additive_inverse 6 1 0
-24187: commutator 1 2 0
-24187: add 18 2 2 0,1,2
-24187: multiply 22 2 0
-24187: associator 4 3 3 0,2
-% SZS status Timeout for RNG021-6.p
-NO CLASH, using fixed ground order
-24214: Facts:
-24214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24214: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24214: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24214: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24214: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24214: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24214: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24214: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24214: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24214: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24214: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24214: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24214: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24214: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24214: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24214: Goal:
-24214: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-24214: Order:
-24214: nrkbo
-24214: Leaf order:
-24214: y 1 0 1 2,2
-24214: x 2 0 2 1,2
-24214: additive_identity 9 0 1 3
-24214: additive_inverse 6 1 0
-24214: commutator 1 2 0
-24214: add 16 2 0
-24214: multiply 22 2 0
-24214: associator 2 3 1 0,2
-NO CLASH, using fixed ground order
-24215: Facts:
-24215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24215: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24215: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24215: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24215: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24215: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24215: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24215: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24215: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24215: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24215: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24215: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24215: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24215: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24215: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24215: Goal:
-24215: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-24215: Order:
-24215: kbo
-24215: Leaf order:
-24215: y 1 0 1 2,2
-24215: x 2 0 2 1,2
-24215: additive_identity 9 0 1 3
-24215: additive_inverse 6 1 0
-24215: commutator 1 2 0
-24215: add 16 2 0
-24215: multiply 22 2 0
-24215: associator 2 3 1 0,2
-NO CLASH, using fixed ground order
-24216: Facts:
-24216: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24216: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24216: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24216: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24216: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24216: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24216: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24216: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24216: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24216: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24216: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24216: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24216: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24216: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24216: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24216: Goal:
-24216: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-24216: Order:
-24216: lpo
-24216: Leaf order:
-24216: y 1 0 1 2,2
-24216: x 2 0 2 1,2
-24216: additive_identity 9 0 1 3
-24216: additive_inverse 6 1 0
-24216: commutator 1 2 0
-24216: add 16 2 0
-24216: multiply 22 2 0
-24216: associator 2 3 1 0,2
-% SZS status Timeout for RNG025-6.p
-NO CLASH, using fixed ground order
-24240: Facts:
-24240: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-24240: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-24240: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-24240: Id : 5, {_}: add c c =>= c [] by idempotence
-24240: Goal:
-24240: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-24240: Order:
-24240: kbo
-24240: Leaf order:
-24240: a 2 0 2 1,1,1,2
-24240: c 3 0 0
-24240: b 3 0 3 1,2,1,1,2
-24240: negate 9 1 5 0,1,2
-24240: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-24239: Facts:
-24239: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-24239: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-24239: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-24239: Id : 5, {_}: add c c =>= c [] by idempotence
-24239: Goal:
-24239: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-24239: Order:
-24239: nrkbo
-24239: Leaf order:
-24239: a 2 0 2 1,1,1,2
-24239: c 3 0 0
-24239: b 3 0 3 1,2,1,1,2
-24239: negate 9 1 5 0,1,2
-24239: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-24241: Facts:
-24241: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-24241: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-24241: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-24241: Id : 5, {_}: add c c =>= c [] by idempotence
-24241: Goal:
-24241: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-24241: Order:
-24241: lpo
-24241: Leaf order:
-24241: a 2 0 2 1,1,1,2
-24241: c 3 0 0
-24241: b 3 0 3 1,2,1,1,2
-24241: negate 9 1 5 0,1,2
-24241: add 13 2 3 0,2
-% SZS status Timeout for ROB005-1.p
-NO CLASH, using fixed ground order
-24337: Facts:
-24337: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-24337: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-24337: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-24337: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-24337: Goal:
-24337: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-24337: Order:
-24337: nrkbo
-24337: Leaf order:
-24337: y 1 0 1 1,2
-24337: x 3 0 3 2,2
-24337: inverse 2 1 0
-24337: multiply 9 3 1 0,2
-NO CLASH, using fixed ground order
-24338: Facts:
-24338: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-24338: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-24338: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-24338: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-24338: Goal:
-24338: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-24338: Order:
-24338: kbo
-24338: Leaf order:
-24338: y 1 0 1 1,2
-24338: x 3 0 3 2,2
-24338: inverse 2 1 0
-24338: multiply 9 3 1 0,2
-NO CLASH, using fixed ground order
-24339: Facts:
-24339: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-24339: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
-24339: Id : 4, {_}:
- multiply (inverse ?11) ?11 ?12 =>= ?12
- [12, 11] by left_inverse ?11 ?12
-24339: Id : 5, {_}:
- multiply ?14 ?15 (inverse ?15) =>= ?14
- [15, 14] by right_inverse ?14 ?15
-24339: Goal:
-24339: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
-24339: Order:
-24339: lpo
-24339: Leaf order:
-24339: y 1 0 1 1,2
-24339: x 3 0 3 2,2
-24339: inverse 2 1 0
-24339: multiply 9 3 1 0,2
-% SZS status Timeout for BOO019-1.p
-CLASH, statistics insufficient
-25312: Facts:
-25312: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25312: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25312: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-25312: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-25312: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-25312: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-25312: Goal:
-25312: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25312: Order:
-25312: nrkbo
-25312: Leaf order:
-25312: a 2 0 2 1,1,2
-25312: inverse 3 1 2 0,2
-25312: multiply 11 2 0
-25312: add 11 2 0
-CLASH, statistics insufficient
-25313: Facts:
-25313: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25313: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25313: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-25313: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-25313: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-25313: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-25313: Goal:
-25313: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25313: Order:
-25313: kbo
-25313: Leaf order:
-25313: a 2 0 2 1,1,2
-25313: inverse 3 1 2 0,2
-25313: multiply 11 2 0
-25313: add 11 2 0
-CLASH, statistics insufficient
-25314: Facts:
-25314: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25314: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25314: Id : 4, {_}:
- multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
- [11, 10] by b1 ?10 ?11
-25314: Id : 5, {_}:
- multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
- [14, 13] by majority1 ?13 ?14
-25314: Id : 6, {_}:
- multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
- [17, 16] by majority2 ?16 ?17
-25314: Id : 7, {_}:
- multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
- [20, 19] by majority3 ?19 ?20
-25314: Goal:
-25314: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25314: Order:
-25314: lpo
-25314: Leaf order:
-25314: a 2 0 2 1,1,2
-25314: inverse 3 1 2 0,2
-25314: multiply 11 2 0
-25314: add 11 2 0
-% SZS status Timeout for BOO030-1.p
-CLASH, statistics insufficient
-25341: Facts:
-25341: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25341: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25341: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-25341: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-25341: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-25341: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-25341: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-25341: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-25341: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-25341: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-25341: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-25341: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-25341: Goal:
-25341: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25341: Order:
-25341: nrkbo
-25341: Leaf order:
-25341: a 2 0 2 1,1,2
-25341: inverse 4 1 2 0,2
-25341: multiply 21 2 0
-25341: add 21 2 0
-CLASH, statistics insufficient
-25342: Facts:
-25342: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25342: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25342: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-25342: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-25342: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-25342: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-25342: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-25342: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-25342: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-25342: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-25342: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-25342: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-25342: Goal:
-25342: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25342: Order:
-25342: kbo
-25342: Leaf order:
-25342: a 2 0 2 1,1,2
-25342: inverse 4 1 2 0,2
-25342: multiply 21 2 0
-25342: add 21 2 0
-CLASH, statistics insufficient
-25343: Facts:
-25343: Id : 2, {_}:
- add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
- [4, 3, 2] by l1 ?2 ?3 ?4
-25343: Id : 3, {_}:
- add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
- [8, 7, 6] by l3 ?6 ?7 ?8
-25343: Id : 4, {_}:
- multiply (add ?10 (inverse ?10)) ?11 =>= ?11
- [11, 10] by property3 ?10 ?11
-25343: Id : 5, {_}:
- multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
- [15, 14, 13] by l2 ?13 ?14 ?15
-25343: Id : 6, {_}:
- multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
- [19, 18, 17] by l4 ?17 ?18 ?19
-25343: Id : 7, {_}:
- add (multiply ?21 (inverse ?21)) ?22 =>= ?22
- [22, 21] by property3_dual ?21 ?22
-25343: Id : 8, {_}:
- add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
- [25, 24] by majority1 ?24 ?25
-25343: Id : 9, {_}:
- add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
- [28, 27] by majority2 ?27 ?28
-25343: Id : 10, {_}:
- add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
- [31, 30] by majority3 ?30 ?31
-25343: Id : 11, {_}:
- multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
- [34, 33] by majority1_dual ?33 ?34
-25343: Id : 12, {_}:
- multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
- [37, 36] by majority2_dual ?36 ?37
-25343: Id : 13, {_}:
- multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
- [40, 39] by majority3_dual ?39 ?40
-25343: Goal:
-25343: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25343: Order:
-25343: lpo
-25343: Leaf order:
-25343: a 2 0 2 1,1,2
-25343: inverse 4 1 2 0,2
-25343: multiply 21 2 0
-25343: add 21 2 0
-% SZS status Timeout for BOO032-1.p
-NO CLASH, using fixed ground order
-25370: Facts:
-25370: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-25370: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-25370: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-25370: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-25370: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-25370: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-25370: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-25370: Goal:
-25370: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25370: Order:
-25370: nrkbo
-25370: Leaf order:
-25370: a 2 0 2 1,1,2
-25370: inverse 3 1 2 0,2
-25370: add 15 2 0 multiply
-25370: multiply 16 2 0 add
-NO CLASH, using fixed ground order
-25371: Facts:
-25371: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-25371: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-25371: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-25371: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-25371: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-25371: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-25371: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-25371: Goal:
-25371: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25371: Order:
-25371: kbo
-25371: Leaf order:
-25371: a 2 0 2 1,1,2
-25371: inverse 3 1 2 0,2
-25371: add 15 2 0 multiply
-25371: multiply 16 2 0 add
-NO CLASH, using fixed ground order
-25372: Facts:
-25372: Id : 2, {_}:
- add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
- =<=
- multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
- [4, 3, 2] by distributivity ?2 ?3 ?4
-25372: Id : 3, {_}:
- add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
- [8, 7, 6] by l1 ?6 ?7 ?8
-25372: Id : 4, {_}:
- add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
- [12, 11, 10] by l3 ?10 ?11 ?12
-25372: Id : 5, {_}:
- multiply (add ?14 (inverse ?14)) ?15 =>= ?15
- [15, 14] by property3 ?14 ?15
-25372: Id : 6, {_}:
- multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
- [18, 17] by majority1 ?17 ?18
-25372: Id : 7, {_}:
- multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
- [21, 20] by majority2 ?20 ?21
-25372: Id : 8, {_}:
- multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
- [24, 23] by majority3 ?23 ?24
-25372: Goal:
-25372: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
-25372: Order:
-25372: lpo
-25372: Leaf order:
-25372: a 2 0 2 1,1,2
-25372: inverse 3 1 2 0,2
-25372: add 15 2 0 multiply
-25372: multiply 16 2 0 add
-% SZS status Timeout for BOO033-1.p
-NO CLASH, using fixed ground order
-25403: Facts:
-25403: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-25403: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-25403: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-25403: Goal:
-25403: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-25403: Order:
-25403: nrkbo
-25403: Leaf order:
-25403: strong_fixed_point 3 0 2 1,2
-25403: fixed_pt 3 0 3 2,2
-25403: w 4 0 0
-25403: b 7 0 0
-25403: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-25404: Facts:
-25404: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-25404: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-25404: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-25404: Goal:
-25404: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-25404: Order:
-25404: kbo
-25404: Leaf order:
-25404: strong_fixed_point 3 0 2 1,2
-25404: fixed_pt 3 0 3 2,2
-25404: w 4 0 0
-25404: b 7 0 0
-25404: apply 20 2 3 0,2
-NO CLASH, using fixed ground order
-25405: Facts:
-25405: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-25405: Id : 3, {_}:
- apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
- [7, 6] by w_definition ?6 ?7
-25405: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply (apply b (apply w w))
- (apply (apply b (apply b w)) (apply (apply b b) b))
- [] by strong_fixed_point
-25405: Goal:
-25405: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-25405: Order:
-25405: lpo
-25405: Leaf order:
-25405: strong_fixed_point 3 0 2 1,2
-25405: fixed_pt 3 0 3 2,2
-25405: w 4 0 0
-25405: b 7 0 0
-25405: apply 20 2 3 0,2
-% SZS status Timeout for COL003-20.p
-NO CLASH, using fixed ground order
-25421: Facts:
-25421: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-25421: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-25421: Goal:
-25421: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-25421: Order:
-25421: nrkbo
-25421: Leaf order:
-25421: x 3 0 3 2,1,2
-25421: y 3 0 3 2,2
-25421: s 7 0 6 1,1,1,1,2
-25421: k 8 0 7 1,2,1,1,1,2
-25421: apply 25 2 17 0,2
-NO CLASH, using fixed ground order
-25422: Facts:
-25422: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-25422: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-25422: Goal:
-25422: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-25422: Order:
-25422: kbo
-25422: Leaf order:
-25422: x 3 0 3 2,1,2
-25422: y 3 0 3 2,2
-25422: s 7 0 6 1,1,1,1,2
-25422: k 8 0 7 1,2,1,1,1,2
-25422: apply 25 2 17 0,2
-NO CLASH, using fixed ground order
-25423: Facts:
-25423: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-25423: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-25423: Goal:
-25423: Id : 1, {_}:
- apply
- (apply
- (apply (apply s (apply k (apply s (apply (apply s k) k))))
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
- x) y
- =>=
- apply y (apply (apply x x) y)
- [] by prove_u_combinator
-25423: Order:
-25423: lpo
-25423: Leaf order:
-25423: x 3 0 3 2,1,2
-25423: y 3 0 3 2,2
-25423: s 7 0 6 1,1,1,1,2
-25423: k 8 0 7 1,2,1,1,1,2
-25423: apply 25 2 17 0,2
-Statistics :
-Max weight : 29
-Found proof, 0.116079s
-% SZS status Unsatisfiable for COL004-3.p
-% SZS output start CNFRefutation for COL004-3.p
-Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4
-Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2
-Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2
-Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2
-Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2
-Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2
-Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2
-Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2
-Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2
-Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2
-Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2
-Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator
-% SZS output end CNFRefutation for COL004-3.p
-25423: solved COL004-3.p in 0.020001 using lpo
-25423: status Unsatisfiable for COL004-3.p
-CLASH, statistics insufficient
-25428: Facts:
-25428: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25428: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-25428: Goal:
-25428: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-25428: Order:
-25428: nrkbo
-25428: Leaf order:
-25428: s 1 0 0
-25428: w 1 0 0
-25428: combinator 1 0 1 1,3
-25428: apply 11 2 1 0,3
-CLASH, statistics insufficient
-25429: Facts:
-25429: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25429: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-25429: Goal:
-25429: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-25429: Order:
-25429: kbo
-25429: Leaf order:
-25429: s 1 0 0
-25429: w 1 0 0
-25429: combinator 1 0 1 1,3
-25429: apply 11 2 1 0,3
-CLASH, statistics insufficient
-25430: Facts:
-25430: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25430: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-25430: Goal:
-25430: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
-25430: Order:
-25430: lpo
-25430: Leaf order:
-25430: s 1 0 0
-25430: w 1 0 0
-25430: combinator 1 0 1 1,3
-25430: apply 11 2 1 0,3
-% SZS status Timeout for COL005-1.p
-CLASH, statistics insufficient
-25470: Facts:
-25470: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25470: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-25470: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-25470: Goal:
-CLASH, statistics insufficient
-25471: Facts:
-25471: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25471: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-25471: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-25471: Goal:
-25471: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25471: Order:
-25471: kbo
-25471: Leaf order:
-25471: b 1 0 0
-25471: m 1 0 0
-25471: v 1 0 0
-25471: f 3 1 3 0,2,2
-25471: apply 15 2 3 0,2
-25470: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25470: Order:
-25470: nrkbo
-25470: Leaf order:
-25470: b 1 0 0
-25470: m 1 0 0
-25470: v 1 0 0
-25470: f 3 1 3 0,2,2
-25470: apply 15 2 3 0,2
-CLASH, statistics insufficient
-25472: Facts:
-25472: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25472: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-25472: Id : 4, {_}:
- apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10
- [11, 10, 9] by v_definition ?9 ?10 ?11
-25472: Goal:
-25472: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25472: Order:
-25472: lpo
-25472: Leaf order:
-25472: b 1 0 0
-25472: m 1 0 0
-25472: v 1 0 0
-25472: f 3 1 3 0,2,2
-25472: apply 15 2 3 0,2
-Goal subsumed
-Statistics :
-Max weight : 78
-Found proof, 6.291189s
-% SZS status Unsatisfiable for COL038-1.p
-% SZS output start CNFRefutation for COL038-1.p
-Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11
-Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
-Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49
-Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2
-Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2
-Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3
-Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3
-Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3
-Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3
-Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2
-Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3
-Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2
-Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3
-Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2
-Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2
-Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
-Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2
-Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3
-Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2
-Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3
-Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2
-Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3
-Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2
-Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3
-Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2
-Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3
-Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3
-Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2
-Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2
-Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3
-Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3
-Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
-Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
-Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
-% SZS output end CNFRefutation for COL038-1.p
-25471: solved COL038-1.p in 3.192199 using kbo
-25471: status Unsatisfiable for COL038-1.p
-CLASH, statistics insufficient
-25477: Facts:
-25477: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25477: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25477: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-25477: Goal:
-25477: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25477: Order:
-25477: nrkbo
-25477: Leaf order:
-25477: s 1 0 0
-25477: b 1 0 0
-25477: m 1 0 0
-25477: f 3 1 3 0,2,2
-25477: apply 16 2 3 0,2
-CLASH, statistics insufficient
-25478: Facts:
-25478: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25478: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25478: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-25478: Goal:
-25478: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25478: Order:
-25478: kbo
-25478: Leaf order:
-25478: s 1 0 0
-25478: b 1 0 0
-25478: m 1 0 0
-25478: f 3 1 3 0,2,2
-25478: apply 16 2 3 0,2
-CLASH, statistics insufficient
-25479: Facts:
-25479: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25479: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25479: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
-25479: Goal:
-25479: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25479: Order:
-25479: lpo
-25479: Leaf order:
-25479: s 1 0 0
-25479: b 1 0 0
-25479: m 1 0 0
-25479: f 3 1 3 0,2,2
-25479: apply 16 2 3 0,2
-% SZS status Timeout for COL046-1.p
-CLASH, statistics insufficient
-25500: Facts:
-25500: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-25500: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-25500: Goal:
-25500: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-25500: Order:
-25500: nrkbo
-25500: Leaf order:
-25500: l 1 0 0
-25500: q 1 0 0
-25500: f 3 1 3 0,2,2
-25500: apply 12 2 3 0,2
-CLASH, statistics insufficient
-25501: Facts:
-25501: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-25501: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-25501: Goal:
-25501: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-25501: Order:
-25501: kbo
-25501: Leaf order:
-25501: l 1 0 0
-25501: q 1 0 0
-25501: f 3 1 3 0,2,2
-25501: apply 12 2 3 0,2
-CLASH, statistics insufficient
-25502: Facts:
-25502: Id : 2, {_}:
- apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
- [4, 3] by l_definition ?3 ?4
-25502: Id : 3, {_}:
- apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
- [8, 7, 6] by q_definition ?6 ?7 ?8
-25502: Goal:
-25502: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_model ?1
-25502: Order:
-25502: lpo
-25502: Leaf order:
-25502: l 1 0 0
-25502: q 1 0 0
-25502: f 3 1 3 0,2,2
-25502: apply 12 2 3 0,2
-% SZS status Timeout for COL047-1.p
-CLASH, statistics insufficient
-25526: Facts:
-25526: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25526: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25526: Goal:
-25526: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-25526: Order:
-25526: nrkbo
-25526: Leaf order:
-25526: b 1 0 0
-25526: t 1 0 0
-25526: f 2 1 2 0,2,1,1,2
-25526: g 2 1 2 0,2,1,2
-25526: h 2 1 2 0,2,2
-25526: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25527: Facts:
-25527: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25527: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25527: Goal:
-25527: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-25527: Order:
-25527: kbo
-25527: Leaf order:
-25527: b 1 0 0
-25527: t 1 0 0
-25527: f 2 1 2 0,2,1,1,2
-25527: g 2 1 2 0,2,1,2
-25527: h 2 1 2 0,2,2
-25527: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25528: Facts:
-25528: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25528: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25528: Goal:
-25528: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (g ?1) (apply (f ?1) (h ?1))
- [1] by prove_q_combinator ?1
-25528: Order:
-25528: lpo
-25528: Leaf order:
-25528: b 1 0 0
-25528: t 1 0 0
-25528: f 2 1 2 0,2,1,1,2
-25528: g 2 1 2 0,2,1,2
-25528: h 2 1 2 0,2,2
-25528: apply 13 2 5 0,2
-Goal subsumed
-Statistics :
-Max weight : 76
-Found proof, 0.356753s
-% SZS status Unsatisfiable for COL060-1.p
-% SZS output start CNFRefutation for COL060-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2
-Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
-% SZS output end CNFRefutation for COL060-1.p
-25526: solved COL060-1.p in 0.368022 using nrkbo
-25526: status Unsatisfiable for COL060-1.p
-CLASH, statistics insufficient
-25533: Facts:
-25533: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25533: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25533: Goal:
-25533: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-25533: Order:
-25533: nrkbo
-25533: Leaf order:
-25533: b 1 0 0
-25533: t 1 0 0
-25533: f 2 1 2 0,2,1,1,2
-25533: g 2 1 2 0,2,1,2
-25533: h 2 1 2 0,2,2
-25533: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25534: Facts:
-25534: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25534: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25534: Goal:
-25534: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-25534: Order:
-25534: kbo
-25534: Leaf order:
-25534: b 1 0 0
-25534: t 1 0 0
-25534: f 2 1 2 0,2,1,1,2
-25534: g 2 1 2 0,2,1,2
-25534: h 2 1 2 0,2,2
-25534: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25535: Facts:
-25535: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25535: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25535: Goal:
-25535: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (f ?1) (apply (h ?1) (g ?1))
- [1] by prove_q1_combinator ?1
-25535: Order:
-25535: lpo
-25535: Leaf order:
-25535: b 1 0 0
-25535: t 1 0 0
-25535: f 2 1 2 0,2,1,1,2
-25535: g 2 1 2 0,2,1,2
-25535: h 2 1 2 0,2,2
-25535: apply 13 2 5 0,2
-Goal subsumed
-Statistics :
-Max weight : 76
-Found proof, 0.641348s
-% SZS status Unsatisfiable for COL061-1.p
-% SZS output start CNFRefutation for COL061-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2
-Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
-% SZS output end CNFRefutation for COL061-1.p
-25533: solved COL061-1.p in 0.344021 using nrkbo
-25533: status Unsatisfiable for COL061-1.p
-CLASH, statistics insufficient
-25541: Facts:
-25541: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25541: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25541: Goal:
-25541: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-25541: Order:
-25541: kbo
-25541: Leaf order:
-25541: b 1 0 0
-25541: t 1 0 0
-25541: f 2 1 2 0,2,1,1,2
-25541: g 2 1 2 0,2,1,2
-25541: h 2 1 2 0,2,2
-25541: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25540: Facts:
-25540: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25540: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25540: Goal:
-25540: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-25540: Order:
-25540: nrkbo
-25540: Leaf order:
-25540: b 1 0 0
-25540: t 1 0 0
-25540: f 2 1 2 0,2,1,1,2
-25540: g 2 1 2 0,2,1,2
-25540: h 2 1 2 0,2,2
-25540: apply 13 2 5 0,2
-CLASH, statistics insufficient
-25542: Facts:
-25542: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25542: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-25542: Goal:
-25542: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (h ?1)) (g ?1)
- [1] by prove_c_combinator ?1
-25542: Order:
-25542: lpo
-25542: Leaf order:
-25542: b 1 0 0
-25542: t 1 0 0
-25542: f 2 1 2 0,2,1,1,2
-25542: g 2 1 2 0,2,1,2
-25542: h 2 1 2 0,2,2
-25542: apply 13 2 5 0,2
-Goal subsumed
-Statistics :
-Max weight : 100
-Found proof, 1.793493s
-% SZS status Unsatisfiable for COL062-1.p
-% SZS output start CNFRefutation for COL062-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2
-Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2
-Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2
-Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1
-% SZS output end CNFRefutation for COL062-1.p
-25540: solved COL062-1.p in 1.808112 using nrkbo
-25540: status Unsatisfiable for COL062-1.p
-CLASH, statistics insufficient
-25547: Facts:
-25547: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-25547: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-25547: Goal:
-25547: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25547: Order:
-25547: nrkbo
-25547: Leaf order:
-25547: n 1 0 0
-25547: q 1 0 0
-25547: f 3 1 3 0,2,2
-25547: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25548: Facts:
-25548: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-25548: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-25548: Goal:
-25548: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25548: Order:
-25548: kbo
-25548: Leaf order:
-25548: n 1 0 0
-25548: q 1 0 0
-25548: f 3 1 3 0,2,2
-25548: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25549: Facts:
-25549: Id : 2, {_}:
- apply (apply (apply n ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?5) ?4) ?5
- [5, 4, 3] by n_definition ?3 ?4 ?5
-25549: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-25549: Goal:
-25549: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25549: Order:
-25549: lpo
-25549: Leaf order:
-25549: n 1 0 0
-25549: q 1 0 0
-25549: f 3 1 3 0,2,2
-25549: apply 14 2 3 0,2
-% SZS status Timeout for COL071-1.p
-CLASH, statistics insufficient
-25572: Facts:
-25572: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-25572: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25572: Goal:
-25572: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-25572: Order:
-25572: nrkbo
-25572: Leaf order:
-25572: n1 1 0 0
-25572: b 1 0 0
-25572: f 3 1 3 0,2,2
-25572: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25573: Facts:
-25573: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-25573: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25573: Goal:
-25573: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-25573: Order:
-25573: kbo
-25573: Leaf order:
-25573: n1 1 0 0
-25573: b 1 0 0
-25573: f 3 1 3 0,2,2
-25573: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25574: Facts:
-25574: Id : 2, {_}:
- apply (apply (apply n1 ?3) ?4) ?5
- =?=
- apply (apply (apply ?3 ?4) ?4) ?5
- [5, 4, 3] by n1_definition ?3 ?4 ?5
-25574: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25574: Goal:
-25574: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-25574: Order:
-25574: lpo
-25574: Leaf order:
-25574: n1 1 0 0
-25574: b 1 0 0
-25574: f 3 1 3 0,2,2
-25574: apply 14 2 3 0,2
-% SZS status Timeout for COL073-1.p
-NO CLASH, using fixed ground order
-25603: Facts:
-25603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25603: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25603: Id : 5, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-25603: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =?=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-25603: Goal:
-25603: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-25603: Order:
-25603: nrkbo
-25603: Leaf order:
-25603: identity 2 0 0
-25603: a 2 0 2 1,2
-25603: b 2 0 2 1,2,2
-25603: c 2 0 2 2,2,2
-25603: inverse 3 1 0
-25603: commutator 7 2 2 0,2,2
-25603: multiply 11 2 2 0,2
-NO CLASH, using fixed ground order
-25604: Facts:
-25604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25604: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25604: Id : 5, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-25604: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =>=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-25604: Goal:
-25604: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-25604: Order:
-25604: kbo
-25604: Leaf order:
-25604: identity 2 0 0
-25604: a 2 0 2 1,2
-25604: b 2 0 2 1,2,2
-25604: c 2 0 2 2,2,2
-25604: inverse 3 1 0
-25604: commutator 7 2 2 0,2,2
-25604: multiply 11 2 2 0,2
-NO CLASH, using fixed ground order
-25605: Facts:
-25605: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25605: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25605: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25605: Id : 5, {_}:
- commutator ?10 ?11
- =<=
- multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
- [11, 10] by name ?10 ?11
-25605: Id : 6, {_}:
- commutator (commutator ?13 ?14) ?15
- =>=
- commutator ?13 (commutator ?14 ?15)
- [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
-25605: Goal:
-25605: Id : 1, {_}:
- multiply a (commutator b c) =<= multiply (commutator b c) a
- [] by prove_center
-25605: Order:
-25605: lpo
-25605: Leaf order:
-25605: identity 2 0 0
-25605: a 2 0 2 1,2
-25605: b 2 0 2 1,2,2
-25605: c 2 0 2 2,2,2
-25605: inverse 3 1 0
-25605: commutator 7 2 2 0,2,2
-25605: multiply 11 2 2 0,2
-% SZS status Timeout for GRP024-5.p
-CLASH, statistics insufficient
-25668: Facts:
-25668: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25668: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25668: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25668: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-25668: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-25668: Id : 7, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-25668: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-25668: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-25668: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-25668: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-25668: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =?=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-25668: Id : 13, {_}:
- union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-25668: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-25668: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-25668: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-25668: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-25668: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-25668: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-25668: Id : 20, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
-25668: Id : 21, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-25668: Goal:
-25668: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-25668: Order:
-25668: nrkbo
-25668: Leaf order:
-25668: a 3 0 3 1,1,2
-25668: identity 6 0 0
-25668: positive_part 2 1 1 0,1,2
-25668: negative_part 2 1 1 0,2,2
-25668: inverse 7 1 0
-25668: intersection 14 2 0
-25668: union 14 2 0
-25668: multiply 21 2 1 0,2
-CLASH, statistics insufficient
-25669: Facts:
-25669: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25669: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25669: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25669: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-25669: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-25669: Id : 7, {_}:
- inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-25669: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-CLASH, statistics insufficient
-25670: Facts:
-25670: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25670: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25670: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25670: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-25670: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-25670: Id : 7, {_}:
- inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13)
- [14, 13] by inverse_product_lemma ?13 ?14
-25670: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
-25669: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-25669: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-25669: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-25669: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =<=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-25669: Id : 13, {_}:
- union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-25669: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-25669: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-25669: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =<=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-25669: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =<=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-25669: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =<=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-25669: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =<=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-25669: Id : 20, {_}:
- positive_part ?56 =<= union ?56 identity
- [56] by positive_part ?56
-25669: Id : 21, {_}:
- negative_part ?58 =<= intersection ?58 identity
- [58] by negative_part ?58
-25669: Goal:
-25669: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-25669: Order:
-25669: kbo
-25669: Leaf order:
-25669: a 3 0 3 1,1,2
-25669: identity 6 0 0
-25669: positive_part 2 1 1 0,1,2
-25669: negative_part 2 1 1 0,2,2
-25669: inverse 7 1 0
-25669: intersection 14 2 0
-25669: union 14 2 0
-25669: multiply 21 2 1 0,2
-25670: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
-25670: Id : 10, {_}:
- intersection ?20 ?21 =?= intersection ?21 ?20
- [21, 20] by intersection_commutative ?20 ?21
-25670: Id : 11, {_}:
- union ?23 ?24 =?= union ?24 ?23
- [24, 23] by union_commutative ?23 ?24
-25670: Id : 12, {_}:
- intersection ?26 (intersection ?27 ?28)
- =<=
- intersection (intersection ?26 ?27) ?28
- [28, 27, 26] by intersection_associative ?26 ?27 ?28
-25670: Id : 13, {_}:
- union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
- [32, 31, 30] by union_associative ?30 ?31 ?32
-25670: Id : 14, {_}:
- union (intersection ?34 ?35) ?35 =>= ?35
- [35, 34] by union_intersection_absorbtion ?34 ?35
-25670: Id : 15, {_}:
- intersection (union ?37 ?38) ?38 =>= ?38
- [38, 37] by intersection_union_absorbtion ?37 ?38
-25670: Id : 16, {_}:
- multiply ?40 (union ?41 ?42)
- =>=
- union (multiply ?40 ?41) (multiply ?40 ?42)
- [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-25670: Id : 17, {_}:
- multiply ?44 (intersection ?45 ?46)
- =>=
- intersection (multiply ?44 ?45) (multiply ?44 ?46)
- [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-25670: Id : 18, {_}:
- multiply (union ?48 ?49) ?50
- =>=
- union (multiply ?48 ?50) (multiply ?49 ?50)
- [50, 49, 48] by multiply_union2 ?48 ?49 ?50
-25670: Id : 19, {_}:
- multiply (intersection ?52 ?53) ?54
- =>=
- intersection (multiply ?52 ?54) (multiply ?53 ?54)
- [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
-25670: Id : 20, {_}:
- positive_part ?56 =>= union ?56 identity
- [56] by positive_part ?56
-25670: Id : 21, {_}:
- negative_part ?58 =>= intersection ?58 identity
- [58] by negative_part ?58
-25670: Goal:
-25670: Id : 1, {_}:
- multiply (positive_part a) (negative_part a) =>= a
- [] by prove_product
-25670: Order:
-25670: lpo
-25670: Leaf order:
-25670: a 3 0 3 1,1,2
-25670: identity 6 0 0
-25670: positive_part 2 1 1 0,1,2
-25670: negative_part 2 1 1 0,2,2
-25670: inverse 7 1 0
-25670: intersection 14 2 0
-25670: union 14 2 0
-25670: multiply 21 2 1 0,2
-Statistics :
-Max weight : 16
-Found proof, 7.917801s
-% SZS status Unsatisfiable for GRP114-1.p
-% SZS output start CNFRefutation for GRP114-1.p
-Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
-Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
-Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
-Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
-Id : 13, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
-Id : 241, {_}: multiply (union ?684 ?685) ?686 =<= union (multiply ?684 ?686) (multiply ?685 ?686) [686, 685, 684] by multiply_union2 ?684 ?685 ?686
-Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
-Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
-Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
-Id : 205, {_}: multiply ?602 (intersection ?603 ?604) =<= intersection (multiply ?602 ?603) (multiply ?602 ?604) [604, 603, 602] by multiply_intersection1 ?602 ?603 ?604
-Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
-Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
-Id : 276, {_}: multiply (intersection ?769 ?770) ?771 =<= intersection (multiply ?769 ?771) (multiply ?770 ?771) [771, 770, 769] by multiply_intersection2 ?769 ?770 ?771
-Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
-Id : 58, {_}: inverse (multiply ?149 ?150) =<= multiply (inverse ?150) (inverse ?149) [150, 149] by inverse_product_lemma ?149 ?150
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =?= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69
-Id : 28, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= multiply ?74 identity [75, 74] by Super 26 with 3 at 2,3
-Id : 59, {_}: inverse (multiply identity ?152) =<= multiply (inverse ?152) identity [152] by Super 58 with 5 at 2,3
-Id : 459, {_}: inverse ?1057 =<= multiply (inverse ?1057) identity [1057] by Demod 59 with 2 at 1,2
-Id : 461, {_}: inverse (inverse ?1060) =<= multiply ?1060 identity [1060] by Super 459 with 6 at 1,3
-Id : 475, {_}: ?1060 =<= multiply ?1060 identity [1060] by Demod 461 with 6 at 2
-Id : 570, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= ?74 [75, 74] by Demod 28 with 475 at 3
-Id : 62, {_}: inverse (multiply ?159 (inverse ?160)) =>= multiply ?160 (inverse ?159) [160, 159] by Super 58 with 6 at 1,3
-Id : 283, {_}: multiply (intersection (inverse ?796) ?797) ?796 =>= intersection identity (multiply ?797 ?796) [797, 796] by Super 276 with 3 at 1,3
-Id : 329, {_}: intersection identity ?869 =>= negative_part ?869 [869] by Super 10 with 21 at 3
-Id : 16231, {_}: multiply (intersection (inverse ?20320) ?20321) ?20320 =>= negative_part (multiply ?20321 ?20320) [20321, 20320] by Demod 283 with 329 at 3
-Id : 16259, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part (multiply identity ?20413) [20413] by Super 16231 with 21 at 1,2
-Id : 16311, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part ?20413 [20413] by Demod 16259 with 2 at 1,3
-Id : 16342, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part (inverse (inverse ?20447)))) [20447] by Super 62 with 16311 at 1,2
-Id : 16414, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part ?20447)) [20447] by Demod 16342 with 6 at 1,1,2,3
-Id : 16644, {_}: multiply (inverse (negative_part (inverse ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Super 570 with 16414 at 1,2
-Id : 60, {_}: inverse (multiply (inverse ?154) ?155) =>= multiply (inverse ?155) ?154 [155, 154] by Super 58 with 6 at 2,3
-Id : 207, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection (multiply (inverse ?609) ?610) identity [610, 609] by Super 205 with 3 at 2,3
-Id : 228, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection identity (multiply (inverse ?609) ?610) [610, 609] by Demod 207 with 10 at 3
-Id : 10379, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= negative_part (multiply (inverse ?609) ?610) [610, 609] by Demod 228 with 329 at 3
-Id : 10396, {_}: inverse (negative_part (multiply (inverse ?14999) ?15000)) =<= multiply (inverse (intersection ?15000 ?14999)) ?14999 [15000, 14999] by Super 60 with 10379 at 1,2
-Id : 309, {_}: union identity ?834 =>= positive_part ?834 [834] by Super 11 with 20 at 3
-Id : 360, {_}: intersection (positive_part ?914) ?914 =>= ?914 [914] by Super 15 with 309 at 1,2
-Id : 686, {_}: intersection ?1353 (positive_part ?1353) =>= ?1353 [1353] by Super 10 with 360 at 3
-Id : 248, {_}: multiply (union (inverse ?711) ?712) ?711 =>= union identity (multiply ?712 ?711) [712, 711] by Super 241 with 3 at 1,3
-Id : 10542, {_}: multiply (union (inverse ?15313) ?15314) ?15313 =>= positive_part (multiply ?15314 ?15313) [15314, 15313] by Demod 248 with 309 at 3
-Id : 359, {_}: union identity (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Super 13 with 309 at 1,3
-Id : 367, {_}: positive_part (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Demod 359 with 309 at 2
-Id : 312, {_}: union ?841 (union ?842 identity) =>= positive_part (union ?841 ?842) [842, 841] by Super 13 with 20 at 3
-Id : 324, {_}: union ?841 (positive_part ?842) =<= positive_part (union ?841 ?842) [842, 841] by Demod 312 with 20 at 2,2
-Id : 709, {_}: union ?911 (positive_part ?912) =?= union (positive_part ?911) ?912 [912, 911] by Demod 367 with 324 at 2
-Id : 487, {_}: multiply ?1085 (union ?1086 identity) =?= union (multiply ?1085 ?1086) ?1085 [1086, 1085] by Super 16 with 475 at 2,3
-Id : 2720, {_}: multiply ?5029 (positive_part ?5030) =<= union (multiply ?5029 ?5030) ?5029 [5030, 5029] by Demod 487 with 20 at 2,2
-Id : 2722, {_}: multiply (inverse ?5034) (positive_part ?5034) =>= union identity (inverse ?5034) [5034] by Super 2720 with 3 at 1,3
-Id : 2784, {_}: multiply (inverse ?5160) (positive_part ?5160) =>= positive_part (inverse ?5160) [5160] by Demod 2722 with 309 at 3
-Id : 307, {_}: positive_part (intersection ?831 identity) =>= identity [831] by Super 14 with 20 at 2
-Id : 514, {_}: positive_part (negative_part ?831) =>= identity [831] by Demod 307 with 21 at 1,2
-Id : 2786, {_}: multiply (inverse (negative_part ?5163)) identity =>= positive_part (inverse (negative_part ?5163)) [5163] by Super 2784 with 514 at 2,2
-Id : 2807, {_}: inverse (negative_part ?5163) =<= positive_part (inverse (negative_part ?5163)) [5163] by Demod 2786 with 475 at 2
-Id : 2823, {_}: union (inverse (negative_part ?5198)) (positive_part ?5199) =>= union (inverse (negative_part ?5198)) ?5199 [5199, 5198] by Super 709 with 2807 at 1,3
-Id : 10564, {_}: multiply (union (inverse (negative_part ?15386)) ?15387) (negative_part ?15386) =>= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15387, 15386] by Super 10542 with 2823 at 1,2
-Id : 10509, {_}: multiply (union (inverse ?711) ?712) ?711 =>= positive_part (multiply ?712 ?711) [712, 711] by Demod 248 with 309 at 3
-Id : 10604, {_}: positive_part (multiply ?15387 (negative_part ?15386)) =<= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15386, 15387] by Demod 10564 with 10509 at 2
-Id : 481, {_}: multiply ?1071 (intersection ?1072 identity) =?= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Super 17 with 475 at 2,3
-Id : 505, {_}: multiply ?1071 (negative_part ?1072) =<= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Demod 481 with 21 at 2,2
-Id : 10568, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part (multiply identity ?15398) [15398] by Super 10542 with 20 at 1,2
-Id : 10608, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part ?15398 [15398] by Demod 10568 with 2 at 1,3
-Id : 10645, {_}: multiply (positive_part (inverse ?15507)) (negative_part ?15507) =>= intersection (positive_part ?15507) (positive_part (inverse ?15507)) [15507] by Super 505 with 10608 at 1,3
-Id : 11493, {_}: positive_part (multiply (inverse ?16415) (negative_part ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Super 10604 with 10645 at 1,3
-Id : 3426, {_}: multiply ?5989 (negative_part ?5990) =<= intersection (multiply ?5989 ?5990) ?5989 [5990, 5989] by Demod 481 with 21 at 2,2
-Id : 3428, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= intersection identity (inverse ?5994) [5994] by Super 3426 with 3 at 1,3
-Id : 3468, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= negative_part (inverse ?5994) [5994] by Demod 3428 with 329 at 3
-Id : 11531, {_}: positive_part (negative_part (inverse ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11493 with 3468 at 1,2
-Id : 11532, {_}: identity =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11531 with 514 at 2
-Id : 52635, {_}: intersection (intersection (positive_part ?60922) (positive_part (inverse ?60922))) identity =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Super 686 with 11532 at 2,2
-Id : 52914, {_}: intersection identity (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52635 with 10 at 2
-Id : 52915, {_}: negative_part (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52914 with 329 at 2
-Id : 332, {_}: intersection ?876 (intersection ?877 identity) =>= negative_part (intersection ?876 ?877) [877, 876] by Super 12 with 21 at 3
-Id : 344, {_}: intersection ?876 (negative_part ?877) =<= negative_part (intersection ?876 ?877) [877, 876] by Demod 332 with 21 at 2,2
-Id : 52916, {_}: intersection (positive_part ?60922) (negative_part (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52915 with 344 at 2
-Id : 52917, {_}: intersection (negative_part (positive_part (inverse ?60922))) (positive_part ?60922) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52916 with 10 at 2
-Id : 421, {_}: intersection identity (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Super 12 with 329 at 1,3
-Id : 435, {_}: negative_part (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Demod 421 with 329 at 2
-Id : 903, {_}: intersection ?1965 (negative_part ?1966) =?= intersection (negative_part ?1965) ?1966 [1966, 1965] by Demod 435 with 344 at 2
-Id : 327, {_}: negative_part (union ?866 identity) =>= identity [866] by Super 15 with 21 at 2
-Id : 346, {_}: negative_part (positive_part ?866) =>= identity [866] by Demod 327 with 20 at 1,2
-Id : 914, {_}: intersection (positive_part ?1997) (negative_part ?1998) =>= intersection identity ?1998 [1998, 1997] by Super 903 with 346 at 1,2
-Id : 945, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= intersection identity ?1998 [1997, 1998] by Demod 914 with 10 at 2
-Id : 946, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= negative_part ?1998 [1997, 1998] by Demod 945 with 329 at 3
-Id : 52918, {_}: negative_part (positive_part (inverse ?60922)) =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52917 with 946 at 2
-Id : 52919, {_}: identity =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52918 with 346 at 2
-Id : 53306, {_}: inverse (negative_part (multiply (inverse (positive_part (inverse ?61296))) (positive_part ?61296))) =>= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Super 10396 with 52919 at 1,1,3
-Id : 10642, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part (inverse (inverse ?15501)))) [15501] by Super 62 with 10608 at 1,2
-Id : 10686, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part ?15501)) [15501] by Demod 10642 with 6 at 1,1,2,3
-Id : 10895, {_}: multiply (inverse (positive_part (inverse ?15767))) (positive_part ?15767) =>= ?15767 [15767] by Super 570 with 10686 at 1,2
-Id : 53366, {_}: inverse (negative_part ?61296) =<= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Demod 53306 with 10895 at 1,1,2
-Id : 53367, {_}: inverse (negative_part ?61296) =<= multiply identity (positive_part (inverse ?61296)) [61296] by Demod 53366 with 5 at 1,3
-Id : 53816, {_}: inverse (negative_part ?61700) =<= positive_part (inverse ?61700) [61700] by Demod 53367 with 2 at 3
-Id : 53819, {_}: inverse (negative_part (multiply (inverse ?61705) ?61706)) =>= positive_part (multiply (inverse ?61706) ?61705) [61706, 61705] by Super 53816 with 60 at 1,3
-Id : 62826, {_}: inverse (positive_part (multiply (inverse ?68982) ?68983)) =>= negative_part (multiply (inverse ?68983) ?68982) [68983, 68982] by Super 6 with 53819 at 1,2
-Id : 62827, {_}: inverse (positive_part (multiply identity ?68985)) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Super 62826 with 5 at 1,1,1,2
-Id : 63051, {_}: inverse (positive_part ?68985) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Demod 62827 with 2 at 1,1,2
-Id : 63052, {_}: inverse (positive_part ?68985) =<= negative_part (inverse ?68985) [68985] by Demod 63051 with 475 at 1,3
-Id : 66930, {_}: multiply (inverse (inverse (positive_part ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Demod 16644 with 63052 at 1,1,2
-Id : 66931, {_}: multiply (positive_part ?20815) (negative_part ?20815) =>= ?20815 [20815] by Demod 66930 with 6 at 1,2
-Id : 67152, {_}: a === a [] by Demod 1 with 66931 at 2
-Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
-% SZS output end CNFRefutation for GRP114-1.p
-25668: solved GRP114-1.p in 7.932495 using nrkbo
-25668: status Unsatisfiable for GRP114-1.p
-NO CLASH, using fixed ground order
-25676: Facts:
-25676: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25676: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25676: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25676: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25676: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25676: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25676: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25676: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25676: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25676: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25676: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25676: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25676: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25676: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25676: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25676: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-25676: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-25676: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-25676: Goal:
-25676: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-25676: Order:
-25676: kbo
-25676: Leaf order:
-25676: a 3 0 3 2
-25676: identity 6 0 2 2,1,3
-25676: inverse 7 1 0
-25676: least_upper_bound 14 2 1 0,1,3
-25676: greatest_lower_bound 14 2 1 0,2,3
-25676: multiply 21 2 1 0,3
-NO CLASH, using fixed ground order
-25675: Facts:
-25675: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25675: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25675: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25675: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25675: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25675: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25675: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25675: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25675: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25675: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25675: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25675: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25675: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25675: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25675: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25675: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-25675: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-25675: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-25675: Goal:
-25675: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-25675: Order:
-25675: nrkbo
-25675: Leaf order:
-25675: a 3 0 3 2
-25675: identity 6 0 2 2,1,3
-25675: inverse 7 1 0
-25675: least_upper_bound 14 2 1 0,1,3
-25675: greatest_lower_bound 14 2 1 0,2,3
-25675: multiply 21 2 1 0,3
-NO CLASH, using fixed ground order
-25677: Facts:
-25677: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25677: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25677: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25677: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25677: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25677: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25677: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25677: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25677: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25677: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25677: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25677: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25677: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25677: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25677: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25677: Id : 17, {_}: inverse identity =>= identity [] by p19_1
-25677: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
-25677: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p19_3 ?53 ?54
-25677: Goal:
-25677: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-25677: Order:
-25677: lpo
-25677: Leaf order:
-25677: a 3 0 3 2
-25677: identity 6 0 2 2,1,3
-25677: inverse 7 1 0
-25677: least_upper_bound 14 2 1 0,1,3
-25677: greatest_lower_bound 14 2 1 0,2,3
-25677: multiply 21 2 1 0,3
-% SZS status Timeout for GRP167-4.p
-NO CLASH, using fixed ground order
-25699: Facts:
-25699: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25699: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25699: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25699: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25699: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25699: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25699: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25699: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25699: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25699: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25699: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25699: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25699: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25699: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25699: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25699: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-25699: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-25699: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-25699: Goal:
-25699: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-25699: Order:
-25699: nrkbo
-25699: Leaf order:
-25699: b 4 0 3 1,2,1,2
-25699: c 4 0 3 2,2,1,2
-25699: a 5 0 4 1,1,2
-25699: identity 8 0 0
-25699: inverse 1 1 0
-25699: least_upper_bound 13 2 0
-25699: multiply 21 2 3 0,2,1,2
-25699: greatest_lower_bound 21 2 5 0,2
-NO CLASH, using fixed ground order
-25700: Facts:
-25700: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25700: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25700: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25700: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25700: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25700: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25700: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25700: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25700: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25700: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25700: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25700: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25700: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25700: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25700: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25700: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-25700: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-25700: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-25700: Goal:
-25700: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-25700: Order:
-25700: kbo
-25700: Leaf order:
-25700: b 4 0 3 1,2,1,2
-25700: c 4 0 3 2,2,1,2
-25700: a 5 0 4 1,1,2
-25700: identity 8 0 0
-25700: inverse 1 1 0
-25700: least_upper_bound 13 2 0
-25700: multiply 21 2 3 0,2,1,2
-25700: greatest_lower_bound 21 2 5 0,2
-NO CLASH, using fixed ground order
-25701: Facts:
-25701: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25701: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25701: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25701: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25701: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25701: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25701: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25701: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25701: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25701: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25701: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25701: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25701: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25701: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25701: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25701: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
-25701: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
-25701: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
-25701: Goal:
-25701: Id : 1, {_}:
- greatest_lower_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- greatest_lower_bound a (multiply b c)
- [] by prove_p08b
-25701: Order:
-25701: lpo
-25701: Leaf order:
-25701: b 4 0 3 1,2,1,2
-25701: c 4 0 3 2,2,1,2
-25701: a 5 0 4 1,1,2
-25701: identity 8 0 0
-25701: inverse 1 1 0
-25701: least_upper_bound 13 2 0
-25701: multiply 21 2 3 0,2,1,2
-25701: greatest_lower_bound 21 2 5 0,2
-% SZS status Timeout for GRP177-2.p
-NO CLASH, using fixed ground order
-25723: Facts:
-NO CLASH, using fixed ground order
-25724: Facts:
-25724: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25724: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25724: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25724: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25724: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25724: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25724: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25724: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-NO CLASH, using fixed ground order
-25725: Facts:
-25725: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25725: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25725: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25725: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25725: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25725: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25725: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25725: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25725: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25725: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25723: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25725: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25723: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25725: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25725: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25725: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25723: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25723: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25725: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25723: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25725: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-25725: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-25723: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25725: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-25725: Goal:
-25725: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-25725: Order:
-25725: lpo
-25725: Leaf order:
-25725: a 2 0 2 1,1,2
-25725: identity 6 0 2 2,2
-25725: inverse 9 1 2 0,1,2
-25725: greatest_lower_bound 14 2 1 0,1,3
-25725: least_upper_bound 14 2 1 0,2
-25723: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25723: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25723: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25723: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25723: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25723: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25723: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25723: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25723: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25723: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-25723: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-25723: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-25723: Goal:
-25723: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-25723: Order:
-25723: nrkbo
-25723: Leaf order:
-25723: a 2 0 2 1,1,2
-25723: identity 6 0 2 2,2
-25723: inverse 9 1 2 0,1,2
-25723: greatest_lower_bound 14 2 1 0,1,3
-25723: least_upper_bound 14 2 1 0,2
-25723: multiply 20 2 0
-25724: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25725: multiply 20 2 0
-25724: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25724: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25724: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25724: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25724: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25724: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25724: Id : 17, {_}: inverse identity =>= identity [] by p18_1
-25724: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
-25724: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p18_3 ?53 ?54
-25724: Goal:
-25724: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-25724: Order:
-25724: kbo
-25724: Leaf order:
-25724: a 2 0 2 1,1,2
-25724: identity 6 0 2 2,2
-25724: inverse 9 1 2 0,1,2
-25724: greatest_lower_bound 14 2 1 0,1,3
-25724: least_upper_bound 14 2 1 0,2
-25724: multiply 20 2 0
-% SZS status Timeout for GRP179-3.p
-NO CLASH, using fixed ground order
-25752: Facts:
-25752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25752: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25752: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25752: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25752: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25752: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25752: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25752: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25752: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25752: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25752: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25752: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25752: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25752: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-25752: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-25752: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-25752: Goal:
-25752: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-25752: Order:
-25752: nrkbo
-25752: Leaf order:
-25752: a 3 0 3 1,2
-25752: b 3 0 3 2,1,1,2,2
-25752: identity 4 0 0
-25752: inverse 8 1 1 0,1,2,2
-25752: greatest_lower_bound 14 2 1 0,1,1,2,2
-25752: least_upper_bound 14 2 1 0,3
-25752: multiply 22 2 2 0,2
-NO CLASH, using fixed ground order
-25753: Facts:
-25753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25753: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25753: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25753: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25753: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25753: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25753: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25753: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25753: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25753: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25753: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25753: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25753: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25753: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-25753: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-25753: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-25753: Goal:
-25753: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-25753: Order:
-25753: kbo
-25753: Leaf order:
-25753: a 3 0 3 1,2
-25753: b 3 0 3 2,1,1,2,2
-25753: identity 4 0 0
-25753: inverse 8 1 1 0,1,2,2
-25753: greatest_lower_bound 14 2 1 0,1,1,2,2
-25753: least_upper_bound 14 2 1 0,3
-25753: multiply 22 2 2 0,2
-NO CLASH, using fixed ground order
-25754: Facts:
-25754: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25754: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25754: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25754: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25754: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25754: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25754: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25754: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25754: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25754: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25754: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25754: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25754: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25754: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25754: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25754: Id : 17, {_}: inverse identity =>= identity [] by p11_1
-25754: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
-25754: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p11_3 ?53 ?54
-25754: Goal:
-25754: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-25754: Order:
-25754: lpo
-25754: Leaf order:
-25754: a 3 0 3 1,2
-25754: b 3 0 3 2,1,1,2,2
-25754: identity 4 0 0
-25754: inverse 8 1 1 0,1,2,2
-25754: greatest_lower_bound 14 2 1 0,1,1,2,2
-25754: least_upper_bound 14 2 1 0,3
-25754: multiply 22 2 2 0,2
-% SZS status Timeout for GRP180-2.p
-CLASH, statistics insufficient
-25775: Facts:
-25775: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25775: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25775: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25775: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25775: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25775: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25775: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25775: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25775: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25775: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25775: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25775: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25775: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25775: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25775: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25775: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-25775: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-25775: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-25775: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-25775: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-25775: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-25775: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-25775: Goal:
-25775: Id : 1, {_}: a =>= b [] by prove_p12x
-25775: Order:
-25775: nrkbo
-25775: Leaf order:
-25775: a 3 0 1 2
-25775: b 3 0 1 3
-25775: identity 4 0 0
-25775: c 4 0 0
-25775: inverse 13 1 0
-25775: greatest_lower_bound 17 2 0
-25775: least_upper_bound 17 2 0
-25775: multiply 20 2 0
-CLASH, statistics insufficient
-25776: Facts:
-25776: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25776: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25776: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25776: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25776: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25776: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25776: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25776: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25776: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25776: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25776: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25776: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25776: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25776: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25776: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25776: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-25776: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-25776: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-25776: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-25776: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-25776: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =<=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-25776: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =<=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-25776: Goal:
-25776: Id : 1, {_}: a =>= b [] by prove_p12x
-25776: Order:
-25776: kbo
-25776: Leaf order:
-25776: a 3 0 1 2
-25776: b 3 0 1 3
-25776: identity 4 0 0
-25776: c 4 0 0
-25776: inverse 13 1 0
-25776: greatest_lower_bound 17 2 0
-25776: least_upper_bound 17 2 0
-25776: multiply 20 2 0
-CLASH, statistics insufficient
-25777: Facts:
-25777: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25777: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25777: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25777: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25777: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25777: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25777: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25777: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25777: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25777: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25777: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25777: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25777: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25777: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25777: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25777: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-25777: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-25777: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12x_3 ?53 ?54
-25777: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12x_4
-25777: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-25777: Id : 22, {_}:
- inverse (greatest_lower_bound ?58 ?59)
- =>=
- least_upper_bound (inverse ?58) (inverse ?59)
- [59, 58] by p12x_6 ?58 ?59
-25777: Id : 23, {_}:
- inverse (least_upper_bound ?61 ?62)
- =>=
- greatest_lower_bound (inverse ?61) (inverse ?62)
- [62, 61] by p12x_7 ?61 ?62
-25777: Goal:
-25777: Id : 1, {_}: a =>= b [] by prove_p12x
-25777: Order:
-25777: lpo
-25777: Leaf order:
-25777: a 3 0 1 2
-25777: b 3 0 1 3
-25777: identity 4 0 0
-25777: c 4 0 0
-25777: inverse 13 1 0
-25777: greatest_lower_bound 17 2 0
-25777: least_upper_bound 17 2 0
-25777: multiply 20 2 0
-Statistics :
-Max weight : 16
-Found proof, 8.150042s
-% SZS status Unsatisfiable for GRP181-4.p
-% SZS output start CNFRefutation for GRP181-4.p
-Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
-Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
-Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588
-Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
-Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930
-Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517
-Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
-Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 17, {_}: inverse identity =>= identity [] by p12x_1
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
-Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846
-Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3
-Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3
-Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3
-Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2
-Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3
-Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2
-Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3
-Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2
-Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3
-Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3
-Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3
-Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2
-Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3
-Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3
-Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3
-Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3
-Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3
-Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3
-Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2
-Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2
-Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3
-Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2
-Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3
-Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2
-Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3
-Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2
-Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2
-Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3
-Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3
-Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2
-Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3
-Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2
-Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3
-Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2
-Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2
-Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2
-Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3
-Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3
-Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2
-Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2
-Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3
-Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2
-Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3
-Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2
-Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3
-Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2
-Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2
-Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2
-Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3
-Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2
-Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2
-Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2
-Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2
-Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3
-Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2
-Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3
-Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3
-Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2
-Id : 1, {_}: a =>= b [] by prove_p12x
-% SZS output end CNFRefutation for GRP181-4.p
-25775: solved GRP181-4.p in 8.112506 using nrkbo
-25775: status Unsatisfiable for GRP181-4.p
-NO CLASH, using fixed ground order
-25788: Facts:
-25788: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25788: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25788: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25788: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25788: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25788: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25788: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25788: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25788: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25788: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25788: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25788: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25788: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25788: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25788: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25788: Goal:
-25788: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-25788: Order:
-25788: nrkbo
-25788: Leaf order:
-25788: a 2 0 2 1,1,2
-25788: identity 5 0 3 2,1,2
-25788: inverse 2 1 1 0,2,2
-25788: least_upper_bound 14 2 1 0,1,2
-25788: greatest_lower_bound 15 2 2 0,2
-25788: multiply 18 2 0
-NO CLASH, using fixed ground order
-25789: Facts:
-25789: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25789: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25789: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25789: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25789: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25789: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25789: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25789: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25789: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25789: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25789: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25789: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-NO CLASH, using fixed ground order
-25790: Facts:
-25790: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25790: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25790: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25790: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25790: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25790: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25790: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25790: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25790: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25790: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25790: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25790: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25790: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25790: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25790: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25790: Goal:
-25790: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-25790: Order:
-25790: lpo
-25790: Leaf order:
-25790: a 2 0 2 1,1,2
-25790: identity 5 0 3 2,1,2
-25790: inverse 2 1 1 0,2,2
-25790: least_upper_bound 14 2 1 0,1,2
-25790: greatest_lower_bound 15 2 2 0,2
-25790: multiply 18 2 0
-25789: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25789: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25789: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25789: Goal:
-25789: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-25789: Order:
-25789: kbo
-25789: Leaf order:
-25789: a 2 0 2 1,1,2
-25789: identity 5 0 3 2,1,2
-25789: inverse 2 1 1 0,2,2
-25789: least_upper_bound 14 2 1 0,1,2
-25789: greatest_lower_bound 15 2 2 0,2
-25789: multiply 18 2 0
-% SZS status Timeout for GRP183-1.p
-NO CLASH, using fixed ground order
-25806: Facts:
-25806: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25806: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25806: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25806: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25806: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25806: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25806: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25806: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25806: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25806: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25806: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25806: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25806: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25806: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25806: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25806: Goal:
-25806: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25806: Order:
-25806: nrkbo
-25806: Leaf order:
-25806: a 2 0 2 1,1,2
-25806: identity 5 0 3 2,1,2
-25806: inverse 2 1 1 0,1,2,2
-25806: greatest_lower_bound 14 2 1 0,2
-25806: least_upper_bound 15 2 2 0,1,2
-25806: multiply 18 2 0
-NO CLASH, using fixed ground order
-25807: Facts:
-25807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25807: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25807: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25807: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25807: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25807: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25807: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25807: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25807: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25807: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25807: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25807: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25807: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25807: Goal:
-25807: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25807: Order:
-25807: kbo
-25807: Leaf order:
-25807: a 2 0 2 1,1,2
-25807: identity 5 0 3 2,1,2
-25807: inverse 2 1 1 0,1,2,2
-25807: greatest_lower_bound 14 2 1 0,2
-25807: least_upper_bound 15 2 2 0,1,2
-25807: multiply 18 2 0
-NO CLASH, using fixed ground order
-25808: Facts:
-25808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25808: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25808: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25808: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25808: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25808: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25808: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25808: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25808: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25808: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25808: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25808: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25808: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25808: Goal:
-25808: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25808: Order:
-25808: lpo
-25808: Leaf order:
-25808: a 2 0 2 1,1,2
-25808: identity 5 0 3 2,1,2
-25808: inverse 2 1 1 0,1,2,2
-25808: greatest_lower_bound 14 2 1 0,2
-25808: least_upper_bound 15 2 2 0,1,2
-25808: multiply 18 2 0
-% SZS status Timeout for GRP183-3.p
-NO CLASH, using fixed ground order
-25839: Facts:
-25839: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25839: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25839: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25839: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25839: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25839: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25839: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25839: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25839: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25839: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25839: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25839: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25839: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25839: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25839: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25839: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-25839: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-25839: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-25839: Goal:
-25839: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25839: Order:
-25839: nrkbo
-25839: Leaf order:
-25839: a 2 0 2 1,1,2
-25839: identity 7 0 3 2,1,2
-25839: inverse 8 1 1 0,1,2,2
-25839: greatest_lower_bound 14 2 1 0,2
-25839: least_upper_bound 15 2 2 0,1,2
-25839: multiply 20 2 0
-NO CLASH, using fixed ground order
-25840: Facts:
-25840: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25840: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25840: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25840: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-NO CLASH, using fixed ground order
-25841: Facts:
-25841: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25841: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25841: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25841: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25841: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25841: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25841: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25841: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25841: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25841: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25841: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25841: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25841: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25841: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25841: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25841: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-25841: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-25841: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-25841: Goal:
-25841: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25841: Order:
-25841: lpo
-25841: Leaf order:
-25841: a 2 0 2 1,1,2
-25841: identity 7 0 3 2,1,2
-25841: inverse 8 1 1 0,1,2,2
-25841: greatest_lower_bound 14 2 1 0,2
-25841: least_upper_bound 15 2 2 0,1,2
-25841: multiply 20 2 0
-25840: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25840: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25840: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25840: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25840: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25840: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25840: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25840: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25840: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25840: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25840: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25840: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
-25840: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
-25840: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20x_3 ?53 ?54
-25840: Goal:
-25840: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (least_upper_bound (inverse a) identity)
- =>=
- identity
- [] by prove_20x
-25840: Order:
-25840: kbo
-25840: Leaf order:
-25840: a 2 0 2 1,1,2
-25840: identity 7 0 3 2,1,2
-25840: inverse 8 1 1 0,1,2,2
-25840: greatest_lower_bound 14 2 1 0,2
-25840: least_upper_bound 15 2 2 0,1,2
-25840: multiply 20 2 0
-% SZS status Timeout for GRP183-4.p
-NO CLASH, using fixed ground order
-25861: Facts:
-25861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25861: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25861: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25861: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25861: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25861: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25861: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25861: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25861: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25861: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25861: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25861: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25861: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25861: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25861: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25861: Goal:
-25861: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-25861: Order:
-25861: nrkbo
-25861: Leaf order:
-25861: a 4 0 4 1,1,2
-25861: identity 6 0 4 2,1,2
-25861: inverse 3 1 2 0,2,2
-25861: least_upper_bound 15 2 2 0,1,2
-25861: greatest_lower_bound 15 2 2 0,1,2,2
-25861: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-25862: Facts:
-25862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25862: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25862: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25862: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25862: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25862: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25862: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25862: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25862: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25862: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25862: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25862: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25862: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25862: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25862: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25862: Goal:
-25862: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-25862: Order:
-25862: kbo
-25862: Leaf order:
-25862: a 4 0 4 1,1,2
-25862: identity 6 0 4 2,1,2
-25862: inverse 3 1 2 0,2,2
-25862: least_upper_bound 15 2 2 0,1,2
-25862: greatest_lower_bound 15 2 2 0,1,2,2
-25862: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-25863: Facts:
-25863: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25863: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25863: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25863: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25863: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25863: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25863: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25863: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25863: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25863: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25863: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25863: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25863: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25863: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25863: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25863: Goal:
-25863: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21
-25863: Order:
-25863: lpo
-25863: Leaf order:
-25863: a 4 0 4 1,1,2
-25863: identity 6 0 4 2,1,2
-25863: inverse 3 1 2 0,2,2
-25863: least_upper_bound 15 2 2 0,1,2
-25863: greatest_lower_bound 15 2 2 0,1,2,2
-25863: multiply 20 2 2 0,2
-% SZS status Timeout for GRP184-1.p
-NO CLASH, using fixed ground order
-25898: Facts:
-25898: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25898: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25898: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25898: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25898: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25898: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25898: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25898: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25898: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25898: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25898: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25898: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25898: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25898: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25898: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25898: Goal:
-25898: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-25898: Order:
-25898: nrkbo
-25898: Leaf order:
-25898: a 4 0 4 1,1,2
-25898: identity 6 0 4 2,1,2
-25898: inverse 3 1 2 0,2,2
-25898: least_upper_bound 15 2 2 0,1,2
-25898: greatest_lower_bound 15 2 2 0,1,2,2
-25898: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-25899: Facts:
-25899: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25899: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25899: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25899: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25899: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25899: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25899: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25899: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25899: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25899: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25899: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25899: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25899: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25899: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25899: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25899: Goal:
-25899: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-25899: Order:
-25899: kbo
-25899: Leaf order:
-25899: a 4 0 4 1,1,2
-25899: identity 6 0 4 2,1,2
-25899: inverse 3 1 2 0,2,2
-25899: least_upper_bound 15 2 2 0,1,2
-25899: greatest_lower_bound 15 2 2 0,1,2,2
-25899: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-25900: Facts:
-25900: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25900: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25900: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25900: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25900: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25900: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25900: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25900: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25900: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25900: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25900: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25900: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25900: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25900: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25900: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25900: Goal:
-25900: Id : 1, {_}:
- multiply (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =<=
- multiply (inverse (greatest_lower_bound a identity))
- (least_upper_bound a identity)
- [] by prove_p21x
-25900: Order:
-25900: lpo
-25900: Leaf order:
-25900: a 4 0 4 1,1,2
-25900: identity 6 0 4 2,1,2
-25900: inverse 3 1 2 0,2,2
-25900: least_upper_bound 15 2 2 0,1,2
-25900: greatest_lower_bound 15 2 2 0,1,2,2
-25900: multiply 20 2 2 0,2
-% SZS status Timeout for GRP184-3.p
-NO CLASH, using fixed ground order
-25933: Facts:
-25933: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25933: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25933: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25933: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25933: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25933: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25933: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25933: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25933: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25933: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25933: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25933: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25933: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-NO CLASH, using fixed ground order
-25934: Facts:
-25934: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25934: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25934: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25934: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25934: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25934: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25934: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25934: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25934: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25934: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25934: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25934: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25934: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25934: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25934: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25934: Goal:
-25934: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25934: Order:
-25934: lpo
-25934: Leaf order:
-25934: a 3 0 3 1,1,1,2
-25934: b 3 0 3 2,1,1,2
-25934: identity 6 0 4 2,1,2
-25934: inverse 1 1 0
-25934: greatest_lower_bound 14 2 1 0,2
-25934: least_upper_bound 17 2 4 0,1,2
-25934: multiply 21 2 3 0,1,1,2
-NO CLASH, using fixed ground order
-25932: Facts:
-25932: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25932: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25932: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25932: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25932: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25932: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25932: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25932: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25932: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25932: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25932: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25932: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25932: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25932: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25932: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25932: Goal:
-25932: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25932: Order:
-25932: nrkbo
-25932: Leaf order:
-25932: a 3 0 3 1,1,1,2
-25932: b 3 0 3 2,1,1,2
-25932: identity 6 0 4 2,1,2
-25932: inverse 1 1 0
-25932: greatest_lower_bound 14 2 1 0,2
-25932: least_upper_bound 17 2 4 0,1,2
-25932: multiply 21 2 3 0,1,1,2
-25933: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25933: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25933: Goal:
-25933: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25933: Order:
-25933: kbo
-25933: Leaf order:
-25933: a 3 0 3 1,1,1,2
-25933: b 3 0 3 2,1,1,2
-25933: identity 6 0 4 2,1,2
-25933: inverse 1 1 0
-25933: greatest_lower_bound 14 2 1 0,2
-25933: least_upper_bound 17 2 4 0,1,2
-25933: multiply 21 2 3 0,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 1.351481s
-% SZS status Unsatisfiable for GRP185-3.p
-% SZS output start CNFRefutation for GRP185-3.p
-Id : 108, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
-Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
-Id : 392, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
-Id : 394, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 392 with 3 at 2,3
-Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
-Id : 400, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 392 with 27 at 2,3
-Id : 525, {_}: ?599 =<= multiply ?599 identity [599] by Demod 394 with 400 at 3
-Id : 815, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 108 with 6 at 2,2
-Id : 822, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 815 with 8 at 2,2
-Id : 2353, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2352 with 822 at 2
-Id : 2352, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2351 with 8 at 2,2,2
-Id : 2351, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2350 with 8 at 2,2
-Id : 2350, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2349 with 6 at 2,2
-Id : 2349, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2348 with 2 at 2,2,2,2,2
-Id : 2348, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2347 with 525 at 1,2,2,2,2
-Id : 2347, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2346 with 2 at 1,2,2,2
-Id : 2346, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2345 with 8 at 2,2
-Id : 2345, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2344 with 15 at 2,2,2
-Id : 2344, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2343 with 15 at 1,2,2
-Id : 2343, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2342 with 6 at 3
-Id : 2342, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2341 with 13 at 2,2
-Id : 2341, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
-% SZS output end CNFRefutation for GRP185-3.p
-25934: solved GRP185-3.p in 0.66004 using lpo
-25934: status Unsatisfiable for GRP185-3.p
-NO CLASH, using fixed ground order
-25939: Facts:
-25939: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25939: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25939: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25939: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25939: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25939: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25939: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25939: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25939: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25939: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25939: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25939: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25939: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25939: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25939: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25939: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-25939: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-25939: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-25939: Goal:
-25939: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25939: Order:
-25939: nrkbo
-25939: Leaf order:
-25939: a 3 0 3 1,1,1,2
-25939: b 3 0 3 2,1,1,2
-25939: identity 8 0 4 2,1,2
-25939: inverse 7 1 0
-25939: greatest_lower_bound 14 2 1 0,2
-25939: least_upper_bound 17 2 4 0,1,2
-25939: multiply 23 2 3 0,1,1,2
-NO CLASH, using fixed ground order
-25940: Facts:
-25940: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25940: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25940: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25940: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25940: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25940: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25940: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25940: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25940: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25940: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25940: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25940: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25940: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25940: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25940: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25940: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-25940: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-25940: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-25940: Goal:
-25940: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25940: Order:
-25940: kbo
-25940: Leaf order:
-25940: a 3 0 3 1,1,1,2
-25940: b 3 0 3 2,1,1,2
-25940: identity 8 0 4 2,1,2
-25940: inverse 7 1 0
-25940: greatest_lower_bound 14 2 1 0,2
-25940: least_upper_bound 17 2 4 0,1,2
-25940: multiply 23 2 3 0,1,1,2
-NO CLASH, using fixed ground order
-25941: Facts:
-25941: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25941: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25941: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25941: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25941: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25941: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25941: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25941: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25941: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25941: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25941: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25941: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25941: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25941: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25941: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25941: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-25941: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-25941: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p22b_3 ?53 ?54
-25941: Goal:
-25941: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound (multiply a b) identity)
- (multiply (least_upper_bound a identity)
- (least_upper_bound b identity))
- =>=
- least_upper_bound (multiply a b) identity
- [] by prove_p22b
-25941: Order:
-25941: lpo
-25941: Leaf order:
-25941: a 3 0 3 1,1,1,2
-25941: b 3 0 3 2,1,1,2
-25941: identity 8 0 4 2,1,2
-25941: inverse 7 1 0
-25941: greatest_lower_bound 14 2 1 0,2
-25941: least_upper_bound 17 2 4 0,1,2
-25941: multiply 23 2 3 0,1,1,2
-Statistics :
-Max weight : 21
-Found proof, 0.930082s
-% SZS status Unsatisfiable for GRP185-4.p
-% SZS output start CNFRefutation for GRP185-4.p
-Id : 111, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258
-Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
-Id : 17, {_}: inverse identity =>= identity [] by p22b_1
-Id : 338, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
-Id : 339, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 338 with 17 at 2,3
-Id : 372, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 339 with 2 at 1,2
-Id : 374, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 372 with 18 at 1,3
-Id : 382, {_}: ?572 =<= multiply ?572 identity [572] by Demod 374 with 18 at 2
-Id : 704, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 111 with 6 at 2,2
-Id : 711, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 704 with 8 at 2,2
-Id : 1908, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 1907 with 711 at 2
-Id : 1907, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1906 with 8 at 2,2,2
-Id : 1906, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 1905 with 8 at 2,2
-Id : 1905, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 1904 with 6 at 2,2
-Id : 1904, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1903 with 2 at 2,2,2,2,2
-Id : 1903, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1902 with 382 at 1,2,2,2,2
-Id : 1902, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1901 with 2 at 1,2,2,2
-Id : 1901, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1900 with 8 at 2,2
-Id : 1900, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1899 with 15 at 2,2,2
-Id : 1899, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1898 with 15 at 1,2,2
-Id : 1898, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1897 with 6 at 3
-Id : 1897, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1896 with 13 at 2,2
-Id : 1896, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
-Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
-% SZS output end CNFRefutation for GRP185-4.p
-25941: solved GRP185-4.p in 0.432027 using lpo
-25941: status Unsatisfiable for GRP185-4.p
-NO CLASH, using fixed ground order
-25948: Facts:
-25948: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25948: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25948: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25948: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25948: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25948: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25948: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25948: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25948: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25948: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25948: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25948: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25948: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25948: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25948: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25948: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-25948: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-25948: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-25948: Goal:
-25948: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-25948: Order:
-25948: nrkbo
-25948: Leaf order:
-25948: b 2 0 2 2,1,2
-25948: a 3 0 3 1,1,2
-25948: identity 5 0 1 2,2
-25948: inverse 9 1 2 0,2,3
-25948: greatest_lower_bound 14 2 1 0,1,2,3
-25948: least_upper_bound 14 2 1 0,2
-25948: multiply 22 2 2 0,1,2
-NO CLASH, using fixed ground order
-25950: Facts:
-25950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25950: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25950: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25950: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25950: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25950: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25950: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25950: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25950: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25950: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25950: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25950: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25950: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25950: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-25950: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-25950: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-25950: Goal:
-25950: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-25950: Order:
-25950: lpo
-25950: Leaf order:
-25950: b 2 0 2 2,1,2
-25950: a 3 0 3 1,1,2
-25950: identity 5 0 1 2,2
-25950: inverse 9 1 2 0,2,3
-25950: greatest_lower_bound 14 2 1 0,1,2,3
-25950: least_upper_bound 14 2 1 0,2
-25950: multiply 22 2 2 0,1,2
-NO CLASH, using fixed ground order
-25949: Facts:
-25949: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25949: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25949: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25949: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25949: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25949: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25949: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25949: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25949: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25949: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25949: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25949: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25949: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25949: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25949: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25949: Id : 17, {_}: inverse identity =>= identity [] by p23_1
-25949: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
-25949: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p23_3 ?53 ?54
-25949: Goal:
-25949: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-25949: Order:
-25949: kbo
-25949: Leaf order:
-25949: b 2 0 2 2,1,2
-25949: a 3 0 3 1,1,2
-25949: identity 5 0 1 2,2
-25949: inverse 9 1 2 0,2,3
-25949: greatest_lower_bound 14 2 1 0,1,2,3
-25949: least_upper_bound 14 2 1 0,2
-25949: multiply 22 2 2 0,1,2
-% SZS status Timeout for GRP186-2.p
-NO CLASH, using fixed ground order
-26073: Facts:
-26073: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26073: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-26073: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =?=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-26073: Goal:
-26073: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-26073: Order:
-26073: nrkbo
-26073: Leaf order:
-26073: identity 2 0 0
-26073: a 2 0 2 1,1,1,2
-26073: c 2 0 2 2,1,2
-26073: b 4 0 4 2,1,1,2
-26073: left_inverse 1 1 0
-26073: multiply 14 2 6 0,2
-NO CLASH, using fixed ground order
-26074: Facts:
-26074: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26074: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-26074: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =>=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-26074: Goal:
-26074: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-26074: Order:
-26074: kbo
-26074: Leaf order:
-26074: identity 2 0 0
-26074: a 2 0 2 1,1,1,2
-26074: c 2 0 2 2,1,2
-26074: b 4 0 4 2,1,1,2
-26074: left_inverse 1 1 0
-26074: multiply 14 2 6 0,2
-NO CLASH, using fixed ground order
-26075: Facts:
-26075: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26075: Id : 3, {_}:
- multiply (left_inverse ?4) ?4 =>= identity
- [4] by left_inverse ?4
-26075: Id : 4, {_}:
- multiply (multiply ?6 (multiply ?7 ?8)) ?6
- =>=
- multiply (multiply ?6 ?7) (multiply ?8 ?6)
- [8, 7, 6] by moufang1 ?6 ?7 ?8
-26075: Goal:
-26075: Id : 1, {_}:
- multiply (multiply (multiply a b) c) b
- =>=
- multiply a (multiply b (multiply c b))
- [] by prove_moufang2
-26075: Order:
-26075: lpo
-26075: Leaf order:
-26075: identity 2 0 0
-26075: a 2 0 2 1,1,1,2
-26075: c 2 0 2 2,1,2
-26075: b 4 0 4 2,1,1,2
-26075: left_inverse 1 1 0
-26075: multiply 14 2 6 0,2
-% SZS status Timeout for GRP204-1.p
-CLASH, statistics insufficient
-26204: Facts:
-26204: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26204: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-26204: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-26204: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-26204: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-26204: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-26204: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-26204: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-26204: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =?=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-26204: Goal:
-26204: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-26204: Order:
-26204: nrkbo
-26204: Leaf order:
-26204: y 2 0 2 1,1,2,2
-26204: z 2 0 2 2,1,2,2
-26204: identity 4 0 0
-26204: x 4 0 4 1,2
-26204: right_inverse 1 1 0
-26204: left_inverse 1 1 0
-26204: left_division 2 2 0
-26204: right_division 2 2 0
-26204: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-26205: Facts:
-26205: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26205: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-26205: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-26205: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-26205: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-26205: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-26205: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-26205: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-26205: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-26205: Goal:
-26205: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-26205: Order:
-26205: kbo
-26205: Leaf order:
-26205: y 2 0 2 1,1,2,2
-26205: z 2 0 2 2,1,2,2
-26205: identity 4 0 0
-26205: x 4 0 4 1,2
-26205: right_inverse 1 1 0
-26205: left_inverse 1 1 0
-26205: left_division 2 2 0
-26205: right_division 2 2 0
-26205: multiply 20 2 6 0,2
-CLASH, statistics insufficient
-26206: Facts:
-26206: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-26206: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-26206: Id : 4, {_}:
- multiply ?6 (left_division ?6 ?7) =>= ?7
- [7, 6] by multiply_left_division ?6 ?7
-26206: Id : 5, {_}:
- left_division ?9 (multiply ?9 ?10) =>= ?10
- [10, 9] by left_division_multiply ?9 ?10
-26206: Id : 6, {_}:
- multiply (right_division ?12 ?13) ?13 =>= ?12
- [13, 12] by multiply_right_division ?12 ?13
-26206: Id : 7, {_}:
- right_division (multiply ?15 ?16) ?16 =>= ?15
- [16, 15] by right_division_multiply ?15 ?16
-26206: Id : 8, {_}:
- multiply ?18 (right_inverse ?18) =>= identity
- [18] by right_inverse ?18
-26206: Id : 9, {_}:
- multiply (left_inverse ?20) ?20 =>= identity
- [20] by left_inverse ?20
-26206: Id : 10, {_}:
- multiply (multiply (multiply ?22 ?23) ?22) ?24
- =>=
- multiply ?22 (multiply ?23 (multiply ?22 ?24))
- [24, 23, 22] by moufang3 ?22 ?23 ?24
-26206: Goal:
-26206: Id : 1, {_}:
- multiply x (multiply (multiply y z) x)
- =<=
- multiply (multiply x y) (multiply z x)
- [] by prove_moufang4
-26206: Order:
-26206: lpo
-26206: Leaf order:
-26206: y 2 0 2 1,1,2,2
-26206: z 2 0 2 2,1,2,2
-26206: identity 4 0 0
-26206: x 4 0 4 1,2
-26206: right_inverse 1 1 0
-26206: left_inverse 1 1 0
-26206: left_division 2 2 0
-26206: right_division 2 2 0
-26206: multiply 20 2 6 0,2
-Statistics :
-Max weight : 20
-Found proof, 29.317631s
-% SZS status Unsatisfiable for GRP205-1.p
-% SZS output start CNFRefutation for GRP205-1.p
-Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
-Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
-Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
-Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
-Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
-Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
-Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
-Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
-Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
-Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
-Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
-Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
-Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
-Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2
-Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
-Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
-Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
-Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
-Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
-Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
-Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
-Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2
-Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2
-Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
-Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2
-Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2
-Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2
-Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2
-Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3
-Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
-Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
-Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2
-Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2
-Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2
-Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2
-Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2
-Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3
-Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2
-Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3
-Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2
-Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
-Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2
-Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
-Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3
-Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3
-Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2
-Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2
-Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3
-Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2
-Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2
-Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3
-Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3
-Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3
-Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3
-Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3
-Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2
-Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3
-Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
-Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
-Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
-Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2
-Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2
-Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3
-Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3
-Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2
-Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2
-Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3
-Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2
-Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3
-Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2
-Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2
-Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3
-Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2
-Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3
-Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2
-Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3
-Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2
-Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3
-Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3
-Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2
-Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2
-Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3
-Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2
-Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3
-Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2
-Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3
-Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3
-Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3
-Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2
-Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3
-Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3
-Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2
-Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3
-Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2
-Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2
-Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3
-Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3
-Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
-Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
-Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3
-Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2
-Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2
-Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2
-Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2
-Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2
-Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3
-Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2
-Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3
-Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2
-Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3
-Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2
-Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3
-Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3
-Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2
-Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2
-Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3
-Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2
-Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
-Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2
-Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3
-Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2
-Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3
-Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2
-Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3
-Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2
-Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2
-Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3
-Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2
-Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3
-Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2
-Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3
-Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2
-Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2
-Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3
-Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3
-Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2
-Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2
-Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2
-Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3
-Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2
-Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2
-Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3
-Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2
-Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3
-Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3
-Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2
-Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2
-Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2
-Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3
-Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2
-Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3
-Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3
-Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3
-Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3
-Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4
-% SZS output end CNFRefutation for GRP205-1.p
-26205: solved GRP205-1.p in 14.680917 using kbo
-26205: status Unsatisfiable for GRP205-1.p
-NO CLASH, using fixed ground order
-26244: Facts:
-26244: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-26244: Goal:
-26244: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-26244: Order:
-26244: nrkbo
-26244: Leaf order:
-26244: z 2 0 2 1,1,1,2,1,2,2
-26244: u 2 0 2 1,1,2,1,2,1,2,2
-26244: y 2 0 2 1,1,2,2
-26244: x 2 0 2 1,2
-26244: inverse 6 1 3 0,2,2
-26244: multiply 12 2 6 0,2
-NO CLASH, using fixed ground order
-26245: Facts:
-26245: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-26245: Goal:
-26245: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-26245: Order:
-26245: kbo
-26245: Leaf order:
-26245: z 2 0 2 1,1,1,2,1,2,2
-26245: u 2 0 2 1,1,2,1,2,1,2,2
-26245: y 2 0 2 1,1,2,2
-26245: x 2 0 2 1,2
-26245: inverse 6 1 3 0,2,2
-26245: multiply 12 2 6 0,2
-NO CLASH, using fixed ground order
-26246: Facts:
-26246: Id : 2, {_}:
- multiply ?2
- (inverse
- (multiply ?3
- (multiply
- (multiply (multiply ?4 (inverse ?4))
- (inverse (multiply ?2 ?3))) ?2)))
- =>=
- ?2
- [4, 3, 2] by single_non_axiom ?2 ?3 ?4
-26246: Goal:
-26246: Id : 1, {_}:
- multiply x
- (inverse
- (multiply y
- (multiply
- (multiply (multiply z (inverse z)) (inverse (multiply u y)))
- x)))
- =>=
- u
- [] by try_prove_this_axiom
-26246: Order:
-26246: lpo
-26246: Leaf order:
-26246: z 2 0 2 1,1,1,2,1,2,2
-26246: u 2 0 2 1,1,2,1,2,1,2,2
-26246: y 2 0 2 1,1,2,2
-26246: x 2 0 2 1,2
-26246: inverse 6 1 3 0,2,2
-26246: multiply 12 2 6 0,2
-% SZS status Timeout for GRP207-1.p
-Fatal error: exception Assert_failure("matitaprover.ml", 269, 46)
-NO CLASH, using fixed ground order
-26289: Facts:
-26289: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26289: Goal:
-26289: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26289: Order:
-26289: nrkbo
-26289: Leaf order:
-26289: a3 2 0 2 1,1,2
-26289: b3 2 0 2 2,1,2
-26289: c3 2 0 2 2,2
-26289: inverse 7 1 0
-26289: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-26290: Facts:
-26290: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26290: Goal:
-26290: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26290: Order:
-26290: kbo
-26290: Leaf order:
-26290: a3 2 0 2 1,1,2
-26290: b3 2 0 2 2,1,2
-26290: c3 2 0 2 2,2
-26290: inverse 7 1 0
-26290: multiply 10 2 4 0,2
-NO CLASH, using fixed ground order
-26291: Facts:
-26291: Id : 2, {_}:
- inverse
- (multiply
- (inverse
- (multiply ?2
- (inverse
- (multiply (inverse ?3)
- (inverse
- (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
- (multiply ?2 ?4))
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26291: Goal:
-26291: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26291: Order:
-26291: lpo
-26291: Leaf order:
-26291: a3 2 0 2 1,1,2
-26291: b3 2 0 2 2,1,2
-26291: c3 2 0 2 2,2
-26291: inverse 7 1 0
-26291: multiply 10 2 4 0,2
-% SZS status Timeout for GRP420-1.p
-NO CLASH, using fixed ground order
-26320: Facts:
-26320: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26320: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-26320: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-26320: Goal:
-26320: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26320: Order:
-26320: nrkbo
-26320: Leaf order:
-26320: a3 2 0 2 1,1,2
-26320: b3 2 0 2 2,1,2
-26320: c3 2 0 2 2,2
-26320: inverse 1 1 0
-26320: multiply 5 2 4 0,2
-26320: divide 13 2 0
-NO CLASH, using fixed ground order
-26321: Facts:
-26321: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26321: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-26321: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-26321: Goal:
-26321: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26321: Order:
-26321: kbo
-26321: Leaf order:
-26321: a3 2 0 2 1,1,2
-26321: b3 2 0 2 2,1,2
-26321: c3 2 0 2 2,2
-26321: inverse 1 1 0
-26321: multiply 5 2 4 0,2
-26321: divide 13 2 0
-NO CLASH, using fixed ground order
-26322: Facts:
-26322: Id : 2, {_}:
- divide
- (divide (divide ?2 ?2)
- (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
- ?4
- =>=
- ?3
- [4, 3, 2] by single_axiom ?2 ?3 ?4
-26322: Id : 3, {_}:
- multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
- [8, 7, 6] by multiply ?6 ?7 ?8
-26322: Id : 4, {_}:
- inverse ?10 =<= divide (divide ?11 ?11) ?10
- [11, 10] by inverse ?10 ?11
-26322: Goal:
-26322: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-26322: Order:
-26322: lpo
-26322: Leaf order:
-26322: a3 2 0 2 1,1,2
-26322: b3 2 0 2 2,1,2
-26322: c3 2 0 2 2,2
-26322: inverse 1 1 0
-26322: multiply 5 2 4 0,2
-26322: divide 13 2 0
-Statistics :
-Max weight : 38
-Found proof, 2.679419s
-% SZS status Unsatisfiable for GRP453-1.p
-% SZS output start CNFRefutation for GRP453-1.p
-Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
-Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
-Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
-Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
-Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
-Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
-Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
-Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
-Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
-Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
-Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
-Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
-Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
-Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
-Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
-Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
-Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
-Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
-Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2
-Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2
-Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2
-Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
-Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3
-Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2
-Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2
-Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3
-Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
-Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2
-Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3
-Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3
-Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3
-Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2
-Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3
-Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2
-Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2
-Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2
-Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2
-Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3
-Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3
-Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2
-Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2
-Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2
-Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2
-Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2
-Id : 2675, {_}: inverse (inverse ?6008) =<= divide (multiply ?6008 (inverse (inverse ?6009))) ?6009 [6009, 6008] by Demod 1854 with 29 at 1,3
-Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
-Id : 2701, {_}: inverse (inverse (inverse (inverse (divide ?6099 ?6099)))) =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Super 2675 with 224 at 1,3
-Id : 2754, {_}: divide ?6099 ?6099 =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Demod 2701 with 1559 at 2
-Id : 2755, {_}: divide ?6099 ?6099 =?= divide ?6100 ?6100 [6100, 6099] by Demod 2754 with 1559 at 1,3
-Id : 2822, {_}: divide (inverse (divide ?6299 (divide (inverse ?6300) (divide (inverse ?6299) ?6301)))) ?6301 =?= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6301, 6300, 6299] by Super 145 with 2755 at 2,1,3
-Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
-Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
-Id : 2899, {_}: inverse ?6300 =<= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6300] by Demod 2822 with 31 at 2
-Id : 2957, {_}: divide ?6663 (divide ?6664 ?6664) =>= inverse (inverse (inverse (inverse ?6663))) [6664, 6663] by Super 1559 with 2899 at 1,1,1,3
-Id : 3011, {_}: divide ?6663 (divide ?6664 ?6664) =>= ?6663 [6664, 6663] by Demod 2957 with 1559 at 3
-Id : 3087, {_}: divide (inverse (divide ?6934 ?6935)) (divide ?6936 ?6936) =>= inverse (inverse (multiply ?6935 (inverse ?6934))) [6936, 6935, 6934] by Super 250 with 3011 at 2,1,1,3
-Id : 3149, {_}: inverse (divide ?6934 ?6935) =<= inverse (inverse (multiply ?6935 (inverse ?6934))) [6935, 6934] by Demod 3087 with 3011 at 2
-Id : 3445, {_}: inverse (divide ?7675 ?7676) =<= divide (inverse (inverse ?7676)) ?7675 [7676, 7675] by Demod 3149 with 936 at 3
-Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2
-Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3
-Id : 3150, {_}: inverse (divide ?6934 ?6935) =<= divide (inverse (inverse ?6935)) ?6934 [6935, 6934] by Demod 3149 with 936 at 3
-Id : 3402, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3150 at 1,1,3
-Id : 3466, {_}: inverse (divide ?7752 (inverse (divide ?7753 ?7754))) =>= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Super 3445 with 3402 at 1,3
-Id : 3559, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =<= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Demod 3466 with 29 at 1,2
-Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
-Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
-Id : 3400, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3150 at 3
-Id : 3405, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3400 with 29 at 1,3
-Id : 3088, {_}: multiply ?6938 (divide ?6939 ?6939) =>= inverse (inverse ?6938) [6939, 6938] by Super 1825 with 3011 at 1,2
-Id : 3773, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3405 with 3088 at 1,3
-Id : 3776, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3773 at 2,2
-Id : 4266, {_}: inverse (multiply ?8883 (divide ?8884 ?8885)) =>= divide (divide ?8885 ?8884) ?8883 [8885, 8884, 8883] by Demod 3559 with 3776 at 1,3
-Id : 3463, {_}: inverse (divide ?7741 (inverse (inverse ?7742))) =>= divide ?7742 ?7741 [7742, 7741] by Super 3445 with 1559 at 1,3
-Id : 3558, {_}: inverse (multiply ?7741 (inverse ?7742)) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3463 with 29 at 1,2
-Id : 3777, {_}: inverse (divide ?7741 ?7742) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3558 with 3776 at 1,2
-Id : 3787, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3777 at 1,2
-Id : 3399, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3150 at 2
-Id : 3783, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3399 with 3777 at 2
-Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2
-Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2
-Id : 3779, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3776 at 2
-Id : 3799, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3783 with 3779 at 2
-Id : 3800, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3787 with 3799 at 3
-Id : 4296, {_}: inverse (divide (divide ?9013 ?9014) ?9015) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9015, 9014, 9013] by Super 4266 with 3800 at 1,2
-Id : 4346, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9014, 9013, 9015] by Demod 4296 with 3777 at 2
-Id : 4347, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (multiply ?9015 ?9014) ?9013 [9014, 9013, 9015] by Demod 4346 with 29 at 1,3
-Id : 4244, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =>= divide (divide ?7754 ?7753) ?7752 [7754, 7753, 7752] by Demod 3559 with 3776 at 1,3
-Id : 4262, {_}: inverse (divide (divide ?8865 ?8866) ?8867) =>= multiply ?8867 (divide ?8866 ?8865) [8867, 8866, 8865] by Super 3799 with 4244 at 1,2
-Id : 4303, {_}: divide ?8867 (divide ?8865 ?8866) =>= multiply ?8867 (divide ?8866 ?8865) [8866, 8865, 8867] by Demod 4262 with 3777 at 2
-Id : 4889, {_}: multiply ?9015 (divide ?9014 ?9013) =<= divide (multiply ?9015 ?9014) ?9013 [9013, 9014, 9015] by Demod 4347 with 4303 at 2
-Id : 4905, {_}: multiply (multiply ?10384 ?10385) ?10386 =<= multiply ?10384 (divide ?10385 (inverse ?10386)) [10386, 10385, 10384] by Super 29 with 4889 at 3
-Id : 4955, {_}: multiply (multiply ?10384 ?10385) ?10386 =>= multiply ?10384 (multiply ?10385 ?10386) [10386, 10385, 10384] by Demod 4905 with 29 at 2,3
-Id : 5096, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 4955 at 2
-Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
-% SZS output end CNFRefutation for GRP453-1.p
-26321: solved GRP453-1.p in 1.372085 using kbo
-26321: status Unsatisfiable for GRP453-1.p
-Fatal error: exception Assert_failure("matitaprover.ml", 269, 46)
-NO CLASH, using fixed ground order
-26331: Facts:
-26331: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-26331: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-26331: Goal:
-26331: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-26331: Order:
-26331: nrkbo
-26331: Leaf order:
-26331: a 2 0 2 1,1,2
-26331: b 2 0 2 2,1,2
-26331: c 2 0 2 2,2
-26331: meet 4 2 0
-26331: join 7 2 4 0,2
-NO CLASH, using fixed ground order
-26332: Facts:
-26332: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-26332: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-26332: Goal:
-26332: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-26332: Order:
-26332: kbo
-26332: Leaf order:
-26332: a 2 0 2 1,1,2
-26332: b 2 0 2 2,1,2
-26332: c 2 0 2 2,2
-26332: meet 4 2 0
-26332: join 7 2 4 0,2
-NO CLASH, using fixed ground order
-26333: Facts:
-26333: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-26333: Id : 3, {_}:
- meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5)
- [7, 6, 5] by distribution ?5 ?6 ?7
-26333: Goal:
-26333: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_associativity_of_join
-26333: Order:
-26333: lpo
-26333: Leaf order:
-26333: a 2 0 2 1,1,2
-26333: b 2 0 2 2,1,2
-26333: c 2 0 2 2,2
-26333: meet 4 2 0
-26333: join 7 2 4 0,2
-Statistics :
-Max weight : 31
-Found proof, 28.344880s
-% SZS status Unsatisfiable for LAT007-1.p
-% SZS output start CNFRefutation for LAT007-1.p
-Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7
-Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
-Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20
-Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3
-Id : 13, {_}: meet (meet ?44 ?45) (meet ?45 (join ?46 ?44)) =>= meet ?44 ?45 [46, 45, 44] by Super 2 with 3 at 2,2
-Id : 15, {_}: meet (meet ?53 ?54) ?54 =>= meet ?53 ?54 [54, 53] by Super 13 with 2 at 2,2
-Id : 21, {_}: meet ?68 (join (meet ?69 ?68) ?70) =<= join (meet ?70 ?68) (meet ?69 ?68) [70, 69, 68] by Super 3 with 15 at 2,3
-Id : 69, {_}: meet ?209 (join (meet ?210 ?209) ?211) =>= meet ?209 (join ?210 ?211) [211, 210, 209] by Demod 21 with 3 at 3
-Id : 74, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =<= meet ?231 (join ?233 (meet ?232 ?231)) [233, 232, 231] by Super 69 with 3 at 2,2
-Id : 22, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =<= join (meet ?74 ?72) (meet ?73 ?72) [74, 73, 72] by Super 3 with 15 at 1,3
-Id : 33, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =>= meet ?72 (join ?73 ?74) [74, 73, 72] by Demod 22 with 3 at 3
-Id : 219, {_}: meet ?572 (meet ?572 (join ?573 ?574)) =>= meet ?572 (join ?574 ?573) [574, 573, 572] by Demod 74 with 33 at 3
-Id : 224, {_}: meet ?597 ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Super 219 with 2 at 2,2
-Id : 244, {_}: meet (join ?635 ?636) (join ?635 ?636) =>= join (meet ?636 ?636) ?635 [636, 635] by Super 8 with 224 at 1,3
-Id : 247, {_}: meet ?644 ?644 =>= ?644 [644] by Super 2 with 224 at 2
-Id : 1803, {_}: join ?635 ?636 =<= join (meet ?636 ?636) ?635 [636, 635] by Demod 244 with 247 at 2
-Id : 1804, {_}: join ?635 ?636 =?= join ?636 ?635 [636, 635] by Demod 1803 with 247 at 1,3
-Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3
-Id : 6, {_}: meet (meet ?14 ?15) (meet ?15 (join ?16 ?14)) =>= meet ?14 ?15 [16, 15, 14] by Super 2 with 3 at 2,2
-Id : 11, {_}: meet (meet ?34 (join ?35 ?36)) (join (meet ?36 ?34) ?37) =<= join (meet ?37 (meet ?34 (join ?35 ?36))) (meet ?36 ?34) [37, 36, 35, 34] by Super 3 with 6 at 2,3
-Id : 364, {_}: meet (meet ?919 (join ?920 ?919)) (join (meet ?919 ?919) ?921) =>= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [921, 920, 919] by Super 11 with 247 at 2,3
-Id : 349, {_}: ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Demod 224 with 247 at 2
-Id : 370, {_}: meet ?919 (join (meet ?919 ?919) ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 364 with 349 at 1,2
-Id : 371, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 370 with 247 at 1,2,2
-Id : 372, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 371 with 349 at 2,1,3
-Id : 411, {_}: ?977 =<= join (meet ?978 ?977) ?977 [978, 977] by Demod 372 with 2 at 2
-Id : 420, {_}: join ?1006 ?1007 =<= join ?1007 (join ?1006 ?1007) [1007, 1006] by Super 411 with 349 at 1,3
-Id : 703, {_}: meet (join ?1582 (join ?1583 ?1582)) (join ?1584 ?1582) =>= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1583, 1582] by Super 9 with 420 at 2,2,3
-Id : 2541, {_}: meet (join ?5116 ?5117) (join ?5118 ?5117) =<= join ?5117 (meet ?5118 (join ?5116 ?5117)) [5118, 5117, 5116] by Demod 703 with 420 at 1,2
-Id : 419, {_}: ?1004 =<= join ?1004 ?1004 [1004] by Super 411 with 247 at 1,3
-Id : 446, {_}: meet ?1028 (join ?1029 ?1029) =>= meet ?1029 ?1028 [1029, 1028] by Super 3 with 419 at 3
-Id : 462, {_}: meet ?1028 ?1029 =?= meet ?1029 ?1028 [1029, 1028] by Demod 446 with 419 at 2,2
-Id : 2566, {_}: meet (join ?5222 ?5223) (join ?5224 ?5223) =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5224, 5223, 5222] by Super 2541 with 462 at 2,3
-Id : 1841, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =<= join ?3986 (meet ?3988 (join ?3987 ?3986)) [3988, 3987, 3986] by Super 9 with 1804 at 2,2,3
-Id : 731, {_}: meet (join ?1583 ?1582) (join ?1584 ?1582) =<= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1582, 1583] by Demod 703 with 420 at 1,2
-Id : 6413, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =?= meet (join ?3987 ?3986) (join ?3988 ?3986) [3988, 3987, 3986] by Demod 1841 with 731 at 3
-Id : 210, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =>= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 74 with 33 at 3
-Id : 449, {_}: meet ?1037 (meet ?1037 ?1038) =?= meet ?1037 (join ?1038 ?1038) [1038, 1037] by Super 210 with 419 at 2,2,2
-Id : 457, {_}: meet ?1037 (meet ?1037 ?1038) =>= meet ?1037 ?1038 [1038, 1037] by Demod 449 with 419 at 2,3
-Id : 754, {_}: meet ?231 (join ?232 ?233) =?= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 210 with 457 at 2
-Id : 32, {_}: meet ?68 (join (meet ?69 ?68) ?70) =>= meet ?68 (join ?69 ?70) [70, 69, 68] by Demod 21 with 3 at 3
-Id : 763, {_}: meet (meet ?1697 ?1698) (join (meet ?1697 ?1698) ?1699) =>= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Super 32 with 457 at 1,2,2
-Id : 793, {_}: meet ?1697 ?1698 =<= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Demod 763 with 2 at 2
-Id : 2682, {_}: meet (join ?5359 ?5360) (join ?5361 (meet ?5359 ?5362)) =<= join (meet ?5359 ?5362) (meet ?5361 (join ?5359 ?5360)) [5362, 5361, 5360, 5359] by Super 3 with 793 at 1,3
-Id : 1421, {_}: meet ?2943 (join ?2944 (meet ?2943 ?2945)) =>= meet ?2943 (join ?2944 ?2945) [2945, 2944, 2943] by Super 33 with 462 at 2,2,2
-Id : 4338, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= join (meet ?8617 (join ?8616 ?8618)) ?8616 [8618, 8617, 8616] by Super 8 with 1421 at 1,3
-Id : 4448, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= meet (join ?8616 ?8618) (join ?8616 ?8617) [8618, 8617, 8616] by Demod 4338 with 8 at 3
-Id : 62692, {_}: meet (join ?135834 ?135835) (join (join ?135834 (meet ?135835 ?135836)) (meet ?135834 ?135837)) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135837, 135836, 135835, 135834] by Super 2682 with 4448 at 2,3
-Id : 62942, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135836, 135837, 135835, 135834] by Demod 62692 with 754 at 2
-Id : 62943, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135836, 135837, 135835, 135834] by Demod 62942 with 2682 at 3
-Id : 373, {_}: ?919 =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 372 with 2 at 2
-Id : 2674, {_}: join ?5321 ?5322 =<= join (meet ?5321 ?5323) (join ?5321 ?5322) [5323, 5322, 5321] by Super 373 with 793 at 1,3
-Id : 62944, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135837, 135836, 135835, 135834] by Demod 62943 with 2674 at 2,2
-Id : 62945, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135836, 135835, 135834] by Demod 62944 with 754 at 3
-Id : 762, {_}: meet (meet ?1693 ?1694) (meet (meet ?1693 ?1694) (join ?1695 ?1693)) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Super 6 with 457 at 1,2
-Id : 794, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Demod 762 with 457 at 2
-Id : 795, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 ?1694 [1695, 1694, 1693] by Demod 794 with 457 at 3
-Id : 2860, {_}: meet (join ?5717 ?5718) (join ?5717 (meet ?5718 ?5719)) =>= join (meet ?5718 ?5719) ?5717 [5719, 5718, 5717] by Super 8 with 795 at 1,3
-Id : 62946, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135834, 135836, 135835] by Demod 62945 with 2860 at 2
-Id : 62947, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join ?135834 ?135836) [135834, 135836, 135835] by Demod 62946 with 2674 at 2,3
-Id : 63610, {_}: meet (join ?137323 ?137324) (join ?137325 ?137323) =>= join (meet ?137324 ?137325) ?137323 [137325, 137324, 137323] by Super 754 with 62947 at 3
-Id : 64209, {_}: join (meet ?3987 ?3988) ?3986 =<= meet (join ?3987 ?3986) (join ?3988 ?3986) [3986, 3988, 3987] by Demod 6413 with 63610 at 2
-Id : 64222, {_}: join (meet ?5222 ?5224) ?5223 =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5223, 5224, 5222] by Demod 2566 with 64209 at 2
-Id : 64386, {_}: join (meet ?139191 (join ?139192 ?139191)) ?139193 =?= join ?139193 (join (meet ?139193 ?139192) ?139191) [139193, 139192, 139191] by Super 64222 with 63610 at 2,3
-Id : 66054, {_}: join ?143110 ?143111 =<= join ?143111 (join (meet ?143111 ?143112) ?143110) [143112, 143111, 143110] by Demod 64386 with 349 at 1,2
-Id : 36, {_}: meet (join ?109 ?110) (join ?109 ?111) =<= join (meet ?111 (join ?109 ?110)) ?109 [111, 110, 109] by Super 7 with 2 at 2,3
-Id : 39, {_}: meet (join ?123 ?124) (join ?123 ?123) =>= join ?123 ?123 [124, 123] by Super 36 with 2 at 1,3
-Id : 438, {_}: meet (join ?123 ?124) ?123 =>= join ?123 ?123 [124, 123] by Demod 39 with 419 at 2,2
-Id : 439, {_}: meet (join ?123 ?124) ?123 =>= ?123 [124, 123] by Demod 438 with 419 at 3
-Id : 66061, {_}: join ?143140 (join ?143141 ?143142) =<= join (join ?143141 ?143142) (join ?143141 ?143140) [143142, 143141, 143140] by Super 66054 with 439 at 1,2,3
-Id : 706, {_}: meet (join ?1593 (join ?1594 ?1593)) (join ?1593 ?1595) =>= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1594, 1593] by Super 8 with 420 at 2,1,3
-Id : 2402, {_}: meet (join ?4835 ?4836) (join ?4836 ?4837) =<= join (meet ?4837 (join ?4835 ?4836)) ?4836 [4837, 4836, 4835] by Demod 706 with 420 at 1,2
-Id : 2426, {_}: meet (join ?4936 ?4937) (join ?4937 ?4938) =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4938, 4937, 4936] by Super 2402 with 462 at 1,3
-Id : 1831, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =<= join (meet ?3950 (join ?3949 ?3948)) ?3948 [3950, 3949, 3948] by Super 8 with 1804 at 2,1,3
-Id : 729, {_}: meet (join ?1594 ?1593) (join ?1593 ?1595) =<= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1593, 1594] by Demod 706 with 420 at 1,2
-Id : 5899, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =?= meet (join ?3949 ?3948) (join ?3948 ?3950) [3950, 3949, 3948] by Demod 1831 with 729 at 3
-Id : 63510, {_}: join (meet ?3949 ?3950) ?3948 =<= meet (join ?3949 ?3948) (join ?3948 ?3950) [3948, 3950, 3949] by Demod 5899 with 62947 at 2
-Id : 63518, {_}: join (meet ?4936 ?4938) ?4937 =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4937, 4938, 4936] by Demod 2426 with 63510 at 2
-Id : 63690, {_}: join (meet ?137703 (join ?137703 ?137704)) ?137705 =?= join (join (meet ?137705 ?137704) ?137703) ?137705 [137705, 137704, 137703] by Super 63518 with 62947 at 1,3
-Id : 65015, {_}: join ?140539 ?140540 =<= join (join (meet ?140540 ?140541) ?140539) ?140540 [140541, 140540, 140539] by Demod 63690 with 2 at 1,2
-Id : 65022, {_}: join ?140569 (join ?140570 ?140571) =<= join (join ?140570 ?140569) (join ?140570 ?140571) [140571, 140570, 140569] by Super 65015 with 439 at 1,1,3
-Id : 71034, {_}: join ?143140 (join ?143141 ?143142) =?= join ?143142 (join ?143141 ?143140) [143142, 143141, 143140] by Demod 66061 with 65022 at 3
-Id : 709, {_}: meet (join ?1606 ?1607) ?1607 =>= ?1607 [1607, 1606] by Super 439 with 420 at 1,2
-Id : 1049, {_}: meet ?2275 (join ?2275 ?2276) =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2277, 2276, 2275] by Super 32 with 709 at 1,2,2
-Id : 1082, {_}: ?2275 =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2276, 2277, 2275] by Demod 1049 with 2 at 2
-Id : 10434, {_}: join (join ?21238 ?21239) ?21240 =<= join ?21239 (join (join ?21238 ?21239) ?21240) [21240, 21239, 21238] by Super 373 with 1082 at 1,3
-Id : 10435, {_}: join (join ?21242 ?21243) ?21244 =<= join ?21243 (join (join ?21243 ?21242) ?21244) [21244, 21243, 21242] by Super 10434 with 1804 at 1,2,3
-Id : 7878, {_}: join ?15712 ?15713 =<= join (meet ?15712 ?15714) (join ?15712 ?15713) [15714, 15713, 15712] by Super 373 with 793 at 1,3
-Id : 7917, {_}: join (join ?15885 ?15886) ?15887 =<= join ?15885 (join (join ?15885 ?15886) ?15887) [15887, 15886, 15885] by Super 7878 with 439 at 1,3
-Id : 21540, {_}: join (join ?21242 ?21243) ?21244 =?= join (join ?21243 ?21242) ?21244 [21244, 21243, 21242] by Demod 10435 with 7917 at 3
-Id : 63854, {_}: join ?137703 ?137705 =<= join (join (meet ?137705 ?137704) ?137703) ?137705 [137704, 137705, 137703] by Demod 63690 with 2 at 1,2
-Id : 67172, {_}: join (join ?145721 (meet ?145722 ?145723)) ?145722 =>= join ?145721 ?145722 [145723, 145722, 145721] by Super 21540 with 63854 at 3
-Id : 67179, {_}: join (join ?145751 ?145752) (join ?145752 ?145753) =>= join ?145751 (join ?145752 ?145753) [145753, 145752, 145751] by Super 67172 with 439 at 2,1,2
-Id : 66065, {_}: join ?143156 (join ?143157 ?143158) =<= join (join ?143157 ?143158) (join ?143158 ?143156) [143158, 143157, 143156] by Super 66054 with 709 at 1,2,3
-Id : 73159, {_}: join ?145753 (join ?145751 ?145752) =?= join ?145751 (join ?145752 ?145753) [145752, 145751, 145753] by Demod 67179 with 66065 at 2
-Id : 359, {_}: meet ?904 (join ?905 ?904) =<= join ?904 (meet ?905 ?904) [905, 904] by Super 3 with 247 at 1,3
-Id : 386, {_}: ?904 =<= join ?904 (meet ?905 ?904) [905, 904] by Demod 359 with 349 at 2
-Id : 1047, {_}: meet ?2267 (meet ?2267 (join ?2268 (join ?2269 ?2267))) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Super 6 with 709 at 1,2
-Id : 1084, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Demod 1047 with 457 at 2
-Id : 1085, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= ?2267 [2269, 2268, 2267] by Demod 1084 with 709 at 3
-Id : 11489, {_}: join ?23526 (join ?23527 ?23528) =<= join (join ?23526 (join ?23527 ?23528)) ?23528 [23528, 23527, 23526] by Super 386 with 1085 at 2,3
-Id : 11490, {_}: join ?23530 (join ?23531 ?23532) =<= join (join ?23530 (join ?23532 ?23531)) ?23532 [23532, 23531, 23530] by Super 11489 with 1804 at 2,1,3
-Id : 2878, {_}: meet (meet ?5800 ?5801) (join ?5802 ?5800) =>= meet ?5800 ?5801 [5802, 5801, 5800] by Demod 794 with 457 at 3
-Id : 2907, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= meet (join ?5929 ?5931) ?5929 [5931, 5930, 5929] by Super 2878 with 439 at 1,2
-Id : 3014, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= ?5929 [5931, 5930, 5929] by Demod 2907 with 439 at 3
-Id : 10163, {_}: join ?20474 (join ?20475 ?20476) =<= join (join ?20474 (join ?20475 ?20476)) ?20475 [20476, 20475, 20474] by Super 386 with 3014 at 2,3
-Id : 22205, {_}: join ?23530 (join ?23531 ?23532) =?= join ?23530 (join ?23532 ?23531) [23532, 23531, 23530] by Demod 11490 with 10163 at 3
-Id : 73995, {_}: join a (join b c) === join a (join b c) [] by Demod 73994 with 22205 at 2
-Id : 73994, {_}: join a (join c b) =>= join a (join b c) [] by Demod 73993 with 73159 at 2
-Id : 73993, {_}: join b (join a c) =>= join a (join b c) [] by Demod 73992 with 71034 at 2
-Id : 73992, {_}: join c (join a b) =>= join a (join b c) [] by Demod 1 with 1804 at 2
-Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join
-% SZS output end CNFRefutation for LAT007-1.p
-26331: solved LAT007-1.p in 28.241764 using nrkbo
-26331: status Unsatisfiable for LAT007-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-26339: Facts:
-26339: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-26339: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-26339: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-26339: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-26339: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-26339: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-26339: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-26339: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-26339: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-26339: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-26339: Goal:
-NO CLASH, using fixed ground order
-26340: Facts:
-26340: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-26340: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-26340: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-26340: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-26340: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-26340: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-26340: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-26340: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-26340: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-26340: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-26340: Goal:
-26338: Facts:
-26340: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-26340: Order:
-26340: lpo
-26340: Leaf order:
-26340: n0 1 0 0
-26340: n1 2 0 1 3
-26340: b 6 0 6 1,2,1,1,1,2
-26340: a 9 0 9 1,1,1,1,2
-26340: complement 18 1 9 0,1,2
-26340: meet 15 2 6 0,1,1,1,2
-26340: join 20 2 8 0,2
-26339: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-26339: Order:
-26339: kbo
-26339: Leaf order:
-26339: n0 1 0 0
-26339: n1 2 0 1 3
-26339: b 6 0 6 1,2,1,1,1,2
-26339: a 9 0 9 1,1,1,1,2
-26339: complement 18 1 9 0,1,2
-26339: meet 15 2 6 0,1,1,1,2
-26339: join 20 2 8 0,2
-26338: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-26338: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-26338: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-26338: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-26338: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-26338: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-26338: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-26338: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-26338: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-26338: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-26338: Goal:
-26338: Id : 1, {_}:
- join (complement (join (meet a (complement b)) (complement a)))
- (join (meet a (complement b))
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (complement (meet (join a (complement b)) (join a b))))))
- =>=
- n1
- [] by prove_e1
-26338: Order:
-26338: nrkbo
-26338: Leaf order:
-26338: n0 1 0 0
-26338: n1 2 0 1 3
-26338: b 6 0 6 1,2,1,1,1,2
-26338: a 9 0 9 1,1,1,1,2
-26338: complement 18 1 9 0,1,2
-26338: meet 15 2 6 0,1,1,1,2
-26338: join 20 2 8 0,2
-% SZS status Timeout for LAT016-1.p
-NO CLASH, using fixed ground order
-26368: Facts:
-26368: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26368: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26368: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-26368: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-26368: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-26368: Id : 7, {_}:
- join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-26368: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-26368: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-26368: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-26368: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-26368: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-26368: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-26368: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-26368: Goal:
-26368: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26368: Order:
-26368: nrkbo
-26368: Leaf order:
-26368: a 2 0 2 1,2
-26368: b 2 0 2 2,2
-26368: meet 14 2 1 0,2
-26368: meet2 14 2 1 0,3
-26368: join 19 2 0
-NO CLASH, using fixed ground order
-26369: Facts:
-26369: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26369: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26369: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-26369: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-26369: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-26369: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-26369: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-26369: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-26369: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-26369: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-26369: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-26369: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-26369: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-26369: Goal:
-26369: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26369: Order:
-26369: kbo
-26369: Leaf order:
-26369: a 2 0 2 1,2
-26369: b 2 0 2 2,2
-26369: meet 14 2 1 0,2
-26369: meet2 14 2 1 0,3
-26369: join 19 2 0
-NO CLASH, using fixed ground order
-26370: Facts:
-26370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26370: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-26370: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-26370: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-26370: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-26370: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-26370: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-26370: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
-26370: Id : 11, {_}:
- meet2 ?30 ?31 =?= meet2 ?31 ?30
- [31, 30] by commutativity_of_meet2 ?30 ?31
-26370: Id : 12, {_}:
- meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
- [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
-26370: Id : 13, {_}:
- join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
- =>=
- meet2 ?37 (join ?38 ?39)
- [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
-26370: Id : 14, {_}:
- meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
- =>=
- join ?41 (meet2 ?42 ?43)
- [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
-26370: Goal:
-26370: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26370: Order:
-26370: lpo
-26370: Leaf order:
-26370: a 2 0 2 1,2
-26370: b 2 0 2 2,2
-26370: meet 14 2 1 0,2
-26370: meet2 14 2 1 0,3
-26370: join 19 2 0
-% SZS status Timeout for LAT024-1.p
-NO CLASH, using fixed ground order
-26386: Facts:
-26386: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26386: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26386: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26386: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26386: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26386: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26386: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-26386: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-26386: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-26386: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-26386: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-26386: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-26386: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-26386: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-26386: Goal:
-26386: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26386: Order:
-26386: nrkbo
-26386: Leaf order:
-26386: a 2 0 2 1,2
-26386: b 2 0 2 2,2
-26386: meet 9 2 1 0,2
-26386: meet2 9 2 1 0,3
-26386: join 13 2 0
-NO CLASH, using fixed ground order
-26387: Facts:
-26387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26387: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26387: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26387: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-26387: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-26387: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-26387: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-26387: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-26387: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-26387: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-NO CLASH, using fixed ground order
-26388: Facts:
-26388: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26388: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26388: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26388: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26388: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26388: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26388: Id : 8, {_}:
- join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
- [20, 19, 18] by tnl_1 ?18 ?19 ?20
-26388: Id : 9, {_}:
- meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
- [24, 23, 22] by tnl_2 ?22 ?23 ?24
-26388: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
-26388: Id : 11, {_}:
- meet2 ?28 (join ?28 ?29) =>= ?28
- [29, 28] by absorption1_2 ?28 ?29
-26388: Id : 12, {_}:
- join ?31 (meet2 ?31 ?32) =>= ?31
- [32, 31] by absorption2_2 ?31 ?32
-26388: Id : 13, {_}:
- meet2 ?34 ?35 =?= meet2 ?35 ?34
- [35, 34] by commutativity_of_meet2 ?34 ?35
-26388: Id : 14, {_}:
- join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
- [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
-26388: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-26388: Goal:
-26388: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26388: Order:
-26388: lpo
-26388: Leaf order:
-26388: a 2 0 2 1,2
-26388: b 2 0 2 2,2
-26388: meet 9 2 1 0,2
-26388: meet2 9 2 1 0,3
-26388: join 13 2 0
-26387: Id : 15, {_}:
- meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
- [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
-26387: Goal:
-26387: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
-26387: Order:
-26387: kbo
-26387: Leaf order:
-26387: a 2 0 2 1,2
-26387: b 2 0 2 2,2
-26387: meet 9 2 1 0,2
-26387: meet2 9 2 1 0,3
-26387: join 13 2 0
-% SZS status Timeout for LAT025-1.p
-CLASH, statistics insufficient
-26417: Facts:
-26417: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26417: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26417: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26417: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26417: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26417: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26417: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26417: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26417: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26417: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26417: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26417: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26417: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26417: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-26417: Goal:
-26417: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-26417: Order:
-26417: nrkbo
-26417: Leaf order:
-26417: n1 1 0 0
-26417: n0 1 0 0
-26417: b 2 0 2 1,2,2
-26417: c 2 0 2 2,2,2
-26417: a 3 0 3 1,2
-26417: complement 10 1 0
-26417: meet 17 2 3 0,2
-26417: join 18 2 2 0,2,2
-CLASH, statistics insufficient
-26418: Facts:
-26418: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26418: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26418: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26418: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26418: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26418: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26418: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26418: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26418: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26418: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26418: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26418: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26418: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26418: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-26418: Goal:
-26418: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-26418: Order:
-26418: kbo
-26418: Leaf order:
-26418: n1 1 0 0
-26418: n0 1 0 0
-26418: b 2 0 2 1,2,2
-26418: c 2 0 2 2,2,2
-26418: a 3 0 3 1,2
-26418: complement 10 1 0
-26418: meet 17 2 3 0,2
-26418: join 18 2 2 0,2,2
-CLASH, statistics insufficient
-26419: Facts:
-26419: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26419: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26419: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26419: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26419: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26419: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26419: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26419: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26419: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26419: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26419: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26419: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26419: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26419: Id : 15, {_}:
- join ?38 (meet ?39 (join ?38 ?40))
- =>=
- meet (join ?38 ?39) (join ?38 ?40)
- [40, 39, 38] by modular_law ?38 ?39 ?40
-26419: Goal:
-26419: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-26419: Order:
-26419: lpo
-26419: Leaf order:
-26419: n1 1 0 0
-26419: n0 1 0 0
-26419: b 2 0 2 1,2,2
-26419: c 2 0 2 2,2,2
-26419: a 3 0 3 1,2
-26419: complement 10 1 0
-26419: meet 17 2 3 0,2
-26419: join 18 2 2 0,2,2
-% SZS status Timeout for LAT046-1.p
-NO CLASH, using fixed ground order
-26436: Facts:
-26436: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26436: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26436: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26436: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26436: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26436: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26436: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26436: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26436: Goal:
-26436: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-26436: Order:
-26436: nrkbo
-26436: Leaf order:
-26436: b 2 0 2 1,2,2
-26436: c 2 0 2 2,2,2,2
-26436: a 4 0 4 1,2
-26436: meet 11 2 2 0,2,2
-26436: join 13 2 4 0,2
-NO CLASH, using fixed ground order
-26437: Facts:
-26437: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26437: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26437: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26437: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26437: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26437: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26437: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26437: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26437: Goal:
-26437: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-26437: Order:
-26437: kbo
-26437: Leaf order:
-26437: b 2 0 2 1,2,2
-26437: c 2 0 2 2,2,2,2
-26437: a 4 0 4 1,2
-26437: meet 11 2 2 0,2,2
-26437: join 13 2 4 0,2
-NO CLASH, using fixed ground order
-26438: Facts:
-26438: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26438: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26438: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26438: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26438: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26438: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26438: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26438: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26438: Goal:
-26438: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modularity
-26438: Order:
-26438: lpo
-26438: Leaf order:
-26438: b 2 0 2 1,2,2
-26438: c 2 0 2 2,2,2,2
-26438: a 4 0 4 1,2
-26438: meet 11 2 2 0,2,2
-26438: join 13 2 4 0,2
-% SZS status Timeout for LAT047-1.p
-NO CLASH, using fixed ground order
-26479: Facts:
-26479: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26479: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26479: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26479: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26479: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26479: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26479: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26479: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26479: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26479: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26479: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26479: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26479: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26479: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-26479: Goal:
-26479: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-26479: Order:
-26479: nrkbo
-26479: Leaf order:
-26479: n0 1 0 0
-26479: n1 2 0 0
-26479: b 2 0 2 2,2,2,2
-26479: a 4 0 4 1,2
-26479: complement 13 1 1 0,1,2,2
-26479: meet 15 2 1 0,2,2
-26479: join 18 2 3 0,2
-NO CLASH, using fixed ground order
-26480: Facts:
-26480: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26480: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26480: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26480: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26480: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26480: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26480: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26480: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26480: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26480: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26480: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26480: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26480: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-NO CLASH, using fixed ground order
-26481: Facts:
-26481: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26481: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26481: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26481: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26481: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26481: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26481: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26481: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26481: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26481: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26481: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26481: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26481: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26481: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-26481: Goal:
-26481: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-26481: Order:
-26481: lpo
-26481: Leaf order:
-26481: n0 1 0 0
-26481: n1 2 0 0
-26481: b 2 0 2 2,2,2,2
-26481: a 4 0 4 1,2
-26481: complement 13 1 1 0,1,2,2
-26481: meet 15 2 1 0,2,2
-26481: join 18 2 3 0,2
-26480: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by weak_orthomodular_law ?38 ?39
-26480: Goal:
-26480: Id : 1, {_}:
- join a (meet (complement a) (join a b)) =>= join a b
- [] by prove_orthomodular_law
-26480: Order:
-26480: kbo
-26480: Leaf order:
-26480: n0 1 0 0
-26480: n1 2 0 0
-26480: b 2 0 2 2,2,2,2
-26480: a 4 0 4 1,2
-26480: complement 13 1 1 0,1,2,2
-26480: meet 15 2 1 0,2,2
-26480: join 18 2 3 0,2
-% SZS status Timeout for LAT048-1.p
-NO CLASH, using fixed ground order
-26500: Facts:
-26500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26500: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26500: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26500: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26500: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26500: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26500: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26500: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26500: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26500: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26500: Goal:
-26500: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-26500: Order:
-26500: nrkbo
-26500: Leaf order:
-26500: n0 1 0 0
-26500: n1 2 0 1 3
-26500: a 3 0 3 1,1,1,2
-26500: b 3 0 3 2,2,1,2
-26500: complement 12 1 2 0,1,1,2
-26500: meet 14 2 2 0,1,2
-26500: join 15 2 3 0,2
-NO CLASH, using fixed ground order
-26501: Facts:
-26501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26501: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26501: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26501: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26501: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26501: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26501: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26501: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26501: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26501: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26501: Goal:
-26501: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-26501: Order:
-26501: kbo
-26501: Leaf order:
-26501: n0 1 0 0
-26501: n1 2 0 1 3
-26501: a 3 0 3 1,1,1,2
-26501: b 3 0 3 2,2,1,2
-26501: complement 12 1 2 0,1,1,2
-26501: meet 14 2 2 0,1,2
-26501: join 15 2 3 0,2
-NO CLASH, using fixed ground order
-26502: Facts:
-26502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26502: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26502: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26502: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26502: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26502: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26502: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26502: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26502: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26502: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26502: Goal:
-26502: Id : 1, {_}:
- join (meet (complement a) (join a b))
- (join (complement b) (meet a b))
- =>=
- n1
- [] by prove_weak_orthomodular_law
-26502: Order:
-26502: lpo
-26502: Leaf order:
-26502: n0 1 0 0
-26502: n1 2 0 1 3
-26502: a 3 0 3 1,1,1,2
-26502: b 3 0 3 2,2,1,2
-26502: complement 12 1 2 0,1,1,2
-26502: meet 14 2 2 0,1,2
-26502: join 15 2 3 0,2
-% SZS status Timeout for LAT049-1.p
-CLASH, statistics insufficient
-26530: Facts:
-26530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26530: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26530: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26530: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26530: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26530: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26530: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26530: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26530: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26530: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26530: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-26530: Goal:
-26530: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-26530: Order:
-26530: nrkbo
-26530: Leaf order:
-26530: n1 1 0 0
-26530: n0 1 0 0
-26530: b 2 0 2 1,2,2
-26530: c 2 0 2 2,2,2,2
-26530: a 4 0 4 1,2
-26530: complement 11 1 0
-26530: meet 15 2 2 0,2,2
-26530: join 19 2 4 0,2
-CLASH, statistics insufficient
-26531: Facts:
-26531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26531: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26531: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26531: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26531: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26531: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26531: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26531: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26531: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26531: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26531: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-26531: Goal:
-26531: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-26531: Order:
-26531: kbo
-26531: Leaf order:
-26531: n1 1 0 0
-26531: n0 1 0 0
-26531: b 2 0 2 1,2,2
-26531: c 2 0 2 2,2,2,2
-26531: a 4 0 4 1,2
-26531: complement 11 1 0
-26531: meet 15 2 2 0,2,2
-26531: join 19 2 4 0,2
-CLASH, statistics insufficient
-26532: Facts:
-26532: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26532: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26532: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26532: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26532: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26532: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26532: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26532: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26532: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26532: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26532: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26532: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26532: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26532: Id : 15, {_}:
- join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
- [39, 38] by orthomodular_law ?38 ?39
-26532: Goal:
-26532: Id : 1, {_}:
- join a (meet b (join a c)) =>= meet (join a b) (join a c)
- [] by prove_modular_law
-26532: Order:
-26532: lpo
-26532: Leaf order:
-26532: n1 1 0 0
-26532: n0 1 0 0
-26532: b 2 0 2 1,2,2
-26532: c 2 0 2 2,2,2,2
-26532: a 4 0 4 1,2
-26532: complement 11 1 0
-26532: meet 15 2 2 0,2,2
-26532: join 19 2 4 0,2
-% SZS status Timeout for LAT050-1.p
-CLASH, statistics insufficient
-26548: Facts:
-26548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26548: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26548: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26548: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26548: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26548: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26548: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26548: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26548: Goal:
-26548: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26548: Order:
-26548: nrkbo
-26548: Leaf order:
-26548: n1 1 0 0
-26548: n0 1 0 0
-26548: a 2 0 2 1,1,2
-26548: b 2 0 2 2,1,2
-26548: complement 7 1 3 0,2
-26548: join 11 2 1 0,1,2
-26548: meet 11 2 1 0,3
-CLASH, statistics insufficient
-26549: Facts:
-26549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26549: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26549: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26549: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26549: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26549: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26549: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26549: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26549: Goal:
-26549: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26549: Order:
-26549: kbo
-26549: Leaf order:
-26549: n1 1 0 0
-26549: n0 1 0 0
-26549: a 2 0 2 1,1,2
-26549: b 2 0 2 2,1,2
-26549: complement 7 1 3 0,2
-26549: join 11 2 1 0,1,2
-26549: meet 11 2 1 0,3
-CLASH, statistics insufficient
-26550: Facts:
-26550: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26550: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26550: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26550: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26550: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26550: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26550: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26550: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26550: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26550: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26550: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26550: Goal:
-26550: Id : 1, {_}:
- complement (join a b) =>= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26550: Order:
-26550: lpo
-26550: Leaf order:
-26550: n1 1 0 0
-26550: n0 1 0 0
-26550: a 2 0 2 1,1,2
-26550: b 2 0 2 2,1,2
-26550: complement 7 1 3 0,2
-26550: join 11 2 1 0,1,2
-26550: meet 11 2 1 0,3
-% SZS status Timeout for LAT051-1.p
-CLASH, statistics insufficient
-26611: Facts:
-26611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26611: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26611: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26611: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26611: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26611: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26611: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26611: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26611: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-26611: Goal:
-26611: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26611: Order:
-26611: kbo
-26611: Leaf order:
-26611: n1 1 0 0
-26611: n0 1 0 0
-26611: a 2 0 2 1,1,2
-26611: b 2 0 2 2,1,2
-26611: complement 7 1 3 0,2
-26611: meet 13 2 1 0,3
-26611: join 15 2 1 0,1,2
-CLASH, statistics insufficient
-26612: Facts:
-26612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26612: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26612: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26612: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26612: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26612: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26612: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26612: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26612: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-26612: Goal:
-26612: Id : 1, {_}:
- complement (join a b) =>= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26612: Order:
-26612: lpo
-26612: Leaf order:
-26612: n1 1 0 0
-26612: n0 1 0 0
-26612: a 2 0 2 1,1,2
-26612: b 2 0 2 2,1,2
-26612: complement 7 1 3 0,2
-26612: meet 13 2 1 0,3
-26612: join 15 2 1 0,1,2
-CLASH, statistics insufficient
-26610: Facts:
-26610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26610: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26610: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26610: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26610: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26610: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
-26610: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
-26610: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
-26610: Id : 13, {_}:
- join ?32 (meet ?33 (join ?32 ?34))
- =>=
- meet (join ?32 ?33) (join ?32 ?34)
- [34, 33, 32] by modular_law ?32 ?33 ?34
-26610: Goal:
-26610: Id : 1, {_}:
- complement (join a b) =<= meet (complement a) (complement b)
- [] by prove_compatibility_law
-26610: Order:
-26610: nrkbo
-26610: Leaf order:
-26610: n1 1 0 0
-26610: n0 1 0 0
-26610: a 2 0 2 1,1,2
-26610: b 2 0 2 2,1,2
-26610: complement 7 1 3 0,2
-26610: meet 13 2 1 0,3
-26610: join 15 2 1 0,1,2
-% SZS status Timeout for LAT052-1.p
-CLASH, statistics insufficient
-26628: Facts:
-26628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26628: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26628: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26628: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26628: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26628: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26628: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26628: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26628: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26628: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26628: Goal:
-26628: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-26628: Order:
-26628: nrkbo
-26628: Leaf order:
-26628: n1 1 0 0
-26628: n0 1 0 0
-26628: b 7 0 7 1,1,2,2
-26628: a 9 0 9 1,2
-26628: complement 21 1 11 0,1,2,2
-26628: join 19 2 7 0,2
-26628: meet 19 2 7 0,2,2
-CLASH, statistics insufficient
-26629: Facts:
-26629: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26629: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26629: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26629: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26629: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26629: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26629: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26629: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26629: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26629: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26629: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26629: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26629: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26629: Goal:
-26629: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-26629: Order:
-26629: kbo
-26629: Leaf order:
-26629: n1 1 0 0
-26629: n0 1 0 0
-26629: b 7 0 7 1,1,2,2
-26629: a 9 0 9 1,2
-26629: complement 21 1 11 0,1,2,2
-26629: join 19 2 7 0,2
-26629: meet 19 2 7 0,2,2
-CLASH, statistics insufficient
-26630: Facts:
-26630: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26630: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26630: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26630: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26630: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26630: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26630: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26630: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26630: Id : 10, {_}:
- complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-26630: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-26630: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-26630: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-26630: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-26630: Goal:
-26630: Id : 1, {_}:
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a (meet (complement b) (complement a))))))
- =<=
- join a
- (meet (complement b)
- (join (complement a)
- (meet (complement b)
- (join a
- (meet (complement b)
- (join (complement a) (meet (complement b) a)))))))
- [] by prove_this
-26630: Order:
-26630: lpo
-26630: Leaf order:
-26630: n1 1 0 0
-26630: n0 1 0 0
-26630: b 7 0 7 1,1,2,2
-26630: a 9 0 9 1,2
-26630: complement 21 1 11 0,1,2,2
-26630: join 19 2 7 0,2
-26630: meet 19 2 7 0,2,2
-% SZS status Timeout for LAT054-1.p
-CLASH, statistics insufficient
-26659: Facts:
-26659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26659: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26659: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26659: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26659: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26659: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26659: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26659: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26659: Goal:
-26659: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-26659: Order:
-26659: nrkbo
-26659: Leaf order:
-26659: n1 1 0 0
-26659: n0 1 0 0
-26659: a 6 0 6 1,1,2
-26659: b 6 0 6 1,2,1,2
-26659: complement 11 1 6 0,2,1,2
-26659: join 15 2 4 0,1,2
-26659: meet 17 2 6 0,2
-CLASH, statistics insufficient
-26660: Facts:
-26660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26660: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26660: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26660: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26660: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26660: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26660: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26660: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26660: Goal:
-26660: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-26660: Order:
-26660: kbo
-26660: Leaf order:
-26660: n1 1 0 0
-26660: n0 1 0 0
-26660: a 6 0 6 1,1,2
-26660: b 6 0 6 1,2,1,2
-26660: complement 11 1 6 0,2,1,2
-26660: join 15 2 4 0,1,2
-26660: meet 17 2 6 0,2
-CLASH, statistics insufficient
-26661: Facts:
-26661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26661: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26661: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26661: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26661: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26661: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26661: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26661: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26661: Goal:
-26661: Id : 1, {_}:
- meet (join a (complement b))
- (join (join (meet a b) (meet (complement a) b))
- (meet (complement a) (complement b)))
- =>=
- join (meet a b) (meet (complement a) (complement b))
- [] by prove_e51
-26661: Order:
-26661: lpo
-26661: Leaf order:
-26661: n1 1 0 0
-26661: n0 1 0 0
-26661: a 6 0 6 1,1,2
-26661: b 6 0 6 1,2,1,2
-26661: complement 11 1 6 0,2,1,2
-26661: join 15 2 4 0,1,2
-26661: meet 17 2 6 0,2
-% SZS status Timeout for LAT062-1.p
-CLASH, statistics insufficient
-26678: Facts:
-26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26678: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26678: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26678: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26678: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26678: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26678: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26678: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26678: Goal:
-26678: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-26678: Order:
-26678: nrkbo
-26678: Leaf order:
-26678: n1 1 0 0
-26678: n0 1 0 0
-26678: b 3 0 3 1,2,2
-26678: a 7 0 7 1,2
-26678: complement 7 1 2 0,1,2,2,2,2
-26678: join 14 2 3 0,2,2
-26678: meet 16 2 5 0,2
-CLASH, statistics insufficient
-26679: Facts:
-26679: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26679: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26679: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26679: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26679: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26679: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26679: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26679: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26679: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26679: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26679: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26679: Goal:
-26679: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-26679: Order:
-26679: kbo
-26679: Leaf order:
-26679: n1 1 0 0
-26679: n0 1 0 0
-26679: b 3 0 3 1,2,2
-26679: a 7 0 7 1,2
-26679: complement 7 1 2 0,1,2,2,2,2
-26679: join 14 2 3 0,2,2
-26679: meet 16 2 5 0,2
-CLASH, statistics insufficient
-26680: Facts:
-26680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26680: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26680: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26680: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26680: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26680: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
-26680: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
-26680: Id : 12, {_}:
- meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
- [31, 30] by compatibility ?30 ?31
-26680: Goal:
-26680: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_e62
-26680: Order:
-26680: lpo
-26680: Leaf order:
-26680: n1 1 0 0
-26680: n0 1 0 0
-26680: b 3 0 3 1,2,2
-26680: a 7 0 7 1,2
-26680: complement 7 1 2 0,1,2,2,2,2
-26680: join 14 2 3 0,2,2
-26680: meet 16 2 5 0,2
-% SZS status Timeout for LAT063-1.p
-NO CLASH, using fixed ground order
-26708: Facts:
-26708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26708: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26708: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26708: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26708: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26708: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-26708: Goal:
-26708: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26708: Order:
-26708: nrkbo
-26708: Leaf order:
-26708: c 3 0 3 2,2,2,2
-26708: b 4 0 4 1,2,2
-26708: a 5 0 5 1,2
-26708: join 17 2 4 0,2,2
-26708: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-26709: Facts:
-26709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26709: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26709: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26709: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26709: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26709: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-26709: Goal:
-26709: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26709: Order:
-26709: kbo
-26709: Leaf order:
-26709: c 3 0 3 2,2,2,2
-26709: b 4 0 4 1,2,2
-26709: a 5 0 5 1,2
-26709: join 17 2 4 0,2,2
-26709: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-26710: Facts:
-26710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26710: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26710: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26710: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26710: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26710: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
- [28, 27, 26] by equation_H2 ?26 ?27 ?28
-26710: Goal:
-26710: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26710: Order:
-26710: lpo
-26710: Leaf order:
-26710: c 3 0 3 2,2,2,2
-26710: b 4 0 4 1,2,2
-26710: a 5 0 5 1,2
-26710: join 17 2 4 0,2,2
-26710: meet 21 2 6 0,2
-% SZS status Timeout for LAT098-1.p
-NO CLASH, using fixed ground order
-26734: Facts:
-26734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26734: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26734: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26734: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26734: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26734: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26734: Goal:
-26734: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26734: Order:
-26734: nrkbo
-26734: Leaf order:
-26734: c 2 0 2 1,2,2,2,2
-26734: b 3 0 3 1,2,2
-26734: d 3 0 3 2,2,2,2,2
-26734: a 4 0 4 1,2
-26734: join 18 2 5 0,2,2
-26734: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26735: Facts:
-26735: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26735: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26735: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26735: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26735: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26735: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26735: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26735: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26735: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26735: Goal:
-26735: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26735: Order:
-26735: kbo
-26735: Leaf order:
-26735: c 2 0 2 1,2,2,2,2
-26735: b 3 0 3 1,2,2
-26735: d 3 0 3 2,2,2,2,2
-26735: a 4 0 4 1,2
-26735: join 18 2 5 0,2,2
-26735: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26736: Facts:
-26736: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26736: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26736: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26736: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26736: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26736: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26736: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26736: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26736: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26736: Goal:
-26736: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26736: Order:
-26736: lpo
-26736: Leaf order:
-26736: c 2 0 2 1,2,2,2,2
-26736: b 3 0 3 1,2,2
-26736: d 3 0 3 2,2,2,2,2
-26736: a 4 0 4 1,2
-26736: join 18 2 5 0,2,2
-26736: meet 20 2 5 0,2
-% SZS status Timeout for LAT100-1.p
-NO CLASH, using fixed ground order
-26775: Facts:
-26775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26775: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26775: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26775: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26775: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26775: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26775: Goal:
-26775: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26775: Order:
-26775: nrkbo
-26775: Leaf order:
-26775: b 3 0 3 1,2,2
-26775: c 3 0 3 2,2,2,2
-26775: a 4 0 4 1,2
-26775: join 16 2 3 0,2,2
-26775: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26776: Facts:
-26776: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26776: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26776: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26776: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26776: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26776: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26776: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26776: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26776: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26776: Goal:
-26776: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26776: Order:
-26776: kbo
-26776: Leaf order:
-26776: b 3 0 3 1,2,2
-26776: c 3 0 3 2,2,2,2
-26776: a 4 0 4 1,2
-26776: join 16 2 3 0,2,2
-26776: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26777: Facts:
-26777: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26777: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26777: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26777: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26777: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26777: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26777: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26777: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26777: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join (meet ?26 (join ?27 (meet ?26 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H6 ?26 ?27 ?28
-26777: Goal:
-26777: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26777: Order:
-26777: lpo
-26777: Leaf order:
-26777: b 3 0 3 1,2,2
-26777: c 3 0 3 2,2,2,2
-26777: a 4 0 4 1,2
-26777: join 16 2 3 0,2,2
-26777: meet 20 2 5 0,2
-% SZS status Timeout for LAT101-1.p
-NO CLASH, using fixed ground order
-26819: Facts:
-26819: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26819: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26819: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26819: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26819: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26819: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26819: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26819: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26819: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-26819: Goal:
-26819: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26819: Order:
-26819: nrkbo
-26819: Leaf order:
-26819: c 2 0 2 1,2,2,2,2
-26819: b 3 0 3 1,2,2
-26819: d 3 0 3 2,2,2,2,2
-26819: a 4 0 4 1,2
-26819: join 18 2 5 0,2,2
-26819: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26820: Facts:
-26820: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26820: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26820: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26820: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26820: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26820: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26820: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26820: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26820: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-26820: Goal:
-26820: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26820: Order:
-26820: kbo
-26820: Leaf order:
-26820: c 2 0 2 1,2,2,2,2
-26820: b 3 0 3 1,2,2
-26820: d 3 0 3 2,2,2,2,2
-26820: a 4 0 4 1,2
-26820: join 18 2 5 0,2,2
-26820: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26821: Facts:
-26821: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26821: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26821: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26821: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26821: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26821: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26821: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26821: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26821: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-26821: Goal:
-26821: Id : 1, {_}:
- meet a (join b (meet a (join c d)))
- =<=
- meet a (join b (meet (join a (meet b d)) (join c d)))
- [] by prove_H4
-26821: Order:
-26821: lpo
-26821: Leaf order:
-26821: c 2 0 2 1,2,2,2,2
-26821: b 3 0 3 1,2,2
-26821: d 3 0 3 2,2,2,2,2
-26821: a 4 0 4 1,2
-26821: join 18 2 5 0,2,2
-26821: meet 20 2 5 0,2
-% SZS status Timeout for LAT102-1.p
-NO CLASH, using fixed ground order
-26896: Facts:
-26896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26896: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26896: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26896: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26896: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26896: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-26896: Goal:
-26896: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-26896: Order:
-26896: nrkbo
-26896: Leaf order:
-26896: b 3 0 3 1,2,2
-26896: c 3 0 3 2,2,2,2
-26896: a 6 0 6 1,2
-26896: join 16 2 4 0,2,2
-26896: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-26897: Facts:
-26897: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26897: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26897: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26897: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26897: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26897: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26897: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26897: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26897: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-26897: Goal:
-26897: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-26897: Order:
-26897: kbo
-26897: Leaf order:
-26897: b 3 0 3 1,2,2
-26897: c 3 0 3 2,2,2,2
-26897: a 6 0 6 1,2
-26897: join 16 2 4 0,2,2
-26897: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-26898: Facts:
-26898: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26898: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26898: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26898: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26898: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26898: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26898: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26898: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26898: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
- [28, 27, 26] by equation_H10 ?26 ?27 ?28
-26898: Goal:
-26898: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-26898: Order:
-26898: lpo
-26898: Leaf order:
-26898: b 3 0 3 1,2,2
-26898: c 3 0 3 2,2,2,2
-26898: a 6 0 6 1,2
-26898: join 16 2 4 0,2,2
-26898: meet 20 2 6 0,2
-% SZS status Timeout for LAT103-1.p
-NO CLASH, using fixed ground order
-26925: Facts:
-26925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26925: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26925: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26925: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26925: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26925: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26925: Goal:
-26925: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26925: Order:
-26925: nrkbo
-26925: Leaf order:
-26925: c 3 0 3 2,2,2,2
-26925: b 4 0 4 1,2,2
-26925: a 5 0 5 1,2
-26925: join 17 2 4 0,2,2
-26925: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-26926: Facts:
-26926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26926: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26926: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26926: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26926: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26926: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26926: Goal:
-26926: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26926: Order:
-26926: kbo
-26926: Leaf order:
-26926: c 3 0 3 2,2,2,2
-26926: b 4 0 4 1,2,2
-26926: a 5 0 5 1,2
-26926: join 17 2 4 0,2,2
-26926: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-26927: Facts:
-26927: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26927: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26927: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26927: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26927: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26927: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26927: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26927: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26927: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26927: Goal:
-26927: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-26927: Order:
-26927: lpo
-26927: Leaf order:
-26927: c 3 0 3 2,2,2,2
-26927: b 4 0 4 1,2,2
-26927: a 5 0 5 1,2
-26927: join 17 2 4 0,2,2
-26927: meet 21 2 6 0,2
-% SZS status Timeout for LAT104-1.p
-NO CLASH, using fixed ground order
-26956: Facts:
-26956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26956: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26956: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26956: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26956: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26956: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26956: Goal:
-26956: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26956: Order:
-26956: nrkbo
-26956: Leaf order:
-26956: b 3 0 3 1,2,2
-26956: c 3 0 3 2,2,2,2
-26956: a 4 0 4 1,2
-26956: join 16 2 3 0,2,2
-26956: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26957: Facts:
-26957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26957: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26957: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26957: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26957: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26957: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26957: Goal:
-26957: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26957: Order:
-26957: kbo
-26957: Leaf order:
-26957: b 3 0 3 1,2,2
-26957: c 3 0 3 2,2,2,2
-26957: a 4 0 4 1,2
-26957: join 16 2 3 0,2,2
-26957: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-26958: Facts:
-26958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-26958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-26958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-26958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-26958: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-26958: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-26958: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-26958: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-26958: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-26958: Goal:
-26958: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-26958: Order:
-26958: lpo
-26958: Leaf order:
-26958: b 3 0 3 1,2,2
-26958: c 3 0 3 2,2,2,2
-26958: a 4 0 4 1,2
-26958: join 16 2 3 0,2,2
-26958: meet 20 2 5 0,2
-% SZS status Timeout for LAT105-1.p
-NO CLASH, using fixed ground order
-27035: Facts:
-27035: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27035: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27035: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27035: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27035: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27035: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27035: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27035: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27035: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27035: Goal:
-27035: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-27035: Order:
-27035: nrkbo
-27035: Leaf order:
-27035: c 3 0 3 2,2,2,2
-27035: b 4 0 4 1,2,2
-27035: a 5 0 5 1,2
-27035: join 17 2 4 0,2,2
-27035: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-27036: Facts:
-27036: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27036: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27036: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27036: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27036: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27036: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27036: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27036: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27036: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27036: Goal:
-27036: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-27036: Order:
-27036: kbo
-27036: Leaf order:
-27036: c 3 0 3 2,2,2,2
-27036: b 4 0 4 1,2,2
-27036: a 5 0 5 1,2
-27036: join 17 2 4 0,2,2
-27036: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-27037: Facts:
-27037: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27037: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27037: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27037: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27037: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27037: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27037: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27037: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27037: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27037: Goal:
-27037: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-27037: Order:
-27037: lpo
-27037: Leaf order:
-27037: c 3 0 3 2,2,2,2
-27037: b 4 0 4 1,2,2
-27037: a 5 0 5 1,2
-27037: join 17 2 4 0,2,2
-27037: meet 21 2 6 0,2
-% SZS status Timeout for LAT106-1.p
-NO CLASH, using fixed ground order
-27073: Facts:
-27073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27073: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27073: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27073: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27073: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27073: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27073: Goal:
-27073: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =<=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-27073: Order:
-27073: nrkbo
-27073: Leaf order:
-27073: c 3 0 3 2,2,2,2
-27073: b 4 0 4 2,1,2,2
-27073: a 6 0 6 1,2
-27073: join 17 2 4 0,2,2
-27073: meet 22 2 7 0,2
-NO CLASH, using fixed ground order
-27074: Facts:
-27074: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27074: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27074: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27074: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27074: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27074: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27074: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27074: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27074: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27074: Goal:
-27074: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =<=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-27074: Order:
-27074: kbo
-27074: Leaf order:
-27074: c 3 0 3 2,2,2,2
-27074: b 4 0 4 2,1,2,2
-27074: a 6 0 6 1,2
-27074: join 17 2 4 0,2,2
-27074: meet 22 2 7 0,2
-NO CLASH, using fixed ground order
-27075: Facts:
-27075: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27075: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27075: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27075: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27075: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27075: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27075: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27075: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27075: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-27075: Goal:
-27075: Id : 1, {_}:
- meet a (join (meet a b) (meet a c))
- =>=
- meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
- [] by prove_H17
-27075: Order:
-27075: lpo
-27075: Leaf order:
-27075: c 3 0 3 2,2,2,2
-27075: b 4 0 4 2,1,2,2
-27075: a 6 0 6 1,2
-27075: join 17 2 4 0,2,2
-27075: meet 22 2 7 0,2
-% SZS status Timeout for LAT107-1.p
-NO CLASH, using fixed ground order
-27091: Facts:
-27091: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27091: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27091: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27091: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27091: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27091: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27091: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27091: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27091: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-27091: Goal:
-27091: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27091: Order:
-27091: nrkbo
-27091: Leaf order:
-27091: d 2 0 2 2,2,2,2,2
-27091: b 3 0 3 1,2,2
-27091: c 3 0 3 1,2,2,2
-27091: a 4 0 4 1,2
-27091: join 17 2 5 0,2,2
-27091: meet 21 2 5 0,2
-NO CLASH, using fixed ground order
-27092: Facts:
-27092: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27092: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27092: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27092: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27092: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27092: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27092: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27092: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27092: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-27092: Goal:
-27092: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27092: Order:
-27092: kbo
-27092: Leaf order:
-27092: d 2 0 2 2,2,2,2,2
-27092: b 3 0 3 1,2,2
-27092: c 3 0 3 1,2,2,2
-27092: a 4 0 4 1,2
-27092: join 17 2 5 0,2,2
-27092: meet 21 2 5 0,2
-NO CLASH, using fixed ground order
-27093: Facts:
-27093: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27093: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27093: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27093: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27093: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27093: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27093: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27093: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27093: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
-27093: Goal:
-27093: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27093: Order:
-27093: lpo
-27093: Leaf order:
-27093: d 2 0 2 2,2,2,2,2
-27093: b 3 0 3 1,2,2
-27093: c 3 0 3 1,2,2,2
-27093: a 4 0 4 1,2
-27093: join 17 2 5 0,2,2
-27093: meet 21 2 5 0,2
-% SZS status Timeout for LAT108-1.p
-NO CLASH, using fixed ground order
-27126: Facts:
-27126: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27126: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27126: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27126: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27126: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27126: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27126: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27126: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27126: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-27126: Goal:
-27126: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27126: Order:
-27126: nrkbo
-27126: Leaf order:
-27126: d 2 0 2 2,2,2,2,2
-27126: b 3 0 3 1,2,2
-27126: c 3 0 3 1,2,2,2
-27126: a 4 0 4 1,2
-27126: meet 19 2 5 0,2
-27126: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-27127: Facts:
-27127: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27127: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27127: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27127: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27127: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27127: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27127: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27127: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27127: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-27127: Goal:
-27127: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27127: Order:
-27127: kbo
-27127: Leaf order:
-27127: d 2 0 2 2,2,2,2,2
-27127: b 3 0 3 1,2,2
-27127: c 3 0 3 1,2,2,2
-27127: a 4 0 4 1,2
-27127: meet 19 2 5 0,2
-27127: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-27128: Facts:
-27128: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27128: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27128: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27128: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27128: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27128: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27128: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27128: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27128: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-27128: Goal:
-27128: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27128: Order:
-27128: lpo
-27128: Leaf order:
-27128: d 2 0 2 2,2,2,2,2
-27128: b 3 0 3 1,2,2
-27128: c 3 0 3 1,2,2,2
-27128: a 4 0 4 1,2
-27128: meet 19 2 5 0,2
-27128: join 19 2 5 0,2,2
-% SZS status Timeout for LAT109-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-27146: Facts:
-NO CLASH, using fixed ground order
-27146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27146: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27146: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27146: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27146: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27146: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-27146: Goal:
-27146: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27146: Order:
-27146: lpo
-27146: Leaf order:
-27146: d 2 0 2 2,2,2,2,2
-27146: b 3 0 3 1,2,2
-27146: c 3 0 3 1,2,2,2
-27146: a 4 0 4 1,2
-27146: join 17 2 5 0,2,2
-27146: meet 21 2 5 0,2
-27144: Facts:
-27144: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27144: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27144: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27144: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27144: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27144: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27144: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27144: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27144: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-27144: Goal:
-27144: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27144: Order:
-27144: nrkbo
-27144: Leaf order:
-27144: d 2 0 2 2,2,2,2,2
-27144: b 3 0 3 1,2,2
-27144: c 3 0 3 1,2,2,2
-27144: a 4 0 4 1,2
-27144: join 17 2 5 0,2,2
-27144: meet 21 2 5 0,2
-27145: Facts:
-27145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27145: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27145: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27145: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27145: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27145: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
-27145: Goal:
-27145: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27145: Order:
-27145: kbo
-27145: Leaf order:
-27145: d 2 0 2 2,2,2,2,2
-27145: b 3 0 3 1,2,2
-27145: c 3 0 3 1,2,2,2
-27145: a 4 0 4 1,2
-27145: join 17 2 5 0,2,2
-27145: meet 21 2 5 0,2
-% SZS status Timeout for LAT111-1.p
-NO CLASH, using fixed ground order
-27177: Facts:
-27177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27177: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27177: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27177: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27177: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27177: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-27177: Goal:
-27177: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27177: Order:
-27177: nrkbo
-27177: Leaf order:
-27177: d 2 0 2 2,2,2,2,2
-27177: b 3 0 3 1,2,2
-27177: c 3 0 3 1,2,2,2
-27177: a 4 0 4 1,2
-27177: join 17 2 5 0,2,2
-27177: meet 21 2 5 0,2
-NO CLASH, using fixed ground order
-27178: Facts:
-27178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27178: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27178: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27178: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27178: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27178: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-27178: Goal:
-27178: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27178: Order:
-27178: kbo
-27178: Leaf order:
-27178: d 2 0 2 2,2,2,2,2
-27178: b 3 0 3 1,2,2
-27178: c 3 0 3 1,2,2,2
-27178: a 4 0 4 1,2
-27178: join 17 2 5 0,2,2
-27178: meet 21 2 5 0,2
-NO CLASH, using fixed ground order
-27179: Facts:
-27179: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27179: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27179: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27179: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27179: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27179: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27179: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27179: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27179: Id : 10, {_}:
- meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
-27179: Goal:
-27179: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-27179: Order:
-27179: lpo
-27179: Leaf order:
-27179: d 2 0 2 2,2,2,2,2
-27179: b 3 0 3 1,2,2
-27179: c 3 0 3 1,2,2,2
-27179: a 4 0 4 1,2
-27179: join 17 2 5 0,2,2
-27179: meet 21 2 5 0,2
-% SZS status Timeout for LAT112-1.p
-NO CLASH, using fixed ground order
-27203: Facts:
-27203: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27203: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27203: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27203: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27203: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27203: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27203: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27203: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27203: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-27203: Goal:
-27203: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27203: Order:
-27203: nrkbo
-27203: Leaf order:
-27203: d 2 0 2 2,2,2,2,2
-27203: b 3 0 3 1,2,2
-27203: c 3 0 3 1,2,2,2
-27203: a 4 0 4 1,2
-27203: meet 19 2 5 0,2
-27203: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-27204: Facts:
-27204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27204: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27204: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27204: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27204: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27204: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-27204: Goal:
-27204: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27204: Order:
-27204: kbo
-27204: Leaf order:
-27204: d 2 0 2 2,2,2,2,2
-27204: b 3 0 3 1,2,2
-27204: c 3 0 3 1,2,2,2
-27204: a 4 0 4 1,2
-27204: meet 19 2 5 0,2
-27204: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-27205: Facts:
-27205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27205: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27205: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27205: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27205: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27205: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-27205: Goal:
-27205: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-27205: Order:
-27205: lpo
-27205: Leaf order:
-27205: d 2 0 2 2,2,2,2,2
-27205: b 3 0 3 1,2,2
-27205: c 3 0 3 1,2,2,2
-27205: a 4 0 4 1,2
-27205: meet 19 2 5 0,2
-27205: join 19 2 5 0,2,2
-% SZS status Timeout for LAT113-1.p
-NO CLASH, using fixed ground order
-27406: Facts:
-27406: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27406: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27406: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27406: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27406: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27406: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27406: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27406: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27406: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27406: Goal:
-27406: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-27406: Order:
-27406: nrkbo
-27406: Leaf order:
-27406: c 2 0 2 2,2,2,2
-27406: a 5 0 5 1,1,2
-27406: b 5 0 5 2,1,2
-27406: meet 17 2 5 0,1,2
-27406: join 19 2 5 0,2
-NO CLASH, using fixed ground order
-27407: Facts:
-27407: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27407: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27407: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27407: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27407: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27407: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27407: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27407: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27407: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27407: Goal:
-27407: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-27407: Order:
-27407: kbo
-27407: Leaf order:
-27407: c 2 0 2 2,2,2,2
-27407: a 5 0 5 1,1,2
-27407: b 5 0 5 2,1,2
-27407: meet 17 2 5 0,1,2
-27407: join 19 2 5 0,2
-NO CLASH, using fixed ground order
-27408: Facts:
-27408: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27408: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27408: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27408: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27408: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27408: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27408: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27408: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27408: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27408: Goal:
-27408: Id : 1, {_}:
- join (meet a b) (meet a (join b c))
- =>=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H56
-27408: Order:
-27408: lpo
-27408: Leaf order:
-27408: c 2 0 2 2,2,2,2
-27408: a 5 0 5 1,1,2
-27408: b 5 0 5 2,1,2
-27408: meet 17 2 5 0,1,2
-27408: join 19 2 5 0,2
-% SZS status Timeout for LAT114-1.p
-NO CLASH, using fixed ground order
-27552: Facts:
-27552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27552: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27552: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27552: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27552: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27552: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27552: Goal:
-27552: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-27552: Order:
-27552: nrkbo
-27552: Leaf order:
-27552: c 2 0 2 2,1,2,2
-27552: d 2 0 2 2,2,2,2
-27552: a 3 0 3 1,2
-27552: b 5 0 5 1,1,2,2
-27552: meet 17 2 5 0,2
-27552: join 19 2 5 0,1,2,2
-NO CLASH, using fixed ground order
-27553: Facts:
-27553: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27553: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27553: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27553: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27553: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27553: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27553: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27553: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27553: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27553: Goal:
-27553: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-27553: Order:
-27553: kbo
-27553: Leaf order:
-27553: c 2 0 2 2,1,2,2
-27553: d 2 0 2 2,2,2,2
-27553: a 3 0 3 1,2
-27553: b 5 0 5 1,1,2,2
-27553: meet 17 2 5 0,2
-27553: join 19 2 5 0,1,2,2
-NO CLASH, using fixed ground order
-27554: Facts:
-27554: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27554: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27554: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27554: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27554: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27554: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27554: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27554: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27554: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27554: Goal:
-27554: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-27554: Order:
-27554: lpo
-27554: Leaf order:
-27554: c 2 0 2 2,1,2,2
-27554: d 2 0 2 2,2,2,2
-27554: a 3 0 3 1,2
-27554: b 5 0 5 1,1,2,2
-27554: meet 17 2 5 0,2
-27554: join 19 2 5 0,1,2,2
-% SZS status Timeout for LAT115-1.p
-NO CLASH, using fixed ground order
-27591: Facts:
-27591: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27591: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27591: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27591: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27591: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27591: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27591: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27591: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27591: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27591: Goal:
-27591: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-27591: Order:
-27591: nrkbo
-27591: Leaf order:
-27591: c 2 0 2 2,1,2,2
-27591: d 2 0 2 2,2,2,2
-27591: a 3 0 3 1,2
-27591: b 5 0 5 1,1,2,2
-27591: meet 17 2 5 0,2
-27591: join 19 2 5 0,1,2,2
-NO CLASH, using fixed ground order
-27592: Facts:
-27592: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27592: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27592: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27592: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27592: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27592: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27592: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27592: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27592: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27592: Goal:
-27592: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-27592: Order:
-27592: kbo
-27592: Leaf order:
-27592: c 2 0 2 2,1,2,2
-27592: d 2 0 2 2,2,2,2
-27592: a 3 0 3 1,2
-27592: b 5 0 5 1,1,2,2
-27592: meet 17 2 5 0,2
-27592: join 19 2 5 0,1,2,2
-NO CLASH, using fixed ground order
-27593: Facts:
-27593: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27593: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27593: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27593: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27593: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27593: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27593: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27593: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27593: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-27593: Goal:
-27593: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b c) (join d (meet a b))))
- [] by prove_H60
-27593: Order:
-27593: lpo
-27593: Leaf order:
-27593: c 2 0 2 2,1,2,2
-27593: d 2 0 2 2,2,2,2
-27593: a 3 0 3 1,2
-27593: b 5 0 5 1,1,2,2
-27593: meet 17 2 5 0,2
-27593: join 19 2 5 0,1,2,2
-% SZS status Timeout for LAT116-1.p
-NO CLASH, using fixed ground order
-27609: Facts:
-27609: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27609: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27609: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27609: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27609: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27609: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27609: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27609: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27609: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-27609: Goal:
-27609: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-27609: Order:
-27609: nrkbo
-27609: Leaf order:
-27609: b 3 0 3 1,2,2
-27609: c 3 0 3 2,2,2
-27609: a 5 0 5 1,2
-27609: join 16 2 4 0,2,2
-27609: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-27610: Facts:
-27610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27610: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27610: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27610: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27610: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27610: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-27610: Goal:
-27610: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-27610: Order:
-27610: kbo
-27610: Leaf order:
-27610: b 3 0 3 1,2,2
-27610: c 3 0 3 2,2,2
-27610: a 5 0 5 1,2
-27610: join 16 2 4 0,2,2
-27610: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-27611: Facts:
-27611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-27611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-27611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-27611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-27611: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-27611: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-27611: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-27611: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-27611: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
- [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
-27611: Goal:
-27611: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-27611: Order:
-27611: lpo
-27611: Leaf order:
-27611: b 3 0 3 1,2,2
-27611: c 3 0 3 2,2,2
-27611: a 5 0 5 1,2
-27611: join 16 2 4 0,2,2
-27611: meet 20 2 5 0,2
-% SZS status Timeout for LAT117-1.p
-NO CLASH, using fixed ground order
-28243: Facts:
-28243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28243: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28243: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28243: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28243: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28243: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-28243: Goal:
-28243: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28243: Order:
-28243: nrkbo
-28243: Leaf order:
-28243: c 3 0 3 2,2,2,2
-28243: b 4 0 4 1,2,2
-28243: a 5 0 5 1,2
-28243: join 17 2 4 0,2,2
-28243: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-28244: Facts:
-28244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28244: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28244: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28244: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28244: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28244: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-28244: Goal:
-28244: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28244: Order:
-28244: kbo
-28244: Leaf order:
-28244: c 3 0 3 2,2,2,2
-28244: b 4 0 4 1,2,2
-28244: a 5 0 5 1,2
-28244: join 17 2 4 0,2,2
-28244: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-28246: Facts:
-28246: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28246: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28246: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28246: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28246: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28246: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28246: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28246: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28246: Id : 10, {_}:
- meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
- =>=
- join (meet ?26 ?27) (meet ?26 ?28)
- [28, 27, 26] by equation_H82 ?26 ?27 ?28
-28246: Goal:
-28246: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28246: Order:
-28246: lpo
-28246: Leaf order:
-28246: c 3 0 3 2,2,2,2
-28246: b 4 0 4 1,2,2
-28246: a 5 0 5 1,2
-28246: join 17 2 4 0,2,2
-28246: meet 20 2 6 0,2
-% SZS status Timeout for LAT119-1.p
-NO CLASH, using fixed ground order
-28653: Facts:
-28653: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28653: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28653: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28653: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28653: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28653: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28653: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28653: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28653: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-28653: Goal:
-28653: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-28653: Order:
-28653: nrkbo
-28653: Leaf order:
-28653: c 2 0 2 2,2,2
-28653: a 4 0 4 1,2
-28653: b 4 0 4 1,2,2
-28653: meet 16 2 4 0,2
-28653: join 18 2 4 0,2,2
-NO CLASH, using fixed ground order
-28654: Facts:
-28654: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28654: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28654: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28654: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28654: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28654: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28654: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28654: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28654: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-28654: Goal:
-28654: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-28654: Order:
-28654: kbo
-28654: Leaf order:
-28654: c 2 0 2 2,2,2
-28654: a 4 0 4 1,2
-28654: b 4 0 4 1,2,2
-28654: meet 16 2 4 0,2
-28654: join 18 2 4 0,2,2
-NO CLASH, using fixed ground order
-28655: Facts:
-28655: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28655: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28655: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28655: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28655: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28655: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28655: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28655: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28655: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
- [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
-28655: Goal:
-28655: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-28655: Order:
-28655: lpo
-28655: Leaf order:
-28655: c 2 0 2 2,2,2
-28655: a 4 0 4 1,2
-28655: b 4 0 4 1,2,2
-28655: meet 16 2 4 0,2
-28655: join 18 2 4 0,2,2
-% SZS status Timeout for LAT120-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-28691: Facts:
-28691: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28691: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28691: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28691: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28691: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28691: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28691: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28691: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28691: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-28691: Goal:
-28691: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28691: Order:
-28691: kbo
-28691: Leaf order:
-28691: b 3 0 3 1,2,2
-28691: c 3 0 3 2,2,2,2
-28691: a 4 0 4 1,2
-28691: meet 16 2 3 0,2,2
-28691: join 20 2 5 0,2
-28690: Facts:
-28690: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28690: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28690: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28690: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28690: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28690: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28690: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28690: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28690: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-28690: Goal:
-28690: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28690: Order:
-28690: nrkbo
-28690: Leaf order:
-28690: b 3 0 3 1,2,2
-28690: c 3 0 3 2,2,2,2
-28690: a 4 0 4 1,2
-28690: meet 16 2 3 0,2,2
-28690: join 20 2 5 0,2
-NO CLASH, using fixed ground order
-28692: Facts:
-28692: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28692: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28692: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28692: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28692: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28692: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28692: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28692: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28692: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?26 ?27)
- (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
- [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
-28692: Goal:
-28692: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28692: Order:
-28692: lpo
-28692: Leaf order:
-28692: b 3 0 3 1,2,2
-28692: c 3 0 3 2,2,2,2
-28692: a 4 0 4 1,2
-28692: meet 16 2 3 0,2,2
-28692: join 20 2 5 0,2
-% SZS status Timeout for LAT121-1.p
-NO CLASH, using fixed ground order
-28708: Facts:
-28708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28708: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28708: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28708: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28708: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28708: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-28708: Goal:
-28708: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28708: Order:
-28708: nrkbo
-28708: Leaf order:
-28708: b 3 0 3 1,2,2
-28708: c 3 0 3 2,2,2,2
-28708: a 4 0 4 1,2
-28708: meet 16 2 3 0,2,2
-28708: join 20 2 5 0,2
-NO CLASH, using fixed ground order
-28709: Facts:
-28709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28709: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28709: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28709: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28709: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28709: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-28709: Goal:
-28709: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28709: Order:
-28709: kbo
-28709: Leaf order:
-28709: b 3 0 3 1,2,2
-28709: c 3 0 3 2,2,2,2
-28709: a 4 0 4 1,2
-28709: meet 16 2 3 0,2,2
-28709: join 20 2 5 0,2
-NO CLASH, using fixed ground order
-28710: Facts:
-28710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28710: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28710: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28710: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28710: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28710: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-28710: Goal:
-28710: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28710: Order:
-28710: lpo
-28710: Leaf order:
-28710: b 3 0 3 1,2,2
-28710: c 3 0 3 2,2,2,2
-28710: a 4 0 4 1,2
-28710: meet 16 2 3 0,2,2
-28710: join 20 2 5 0,2
-% SZS status Timeout for LAT122-1.p
-NO CLASH, using fixed ground order
-28742: Facts:
-28742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28742: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28742: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28742: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28742: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28742: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-28742: Goal:
-28742: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28742: Order:
-28742: nrkbo
-28742: Leaf order:
-28742: b 3 0 3 1,2,2
-28742: c 3 0 3 2,2,2,2
-28742: a 4 0 4 1,2
-28742: meet 16 2 3 0,2,2
-28742: join 20 2 5 0,2
-NO CLASH, using fixed ground order
-28743: Facts:
-28743: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28743: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28743: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28743: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28743: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28743: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28743: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28743: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28743: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-28743: Goal:
-28743: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28743: Order:
-28743: kbo
-28743: Leaf order:
-28743: b 3 0 3 1,2,2
-28743: c 3 0 3 2,2,2,2
-28743: a 4 0 4 1,2
-28743: meet 16 2 3 0,2,2
-28743: join 20 2 5 0,2
-NO CLASH, using fixed ground order
-28744: Facts:
-28744: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28744: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28744: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28744: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28744: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28744: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28744: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28744: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28744: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?28 (join ?26 ?27)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
-28744: Goal:
-28744: Id : 1, {_}:
- join a (meet b (join a c))
- =>=
- join a (meet b (join c (meet a (join c b))))
- [] by prove_H55
-28744: Order:
-28744: lpo
-28744: Leaf order:
-28744: b 3 0 3 1,2,2
-28744: c 3 0 3 2,2,2,2
-28744: a 4 0 4 1,2
-28744: meet 16 2 3 0,2,2
-28744: join 20 2 5 0,2
-% SZS status Timeout for LAT123-1.p
-NO CLASH, using fixed ground order
-28780: Facts:
-28780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28780: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28780: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28780: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28780: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28780: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-28780: Goal:
-28780: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28780: Order:
-28780: nrkbo
-28780: Leaf order:
-28780: b 3 0 3 1,2,2
-28780: c 3 0 3 2,2,2
-28780: a 5 0 5 1,2
-28780: meet 17 2 5 0,2
-28780: join 20 2 4 0,2,2
-NO CLASH, using fixed ground order
-28781: Facts:
-28781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28781: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28781: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28781: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28781: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28781: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-28781: Goal:
-28781: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28781: Order:
-28781: kbo
-28781: Leaf order:
-28781: b 3 0 3 1,2,2
-28781: c 3 0 3 2,2,2
-28781: a 5 0 5 1,2
-28781: meet 17 2 5 0,2
-28781: join 20 2 4 0,2,2
-NO CLASH, using fixed ground order
-28782: Facts:
-28782: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28782: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28782: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28782: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28782: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28782: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28782: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28782: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28782: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
-28782: Goal:
-28782: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28782: Order:
-28782: lpo
-28782: Leaf order:
-28782: b 3 0 3 1,2,2
-28782: c 3 0 3 2,2,2
-28782: a 5 0 5 1,2
-28782: meet 17 2 5 0,2
-28782: join 20 2 4 0,2,2
-% SZS status Timeout for LAT124-1.p
-NO CLASH, using fixed ground order
-28810: Facts:
-28810: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28810: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28810: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28810: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28810: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28810: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28810: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28810: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28810: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-28810: Goal:
-28810: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28810: Order:
-28810: nrkbo
-28810: Leaf order:
-28810: b 3 0 3 1,2,2
-28810: c 3 0 3 2,2,2
-28810: a 5 0 5 1,2
-28810: join 18 2 4 0,2,2
-28810: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-28811: Facts:
-28811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28811: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28811: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28811: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28811: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28811: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-28811: Goal:
-28811: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28811: Order:
-28811: kbo
-28811: Leaf order:
-28811: b 3 0 3 1,2,2
-28811: c 3 0 3 2,2,2
-NO CLASH, using fixed ground order
-28812: Facts:
-28812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28812: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28812: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28812: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28812: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28811: a 5 0 5 1,2
-28811: join 18 2 4 0,2,2
-28811: meet 18 2 5 0,2
-28812: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 ?29))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
-28812: Goal:
-28812: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28812: Order:
-28812: lpo
-28812: Leaf order:
-28812: b 3 0 3 1,2,2
-28812: c 3 0 3 2,2,2
-28812: a 5 0 5 1,2
-28812: join 18 2 4 0,2,2
-28812: meet 18 2 5 0,2
-% SZS status Timeout for LAT125-1.p
-NO CLASH, using fixed ground order
-28829: Facts:
-28829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28829: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28829: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28829: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28829: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28829: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-28829: Goal:
-28829: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28829: Order:
-28829: kbo
-28829: Leaf order:
-28829: b 3 0 3 1,2,2
-28829: c 3 0 3 2,2,2
-28829: a 5 0 5 1,2
-28829: join 18 2 4 0,2,2
-28829: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-28828: Facts:
-28828: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28828: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28828: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28828: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28828: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28828: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28828: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28828: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28828: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-28828: Goal:
-28828: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28828: Order:
-28828: nrkbo
-28828: Leaf order:
-28828: b 3 0 3 1,2,2
-28828: c 3 0 3 2,2,2
-28828: a 5 0 5 1,2
-28828: join 18 2 4 0,2,2
-28828: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-28830: Facts:
-28830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28830: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28830: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28830: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28830: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28830: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
- [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
-28830: Goal:
-28830: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-28830: Order:
-28830: lpo
-28830: Leaf order:
-28830: b 3 0 3 1,2,2
-28830: c 3 0 3 2,2,2
-28830: a 5 0 5 1,2
-28830: join 18 2 4 0,2,2
-28830: meet 18 2 5 0,2
-% SZS status Timeout for LAT126-1.p
-NO CLASH, using fixed ground order
-28859: Facts:
-28859: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28859: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28859: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28859: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28859: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28859: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28859: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28859: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28859: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-28859: Goal:
-28859: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-28859: Order:
-28859: nrkbo
-28859: Leaf order:
-28859: b 3 0 3 1,2,2
-28859: c 3 0 3 2,2,2,2
-28859: a 6 0 6 1,2
-28859: join 16 2 4 0,2,2
-28859: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-28860: Facts:
-28860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28860: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28860: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28860: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28860: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28860: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-28860: Goal:
-28860: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-28860: Order:
-28860: kbo
-28860: Leaf order:
-28860: b 3 0 3 1,2,2
-28860: c 3 0 3 2,2,2,2
-28860: a 6 0 6 1,2
-28860: join 16 2 4 0,2,2
-28860: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-28861: Facts:
-28861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28861: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28861: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28861: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28861: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28861: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
- [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
-28861: Goal:
-28861: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-28861: Order:
-28861: lpo
-28861: Leaf order:
-28861: b 3 0 3 1,2,2
-28861: c 3 0 3 2,2,2,2
-28861: a 6 0 6 1,2
-28861: join 16 2 4 0,2,2
-28861: meet 20 2 6 0,2
-% SZS status Timeout for LAT127-1.p
-NO CLASH, using fixed ground order
-28878: Facts:
-28878: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28878: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28878: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28878: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28878: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28878: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28878: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28878: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28878: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28878: Goal:
-28878: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28878: Order:
-28878: nrkbo
-28878: Leaf order:
-28878: c 3 0 3 2,2,2,2
-28878: b 4 0 4 1,2,2
-28878: a 5 0 5 1,2
-28878: join 17 2 4 0,2,2
-28878: meet 19 2 6 0,2
-NO CLASH, using fixed ground order
-28879: Facts:
-28879: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28879: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28879: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28879: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28879: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28879: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28879: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28879: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28879: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28879: Goal:
-28879: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28879: Order:
-28879: kbo
-28879: Leaf order:
-28879: c 3 0 3 2,2,2,2
-28879: b 4 0 4 1,2,2
-NO CLASH, using fixed ground order
-28880: Facts:
-28880: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28880: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28880: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28880: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28880: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28880: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28880: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28880: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28880: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28880: Goal:
-28880: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join b (meet a (join c (meet a b))))))
- [] by prove_H3
-28880: Order:
-28880: lpo
-28880: Leaf order:
-28880: c 3 0 3 2,2,2,2
-28880: b 4 0 4 1,2,2
-28880: a 5 0 5 1,2
-28880: join 17 2 4 0,2,2
-28880: meet 19 2 6 0,2
-28879: a 5 0 5 1,2
-28879: join 17 2 4 0,2,2
-28879: meet 19 2 6 0,2
-% SZS status Timeout for LAT128-1.p
-NO CLASH, using fixed ground order
-28929: Facts:
-28929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28929: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28929: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28929: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28929: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28929: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28929: Goal:
-28929: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-28929: Order:
-28929: nrkbo
-28929: Leaf order:
-28929: b 3 0 3 1,2,2
-28929: c 3 0 3 2,2,2,2
-28929: a 4 0 4 1,2
-28929: join 16 2 3 0,2,2
-28929: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-28930: Facts:
-28930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28930: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28930: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28930: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28930: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28930: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28930: Goal:
-28930: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-28930: Order:
-28930: kbo
-28930: Leaf order:
-28930: b 3 0 3 1,2,2
-28930: c 3 0 3 2,2,2,2
-28930: a 4 0 4 1,2
-28930: join 16 2 3 0,2,2
-28930: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-28931: Facts:
-28931: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28931: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28931: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28931: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28931: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28931: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28931: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28931: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28931: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
-28931: Goal:
-28931: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-28931: Order:
-28931: lpo
-28931: Leaf order:
-28931: b 3 0 3 1,2,2
-28931: c 3 0 3 2,2,2,2
-28931: a 4 0 4 1,2
-28931: join 16 2 3 0,2,2
-28931: meet 18 2 5 0,2
-% SZS status Timeout for LAT129-1.p
-NO CLASH, using fixed ground order
-28978: Facts:
-28978: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28978: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28978: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28978: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28978: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28978: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28978: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28978: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28978: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-28978: Goal:
-28978: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-28978: Order:
-28978: nrkbo
-28978: Leaf order:
-28978: b 2 0 2 1,2,2
-28978: d 2 0 2 2,2,2,2,2
-28978: c 3 0 3 1,2,2,2
-28978: a 4 0 4 1,2
-28978: join 17 2 4 0,2,2
-28978: meet 17 2 5 0,2
-NO CLASH, using fixed ground order
-28979: Facts:
-28979: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28979: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28979: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28979: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28979: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28979: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28979: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28979: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28979: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-28979: Goal:
-28979: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-28979: Order:
-28979: kbo
-28979: Leaf order:
-28979: b 2 0 2 1,2,2
-28979: d 2 0 2 2,2,2,2,2
-28979: c 3 0 3 1,2,2,2
-28979: a 4 0 4 1,2
-28979: join 17 2 4 0,2,2
-28979: meet 17 2 5 0,2
-NO CLASH, using fixed ground order
-28980: Facts:
-28980: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-28980: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-28980: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-28980: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-28980: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-28980: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-28980: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-28980: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-28980: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-28980: Goal:
-28980: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet a c))))
- [] by prove_H39
-28980: Order:
-28980: lpo
-28980: Leaf order:
-28980: b 2 0 2 1,2,2
-28980: d 2 0 2 2,2,2,2,2
-28980: c 3 0 3 1,2,2,2
-28980: a 4 0 4 1,2
-28980: join 17 2 4 0,2,2
-28980: meet 17 2 5 0,2
-% SZS status Timeout for LAT130-1.p
-NO CLASH, using fixed ground order
-29013: Facts:
-29013: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29013: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29013: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29013: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29013: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29013: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29013: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29013: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29013: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-29013: Goal:
-29013: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29013: Order:
-29013: nrkbo
-29013: Leaf order:
-29013: d 2 0 2 2,2,2,2,2
-29013: b 3 0 3 1,2,2
-29013: c 3 0 3 1,2,2,2
-29013: a 4 0 4 1,2
-29013: meet 17 2 5 0,2
-29013: join 18 2 5 0,2,2
-NO CLASH, using fixed ground order
-29014: Facts:
-29014: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29014: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29014: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29014: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29014: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29014: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29014: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29014: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29014: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-29014: Goal:
-29014: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29014: Order:
-29014: kbo
-29014: Leaf order:
-29014: d 2 0 2 2,2,2,2,2
-29014: b 3 0 3 1,2,2
-29014: c 3 0 3 1,2,2,2
-29014: a 4 0 4 1,2
-29014: meet 17 2 5 0,2
-29014: join 18 2 5 0,2,2
-NO CLASH, using fixed ground order
-29015: Facts:
-29015: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29015: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29015: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29015: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29015: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29015: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29015: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29015: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29015: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
- [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
-29015: Goal:
-29015: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29015: Order:
-29015: lpo
-29015: Leaf order:
-29015: d 2 0 2 2,2,2,2,2
-29015: b 3 0 3 1,2,2
-29015: c 3 0 3 1,2,2,2
-29015: a 4 0 4 1,2
-29015: meet 17 2 5 0,2
-29015: join 18 2 5 0,2,2
-% SZS status Timeout for LAT131-1.p
-NO CLASH, using fixed ground order
-29032: Facts:
-29032: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29032: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29032: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29032: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29032: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29032: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29032: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29032: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29032: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-29032: Goal:
-29032: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29032: Order:
-29032: nrkbo
-29032: Leaf order:
-29032: d 2 0 2 2,2,2,2,2
-29032: b 3 0 3 1,2,2
-29032: c 3 0 3 1,2,2,2
-29032: a 4 0 4 1,2
-29032: meet 18 2 5 0,2
-29032: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-29033: Facts:
-29033: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29033: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29033: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29033: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29033: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29033: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29033: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29033: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29033: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-29033: Goal:
-29033: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29033: Order:
-29033: kbo
-29033: Leaf order:
-29033: d 2 0 2 2,2,2,2,2
-29033: b 3 0 3 1,2,2
-29033: c 3 0 3 1,2,2,2
-29033: a 4 0 4 1,2
-29033: meet 18 2 5 0,2
-29033: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-29034: Facts:
-29034: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29034: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29034: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29034: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29034: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29034: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29034: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29034: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29034: Id : 10, {_}:
- join ?26 (meet ?27 ?28)
- =<=
- meet (join ?26 (meet ?28 (join ?26 ?27)))
- (join ?26 (meet ?27 (join ?26 ?28)))
- [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
-29034: Goal:
-29034: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-29034: Order:
-29034: lpo
-29034: Leaf order:
-29034: d 2 0 2 2,2,2,2,2
-29034: b 3 0 3 1,2,2
-29034: c 3 0 3 1,2,2,2
-29034: a 4 0 4 1,2
-29034: meet 18 2 5 0,2
-29034: join 19 2 5 0,2,2
-% SZS status Timeout for LAT132-1.p
-NO CLASH, using fixed ground order
-29065: Facts:
-29065: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29065: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29065: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29065: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29065: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29065: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29065: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29065: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29065: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-29065: Goal:
-29065: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-29065: Order:
-29065: nrkbo
-29065: Leaf order:
-29065: b 3 0 3 1,2,2
-29065: c 3 0 3 2,2,2,2
-29065: a 6 0 6 1,2
-29065: meet 16 2 4 0,2,2
-29065: join 20 2 6 0,2
-NO CLASH, using fixed ground order
-29066: Facts:
-29066: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29066: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29066: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29066: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29066: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29066: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29066: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29066: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29066: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-29066: Goal:
-29066: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-29066: Order:
-29066: kbo
-29066: Leaf order:
-29066: b 3 0 3 1,2,2
-29066: c 3 0 3 2,2,2,2
-29066: a 6 0 6 1,2
-29066: meet 16 2 4 0,2,2
-29066: join 20 2 6 0,2
-NO CLASH, using fixed ground order
-29067: Facts:
-29067: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29067: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29067: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29067: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29067: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29067: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29067: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29067: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29067: Id : 10, {_}:
- join ?26 (meet ?27 (join ?26 ?28))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
- [28, 27, 26] by equation_H55 ?26 ?27 ?28
-29067: Goal:
-29067: Id : 1, {_}:
- join a (meet b (join a c))
- =<=
- join a (meet (join a (meet b (join a c))) (join c (meet a b)))
- [] by prove_H6_dual
-29067: Order:
-29067: lpo
-29067: Leaf order:
-29067: b 3 0 3 1,2,2
-29067: c 3 0 3 2,2,2,2
-29067: a 6 0 6 1,2
-29067: meet 16 2 4 0,2,2
-29067: join 20 2 6 0,2
-% SZS status Timeout for LAT133-1.p
-NO CLASH, using fixed ground order
-29084: Facts:
-29084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29084: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29084: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29084: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29084: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29084: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-29084: Goal:
-29084: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-29084: Order:
-29084: nrkbo
-29084: Leaf order:
-29084: c 3 0 3 2,2,2
-29084: b 4 0 4 2,1,2
-29084: a 5 0 5 1,1,2
-29084: meet 16 2 4 0,2
-29084: join 20 2 6 0,1,2
-NO CLASH, using fixed ground order
-29085: Facts:
-29085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29085: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29085: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29085: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29085: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29085: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-29085: Goal:
-29085: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-29085: Order:
-29085: kbo
-29085: Leaf order:
-29085: c 3 0 3 2,2,2
-29085: b 4 0 4 2,1,2
-29085: a 5 0 5 1,1,2
-29085: meet 16 2 4 0,2
-29085: join 20 2 6 0,1,2
-NO CLASH, using fixed ground order
-29086: Facts:
-29086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29086: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29086: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29086: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29086: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29086: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
- [28, 27, 26] by equation_H61 ?26 ?27 ?28
-29086: Goal:
-29086: Id : 1, {_}:
- meet (join a b) (join a c)
- =<=
- join a (meet (join b (meet c (join a b))) (join c (meet a b)))
- [] by prove_H22_dual
-29086: Order:
-29086: lpo
-29086: Leaf order:
-29086: c 3 0 3 2,2,2
-29086: b 4 0 4 2,1,2
-29086: a 5 0 5 1,1,2
-29086: meet 16 2 4 0,2
-29086: join 20 2 6 0,1,2
-% SZS status Timeout for LAT134-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-29118: Facts:
-29118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29118: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29118: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29118: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29118: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29118: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-29118: Goal:
-29118: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29118: Order:
-29118: kbo
-29118: Leaf order:
-29118: b 2 0 2 1,2,2
-29118: d 2 0 2 2,2,2,2,2
-29118: c 3 0 3 1,2,2,2
-29118: a 4 0 4 1,2
-29118: meet 17 2 4 0,2,2
-29118: join 17 2 5 0,2
-29117: Facts:
-29117: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29117: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29117: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29117: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29117: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29117: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29117: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29117: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29117: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-29117: Goal:
-29117: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29117: Order:
-29117: nrkbo
-29117: Leaf order:
-29117: b 2 0 2 1,2,2
-29117: d 2 0 2 2,2,2,2,2
-29117: c 3 0 3 1,2,2,2
-29117: a 4 0 4 1,2
-29117: meet 17 2 4 0,2,2
-29117: join 17 2 5 0,2
-NO CLASH, using fixed ground order
-29119: Facts:
-29119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29119: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29119: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29119: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29119: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29119: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-29119: Goal:
-29119: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29119: Order:
-29119: lpo
-29119: Leaf order:
-29119: b 2 0 2 1,2,2
-29119: d 2 0 2 2,2,2,2,2
-29119: c 3 0 3 1,2,2,2
-29119: a 4 0 4 1,2
-29119: meet 17 2 4 0,2,2
-29119: join 17 2 5 0,2
-% SZS status Timeout for LAT135-1.p
-NO CLASH, using fixed ground order
-29145: Facts:
-29145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29145: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29145: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29145: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29145: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29145: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29145: Goal:
-29145: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29145: Order:
-29145: nrkbo
-29145: Leaf order:
-29145: b 2 0 2 1,2,2
-29145: d 2 0 2 2,2,2,2,2
-29145: c 3 0 3 1,2,2,2
-29145: a 4 0 4 1,2
-29145: meet 18 2 4 0,2,2
-29145: join 18 2 5 0,2
-NO CLASH, using fixed ground order
-29146: Facts:
-29146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29146: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29146: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29146: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29146: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29146: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29146: Goal:
-29146: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29146: Order:
-29146: kbo
-29146: Leaf order:
-29146: b 2 0 2 1,2,2
-29146: d 2 0 2 2,2,2,2,2
-29146: c 3 0 3 1,2,2,2
-29146: a 4 0 4 1,2
-29146: meet 18 2 4 0,2,2
-29146: join 18 2 5 0,2
-NO CLASH, using fixed ground order
-29147: Facts:
-29147: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29147: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29147: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29147: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29147: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29147: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29147: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29147: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29147: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29147: Goal:
-29147: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join a c))))
- [] by prove_H39_dual
-29147: Order:
-29147: lpo
-29147: Leaf order:
-29147: b 2 0 2 1,2,2
-29147: d 2 0 2 2,2,2,2,2
-29147: c 3 0 3 1,2,2,2
-29147: a 4 0 4 1,2
-29147: meet 18 2 4 0,2,2
-29147: join 18 2 5 0,2
-% SZS status Timeout for LAT136-1.p
-NO CLASH, using fixed ground order
-29176: Facts:
-29176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29176: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29176: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29176: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29176: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29176: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29176: Goal:
-29176: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-29176: Order:
-29176: nrkbo
-29176: Leaf order:
-29176: d 2 0 2 2,2,2,2,2
-29176: b 3 0 3 1,2,2
-29176: c 3 0 3 1,2,2,2
-29176: a 4 0 4 1,2
-29176: join 18 2 5 0,2
-29176: meet 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-29177: Facts:
-29177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29177: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29177: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29177: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29177: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29177: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29177: Goal:
-29177: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-29177: Order:
-29177: kbo
-29177: Leaf order:
-29177: d 2 0 2 2,2,2,2,2
-29177: b 3 0 3 1,2,2
-29177: c 3 0 3 1,2,2,2
-29177: a 4 0 4 1,2
-29177: join 18 2 5 0,2
-29177: meet 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-29178: Facts:
-29178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29178: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29178: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29178: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29178: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29178: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- join (meet ?26 (join ?28 (meet ?26 ?27)))
- (meet ?26 (join ?27 (meet ?26 ?28)))
- [28, 27, 26] by equation_H69 ?26 ?27 ?28
-29178: Goal:
-29178: Id : 1, {_}:
- join a (meet b (join c (meet a d)))
- =<=
- join a (meet b (join c (meet d (join c (meet a b)))))
- [] by prove_H40_dual
-29178: Order:
-29178: lpo
-29178: Leaf order:
-29178: d 2 0 2 2,2,2,2,2
-29178: b 3 0 3 1,2,2
-29178: c 3 0 3 1,2,2,2
-29178: a 4 0 4 1,2
-29178: join 18 2 5 0,2
-29178: meet 19 2 5 0,2,2
-% SZS status Timeout for LAT137-1.p
-NO CLASH, using fixed ground order
-29197: Facts:
-29197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29197: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29197: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29197: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29197: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29197: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-29197: Goal:
-29197: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29197: Order:
-29197: nrkbo
-29197: Leaf order:
-29197: b 3 0 3 1,2,2
-29197: c 3 0 3 2,2,2,2
-29197: a 6 0 6 1,2
-29197: join 16 2 4 0,2,2
-29197: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-29198: Facts:
-29198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29198: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29198: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29198: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29198: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29198: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-29198: Goal:
-29198: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29198: Order:
-29198: kbo
-29198: Leaf order:
-29198: b 3 0 3 1,2,2
-29198: c 3 0 3 2,2,2,2
-29198: a 6 0 6 1,2
-29198: join 16 2 4 0,2,2
-29198: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-29199: Facts:
-29199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-29199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-29199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-29199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-29199: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-29199: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-29199: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-29199: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-29199: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
- [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
-29199: Goal:
-29199: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-29199: Order:
-29199: lpo
-29199: Leaf order:
-29199: b 3 0 3 1,2,2
-29199: c 3 0 3 2,2,2,2
-29199: a 6 0 6 1,2
-29199: join 16 2 4 0,2,2
-29199: meet 20 2 6 0,2
-% SZS status Timeout for LAT171-1.p
-NO CLASH, using fixed ground order
-29274: Facts:
-29274: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29274: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29274: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29274: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29274: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-29274: Goal:
-29274: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-29274: Order:
-29274: nrkbo
-29274: Leaf order:
-29274: y 2 0 0
-29274: x 2 0 1 1,2
-29274: z 2 0 1 2,2
-29274: truth 4 0 1 3
-29274: not 2 1 0
-29274: implies 16 2 1 0,2
-NO CLASH, using fixed ground order
-29275: Facts:
-29275: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29275: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29275: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29275: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29275: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-29275: Goal:
-29275: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-29275: Order:
-29275: kbo
-29275: Leaf order:
-29275: y 2 0 0
-29275: x 2 0 1 1,2
-29275: z 2 0 1 2,2
-29275: truth 4 0 1 3
-29275: not 2 1 0
-29275: implies 16 2 1 0,2
-NO CLASH, using fixed ground order
-29276: Facts:
-29276: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29276: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29276: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29276: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29276: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
-29276: Goal:
-29276: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
-29276: Order:
-29276: lpo
-29276: Leaf order:
-29276: y 2 0 0
-29276: x 2 0 1 1,2
-29276: z 2 0 1 2,2
-29276: truth 4 0 1 3
-29276: not 2 1 0
-29276: implies 16 2 1 0,2
-% SZS status Timeout for LCL136-1.p
-NO CLASH, using fixed ground order
-29293: Facts:
-29293: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29293: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29293: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29293: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29293: Goal:
-29293: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-29293: Order:
-29293: nrkbo
-29293: Leaf order:
-29293: x 2 0 2 1,1,1,2
-29293: z 2 0 2 2,1,2,2
-29293: y 3 0 3 2,1,1,2
-29293: truth 4 0 1 3
-29293: not 2 1 0
-29293: implies 19 2 6 0,2
-NO CLASH, using fixed ground order
-29294: Facts:
-29294: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29294: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29294: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29294: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29294: Goal:
-29294: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-29294: Order:
-29294: kbo
-29294: Leaf order:
-29294: x 2 0 2 1,1,1,2
-29294: z 2 0 2 2,1,2,2
-29294: y 3 0 3 2,1,1,2
-29294: truth 4 0 1 3
-29294: not 2 1 0
-29294: implies 19 2 6 0,2
-NO CLASH, using fixed ground order
-29295: Facts:
-29295: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29295: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29295: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29295: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29295: Goal:
-29295: Id : 1, {_}:
- implies (implies (implies x y) y)
- (implies (implies y z) (implies x z))
- =>=
- truth
- [] by prove_wajsberg_lemma
-29295: Order:
-29295: lpo
-29295: Leaf order:
-29295: x 2 0 2 1,1,1,2
-29295: z 2 0 2 2,1,2,2
-29295: y 3 0 3 2,1,1,2
-29295: truth 4 0 1 3
-29295: not 2 1 0
-29295: implies 19 2 6 0,2
-% SZS status Timeout for LCL137-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-29381: Facts:
-29381: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29381: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29381: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29381: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29381: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-29381: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-29381: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-29381: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-29381: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-29381: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-29381: Goal:
-29381: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-29381: Order:
-29381: kbo
-29381: Leaf order:
-29381: truth 3 0 0
-29381: x 10 0 10 1,1,1,2
-29381: not 12 1 6 0,2
-29381: and 11 2 4 0,1,1,2
-29381: or 12 2 4 0,1,2
-29381: implies 14 2 0
-29380: Facts:
-29380: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29380: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29380: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29380: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29380: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-29380: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-29380: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-29380: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-29380: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-29380: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-29380: Goal:
-29380: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-29380: Order:
-29380: nrkbo
-29380: Leaf order:
-29380: truth 3 0 0
-29380: x 10 0 10 1,1,1,2
-29380: not 12 1 6 0,2
-29380: and 11 2 4 0,1,1,2
-29380: or 12 2 4 0,1,2
-29380: implies 14 2 0
-NO CLASH, using fixed ground order
-29382: Facts:
-29382: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-29382: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-29382: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-29382: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-29382: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-29382: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-29382: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-29382: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-29382: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-29382: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-29382: Goal:
-29382: Id : 1, {_}:
- not (or (and x (or x x)) (and x x))
- =<=
- and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
- [] by prove_wajsberg_theorem
-29382: Order:
-29382: lpo
-29382: Leaf order:
-29382: truth 3 0 0
-29382: x 10 0 10 1,1,1,2
-29382: not 12 1 6 0,2
-29382: and 11 2 4 0,1,1,2
-29382: or 12 2 4 0,1,2
-29382: implies 14 2 0
-% SZS status Timeout for LCL165-1.p
-NO CLASH, using fixed ground order
-29399: Facts:
-29399: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29399: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29399: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29399: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29399: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29399: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29399: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29399: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29399: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29399: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29399: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29399: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29399: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29399: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29399: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29399: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29399: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29399: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29399: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29399: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29399: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29399: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29399: Goal:
-29399: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-29399: Order:
-29399: nrkbo
-29399: Leaf order:
-29399: u 2 0 2 1,3,2
-29399: v 2 0 2 2,3,2
-29399: x 3 0 3 1,2
-29399: y 3 0 3 2,2
-29399: additive_identity 8 0 0
-29399: additive_inverse 22 1 0
-29399: commutator 1 2 0
-29399: add 26 2 2 0,3,2
-29399: multiply 40 2 0
-29399: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29400: Facts:
-29400: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29400: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29400: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29400: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29400: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29400: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29400: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29400: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29400: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29400: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29400: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29400: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29400: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29400: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29400: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29400: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29400: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29400: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29400: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29400: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29400: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29400: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29400: Goal:
-29400: Id : 1, {_}:
- associator x y (add u v)
- =<=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-29400: Order:
-29400: kbo
-29400: Leaf order:
-29400: u 2 0 2 1,3,2
-29400: v 2 0 2 2,3,2
-29400: x 3 0 3 1,2
-29400: y 3 0 3 2,2
-29400: additive_identity 8 0 0
-29400: additive_inverse 22 1 0
-29400: commutator 1 2 0
-29400: add 26 2 2 0,3,2
-29400: multiply 40 2 0
-29400: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29401: Facts:
-29401: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29401: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29401: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29401: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29401: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29401: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29401: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29401: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29401: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29401: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29401: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29401: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29401: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29401: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29401: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29401: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29401: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29401: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29401: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29401: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29401: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29401: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29401: Goal:
-29401: Id : 1, {_}:
- associator x y (add u v)
- =>=
- add (associator x y u) (associator x y v)
- [] by prove_linearised_form1
-29401: Order:
-29401: lpo
-29401: Leaf order:
-29401: u 2 0 2 1,3,2
-29401: v 2 0 2 2,3,2
-29401: x 3 0 3 1,2
-29401: y 3 0 3 2,2
-29401: additive_identity 8 0 0
-29401: additive_inverse 22 1 0
-29401: commutator 1 2 0
-29401: add 26 2 2 0,3,2
-29401: multiply 40 2 0
-29401: associator 4 3 3 0,2
-% SZS status Timeout for RNG019-7.p
-NO CLASH, using fixed ground order
-29433: Facts:
-29433: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29433: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29433: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29433: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29433: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29433: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29433: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29433: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29433: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29433: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29433: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29433: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29433: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29433: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29433: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29433: Goal:
-29433: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29433: Order:
-29433: kbo
-29433: Leaf order:
-29433: u 2 0 2 1,2,2
-29433: v 2 0 2 2,2,2
-29433: x 3 0 3 1,2
-29433: y 3 0 3 3,2
-29433: additive_identity 8 0 0
-29433: additive_inverse 6 1 0
-29433: commutator 1 2 0
-29433: add 18 2 2 0,2,2
-29433: multiply 22 2 0
-29433: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29434: Facts:
-29434: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29434: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29434: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29434: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29434: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29434: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29434: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29434: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29434: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29434: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29434: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29434: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29434: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29434: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29434: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29434: Goal:
-29434: Id : 1, {_}:
- associator x (add u v) y
- =>=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29434: Order:
-29434: lpo
-29434: Leaf order:
-29434: u 2 0 2 1,2,2
-29434: v 2 0 2 2,2,2
-29434: x 3 0 3 1,2
-29434: y 3 0 3 3,2
-29434: additive_identity 8 0 0
-29434: additive_inverse 6 1 0
-29434: commutator 1 2 0
-29434: add 18 2 2 0,2,2
-29434: multiply 22 2 0
-29434: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29432: Facts:
-29432: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29432: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29432: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29432: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29432: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29432: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29432: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29432: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29432: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29432: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29432: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29432: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29432: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29432: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29432: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29432: Goal:
-29432: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29432: Order:
-29432: nrkbo
-29432: Leaf order:
-29432: u 2 0 2 1,2,2
-29432: v 2 0 2 2,2,2
-29432: x 3 0 3 1,2
-29432: y 3 0 3 3,2
-29432: additive_identity 8 0 0
-29432: additive_inverse 6 1 0
-29432: commutator 1 2 0
-29432: add 18 2 2 0,2,2
-29432: multiply 22 2 0
-29432: associator 4 3 3 0,2
-% SZS status Timeout for RNG020-6.p
-NO CLASH, using fixed ground order
-29471: Facts:
-29471: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29471: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29471: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29471: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29471: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29471: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29471: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29471: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29471: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29471: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29471: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29471: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29471: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29471: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29471: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29471: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29471: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29471: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29471: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29471: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29471: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29471: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29471: Goal:
-29471: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29471: Order:
-29471: nrkbo
-29471: Leaf order:
-29471: u 2 0 2 1,2,2
-29471: v 2 0 2 2,2,2
-29471: x 3 0 3 1,2
-29471: y 3 0 3 3,2
-29471: additive_identity 8 0 0
-29471: additive_inverse 22 1 0
-29471: commutator 1 2 0
-29471: add 26 2 2 0,2,2
-29471: multiply 40 2 0
-29471: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29472: Facts:
-29472: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29472: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29472: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29472: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29472: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29472: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29472: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29472: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29472: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29472: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29472: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29472: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29472: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29472: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29472: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29472: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29472: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29472: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29472: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29472: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29472: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29472: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29472: Goal:
-29472: Id : 1, {_}:
- associator x (add u v) y
- =<=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29472: Order:
-29472: kbo
-29472: Leaf order:
-29472: u 2 0 2 1,2,2
-29472: v 2 0 2 2,2,2
-29472: x 3 0 3 1,2
-29472: y 3 0 3 3,2
-29472: additive_identity 8 0 0
-29472: additive_inverse 22 1 0
-29472: commutator 1 2 0
-29472: add 26 2 2 0,2,2
-29472: multiply 40 2 0
-29472: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29473: Facts:
-29473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29473: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29473: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29473: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29473: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29473: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29473: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29473: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29473: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29473: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29473: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29473: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29473: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29473: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29473: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29473: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29473: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29473: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29473: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29473: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29473: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29473: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29473: Goal:
-29473: Id : 1, {_}:
- associator x (add u v) y
- =>=
- add (associator x u y) (associator x v y)
- [] by prove_linearised_form2
-29473: Order:
-29473: lpo
-29473: Leaf order:
-29473: u 2 0 2 1,2,2
-29473: v 2 0 2 2,2,2
-29473: x 3 0 3 1,2
-29473: y 3 0 3 3,2
-29473: additive_identity 8 0 0
-29473: additive_inverse 22 1 0
-29473: commutator 1 2 0
-29473: add 26 2 2 0,2,2
-29473: multiply 40 2 0
-29473: associator 4 3 3 0,2
-% SZS status Timeout for RNG020-7.p
-NO CLASH, using fixed ground order
-29501: Facts:
-29501: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29501: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29501: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29501: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29501: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29501: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29501: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29501: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29501: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29501: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29501: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29501: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29501: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29501: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29501: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29501: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29501: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29501: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29501: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29501: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29501: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29501: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29501: Goal:
-29501: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-29501: Order:
-29501: nrkbo
-29501: Leaf order:
-29501: u 2 0 2 1,1,2
-29501: v 2 0 2 2,1,2
-29501: x 3 0 3 2,2
-29501: y 3 0 3 3,2
-29501: additive_identity 8 0 0
-29501: additive_inverse 22 1 0
-29501: commutator 1 2 0
-29501: add 26 2 2 0,1,2
-29501: multiply 40 2 0
-29501: associator 4 3 3 0,2
-NO CLASH, using fixed ground order
-29502: Facts:
-29502: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29502: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-NO CLASH, using fixed ground order
-29503: Facts:
-29502: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29502: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29502: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29502: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29502: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29502: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29502: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29502: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29502: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29502: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29502: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29502: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29502: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29502: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29502: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29502: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29502: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29502: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29502: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29502: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29502: Goal:
-29502: Id : 1, {_}:
- associator (add u v) x y
- =<=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-29502: Order:
-29502: kbo
-29502: Leaf order:
-29502: u 2 0 2 1,1,2
-29502: v 2 0 2 2,1,2
-29502: x 3 0 3 2,2
-29502: y 3 0 3 3,2
-29502: additive_identity 8 0 0
-29502: additive_inverse 22 1 0
-29502: commutator 1 2 0
-29502: add 26 2 2 0,1,2
-29502: multiply 40 2 0
-29502: associator 4 3 3 0,2
-29503: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29503: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29503: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29503: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29503: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29503: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29503: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29503: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29503: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29503: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29503: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29503: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29503: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29503: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29503: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29503: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-29503: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-29503: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-29503: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-29503: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-29503: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-29503: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-29503: Goal:
-29503: Id : 1, {_}:
- associator (add u v) x y
- =>=
- add (associator u x y) (associator v x y)
- [] by prove_linearised_form3
-29503: Order:
-29503: lpo
-29503: Leaf order:
-29503: u 2 0 2 1,1,2
-29503: v 2 0 2 2,1,2
-29503: x 3 0 3 2,2
-29503: y 3 0 3 3,2
-29503: additive_identity 8 0 0
-29503: additive_inverse 22 1 0
-29503: commutator 1 2 0
-29503: add 26 2 2 0,1,2
-29503: multiply 40 2 0
-29503: associator 4 3 3 0,2
-% SZS status Timeout for RNG021-7.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-29520: Facts:
-29520: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29520: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29520: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29520: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29520: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29520: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29520: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29520: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29520: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29520: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29520: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29520: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29520: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29520: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29520: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29520: Goal:
-29520: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-29520: Order:
-29520: kbo
-29520: Leaf order:
-29520: x 2 0 2 1,1,2
-29520: y 2 0 2 2,1,2
-29520: z 2 0 2 3,1,2
-29520: additive_identity 9 0 1 3
-29520: additive_inverse 6 1 0
-29520: commutator 1 2 0
-29520: add 17 2 1 0,2
-29520: multiply 22 2 0
-29520: associator 3 3 2 0,1,2
-29519: Facts:
-29519: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29519: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29519: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29519: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29519: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29519: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29519: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29519: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29519: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29519: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29519: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29519: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29519: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29519: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29519: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29519: Goal:
-29519: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-29519: Order:
-29519: nrkbo
-29519: Leaf order:
-29519: x 2 0 2 1,1,2
-29519: y 2 0 2 2,1,2
-29519: z 2 0 2 3,1,2
-29519: additive_identity 9 0 1 3
-29519: additive_inverse 6 1 0
-29519: commutator 1 2 0
-29519: add 17 2 1 0,2
-29519: multiply 22 2 0
-29519: associator 3 3 2 0,1,2
-NO CLASH, using fixed ground order
-29521: Facts:
-29521: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-29521: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-29521: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-29521: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-29521: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-29521: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-29521: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-29521: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-29521: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-29521: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-29521: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-29521: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29521: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29521: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-29521: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-29521: Goal:
-29521: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-29521: Order:
-29521: lpo
-29521: Leaf order:
-29521: x 2 0 2 1,1,2
-29521: y 2 0 2 2,1,2
-29521: z 2 0 2 3,1,2
-29521: additive_identity 9 0 1 3
-29521: additive_inverse 6 1 0
-29521: commutator 1 2 0
-29521: add 17 2 1 0,2
-29521: multiply 22 2 0
-29521: associator 3 3 2 0,1,2
-% SZS status Timeout for RNG025-4.p
-NO CLASH, using fixed ground order
-29553: Facts:
-29553: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29553: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29553: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29553: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29553: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29553: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29553: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29553: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29553: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29553: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29553: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29553: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29553: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29553: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =<=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-29553: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =<=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-29553: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =<=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-29553: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-29553: Goal:
-29553: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29553: Order:
-29553: nrkbo
-29553: Leaf order:
-29553: a 2 0 2 1,1,2
-29553: b 2 0 2 2,1,2
-29553: c 2 0 2 3,1,2
-29553: additive_identity 9 0 1 3
-29553: additive_inverse 5 1 0
-29553: commutator 1 2 0
-29553: multiply 18 2 0
-29553: add 22 2 1 0,2
-29553: associator 11 3 2 0,1,2
-NO CLASH, using fixed ground order
-29554: Facts:
-29554: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29554: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29554: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29554: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29554: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29554: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29554: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29554: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29554: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29554: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29554: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29554: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29554: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29554: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =<=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-29554: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =<=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-29554: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =<=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-29554: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-29554: Goal:
-29554: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29554: Order:
-29554: kbo
-29554: Leaf order:
-29554: a 2 0 2 1,1,2
-29554: b 2 0 2 2,1,2
-29554: c 2 0 2 3,1,2
-29554: additive_identity 9 0 1 3
-29554: additive_inverse 5 1 0
-29554: commutator 1 2 0
-29554: multiply 18 2 0
-29554: add 22 2 1 0,2
-29554: associator 11 3 2 0,1,2
-NO CLASH, using fixed ground order
-29555: Facts:
-29555: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-29555: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-29555: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-29555: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-29555: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-29555: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-29555: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-29555: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-29555: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-29555: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-29555: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-29555: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-29555: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-29555: Id : 15, {_}:
- associator ?37 ?38 (add ?39 ?40)
- =>=
- add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
- [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
-29555: Id : 16, {_}:
- associator ?42 (add ?43 ?44) ?45
- =>=
- add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
- [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
-29555: Id : 17, {_}:
- associator (add ?47 ?48) ?49 ?50
- =>=
- add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
- [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
-29555: Id : 18, {_}:
- commutator ?52 ?53
- =<=
- add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
- [53, 52] by commutator ?52 ?53
-29555: Goal:
-29555: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29555: Order:
-29555: lpo
-29555: Leaf order:
-29555: a 2 0 2 1,1,2
-29555: b 2 0 2 2,1,2
-29555: c 2 0 2 3,1,2
-29555: additive_identity 9 0 1 3
-29555: additive_inverse 5 1 0
-29555: commutator 1 2 0
-29555: multiply 18 2 0
-29555: add 22 2 1 0,2
-29555: associator 11 3 2 0,1,2
-% SZS status Timeout for RNG025-8.p
-NO CLASH, using fixed ground order
-29571: Facts:
-29571: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29571: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29571: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29571: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29571: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29571: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29571: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29571: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29571: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29571: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29571: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29571: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29571: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29571: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29571: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29571: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29571: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29571: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29571: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29571: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-29571: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =<=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-29571: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =<=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-29571: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =<=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-29571: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-29571: Goal:
-29571: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29571: Order:
-29571: nrkbo
-29571: Leaf order:
-29571: a 2 0 2 1,1,2
-29571: b 2 0 2 2,1,2
-29571: c 2 0 2 3,1,2
-29571: additive_identity 9 0 1 3
-29571: additive_inverse 21 1 0
-29571: commutator 1 2 0
-29571: add 30 2 1 0,2
-29571: multiply 36 2 0 add
-29571: associator 11 3 2 0,1,2
-NO CLASH, using fixed ground order
-29572: Facts:
-NO CLASH, using fixed ground order
-29572: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29572: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29572: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29572: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29572: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29572: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29572: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29572: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29572: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29572: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29572: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29572: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29572: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29572: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29572: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29572: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29572: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29572: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29572: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29572: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-29572: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =<=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-29572: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =<=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-29572: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =<=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-29572: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-29572: Goal:
-29572: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29572: Order:
-29572: kbo
-29572: Leaf order:
-29572: a 2 0 2 1,1,2
-29572: b 2 0 2 2,1,2
-29572: c 2 0 2 3,1,2
-29572: additive_identity 9 0 1 3
-29572: additive_inverse 21 1 0
-29572: commutator 1 2 0
-29572: add 30 2 1 0,2
-29572: multiply 36 2 0 add
-29572: associator 11 3 2 0,1,2
-29573: Facts:
-29573: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-29573: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-29573: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-29573: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-29573: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-29573: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-29573: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-29573: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-29573: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-29573: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-29573: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-29573: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-29573: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-29573: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-29573: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-29573: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-29573: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-29573: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-29573: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-29573: Id : 21, {_}:
- multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
- [60, 59] by left_alternative ?59 ?60
-29573: Id : 22, {_}:
- associator ?62 ?63 (add ?64 ?65)
- =>=
- add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
- [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
-29573: Id : 23, {_}:
- associator ?67 (add ?68 ?69) ?70
- =>=
- add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
- [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
-29573: Id : 24, {_}:
- associator (add ?72 ?73) ?74 ?75
- =>=
- add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
- [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
-29573: Id : 25, {_}:
- commutator ?77 ?78
- =<=
- add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
- [78, 77] by commutator ?77 ?78
-29573: Goal:
-29573: Id : 1, {_}:
- add (associator a b c) (associator a c b) =>= additive_identity
- [] by prove_flexible_law
-29573: Order:
-29573: lpo
-29573: Leaf order:
-29573: a 2 0 2 1,1,2
-29573: b 2 0 2 2,1,2
-29573: c 2 0 2 3,1,2
-29573: additive_identity 9 0 1 3
-29573: additive_inverse 21 1 0
-29573: commutator 1 2 0
-29573: add 30 2 1 0,2
-29573: multiply 36 2 0 add
-29573: associator 11 3 2 0,1,2
-% SZS status Timeout for RNG025-9.p
-NO CLASH, using fixed ground order
-29618: Facts:
-29618: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-29618: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-29618: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-29618: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =<=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-29618: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-29618: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-29618: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-29618: Goal:
-29618: Id : 1, {_}:
- add a (multiply b c) =<= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-29618: Order:
-29618: nrkbo
-29618: Leaf order:
-29618: n1 1 0 0
-29618: b 2 0 2 1,2,2
-29618: c 2 0 2 2,2,2
-29618: a 3 0 3 1,2
-29618: inverse 3 1 0
-29618: multiply 9 2 2 0,2,2
-29618: add 9 2 3 0,2
-29618: pixley 4 3 0
-NO CLASH, using fixed ground order
-29619: Facts:
-29619: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-29619: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-29619: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-29619: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =<=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-29619: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-29619: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-29619: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-29619: Goal:
-29619: Id : 1, {_}:
- add a (multiply b c) =<= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-29619: Order:
-29619: kbo
-29619: Leaf order:
-29619: n1 1 0 0
-29619: b 2 0 2 1,2,2
-29619: c 2 0 2 2,2,2
-29619: a 3 0 3 1,2
-29619: inverse 3 1 0
-29619: multiply 9 2 2 0,2,2
-29619: add 9 2 3 0,2
-29619: pixley 4 3 0
-NO CLASH, using fixed ground order
-29621: Facts:
-29621: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-29621: Id : 3, {_}:
- multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
- [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-29621: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-29621: Id : 5, {_}:
- pixley ?11 ?12 ?13
- =>=
- add (multiply ?11 (inverse ?12))
- (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
- [13, 12, 11] by pixley_defn ?11 ?12 ?13
-29621: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-29621: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-29621: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-29621: Goal:
-29621: Id : 1, {_}:
- add a (multiply b c) =>= multiply (add a b) (add a c)
- [] by prove_add_multiply_property
-29621: Order:
-29621: lpo
-29621: Leaf order:
-29621: n1 1 0 0
-29621: b 2 0 2 1,2,2
-29621: c 2 0 2 2,2,2
-29621: a 3 0 3 1,2
-29621: inverse 3 1 0
-29621: multiply 9 2 2 0,2,2
-29621: add 9 2 3 0,2
-29621: pixley 4 3 0
-Statistics :
-Max weight : 25
-Found proof, 25.954748s
-% SZS status Unsatisfiable for BOO023-1.p
-% SZS output start CNFRefutation for BOO023-1.p
-Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
-Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
-Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
-Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13
-Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
-Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35
-Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
-Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7
-Id : 45, {_}: multiply (multiply ?127 (add ?128 ?129)) (multiply ?129 ?127) =>= multiply ?129 ?127 [129, 128, 127] by Super 2 with 3 at 1,2
-Id : 52, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 (add ?156 ?157))) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Super 45 with 2 at 1,2
-Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3
-Id : 49, {_}: multiply (multiply ?143 n1) (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Super 45 with 4 at 2,1,2
-Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3
-Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3
-Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3
-Id : 162, {_}: multiply (pixley ?407 ?408 ?409) (multiply ?409 (add ?407 (inverse ?408))) =>= multiply ?409 (add ?407 (inverse ?408)) [409, 408, 407] by Super 2 with 19 at 1,2
-Id : 500, {_}: multiply ?959 (multiply ?960 (add ?959 (inverse ?960))) =>= multiply ?960 (add ?959 (inverse ?960)) [960, 959] by Super 162 with 7 at 1,2
-Id : 207, {_}: multiply (multiply ?494 n1) (multiply (inverse ?495) ?494) =>= multiply (inverse ?495) ?494 [495, 494] by Super 45 with 4 at 2,1,2
-Id : 211, {_}: multiply n1 (multiply (inverse ?507) (add ?508 n1)) =>= multiply (inverse ?507) (add ?508 n1) [508, 507] by Super 207 with 2 at 1,2
-Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2
-Id : 60, {_}: multiply (inverse ?174) (add ?175 n1) =<= add (multiply ?175 (inverse ?174)) (inverse ?174) [175, 174] by Super 3 with 16 at 2,3
-Id : 61, {_}: multiply (inverse ?177) (add (add ?178 (inverse ?177)) n1) =>= add (inverse ?177) (inverse ?177) [178, 177] by Super 60 with 2 at 1,3
-Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3
-Id : 283, {_}: add (inverse ?177) (multiply n1 (inverse ?177)) =>= add (inverse ?177) (inverse ?177) [177] by Demod 61 with 14 at 2
-Id : 40, {_}: multiply (inverse ?110) (add n1 ?111) =<= add (inverse ?110) (multiply ?111 (inverse ?110)) [111, 110] by Super 3 with 16 at 1,3
-Id : 284, {_}: multiply (inverse ?177) (add n1 n1) =?= add (inverse ?177) (inverse ?177) [177] by Demod 283 with 40 at 2
-Id : 297, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) (add n1 n1) [660] by Super 211 with 284 at 2,2
-Id : 505, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 500 with 297 at 2,2
-Id : 513, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 505 with 284 at 2,2
-Id : 514, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 513 with 297 at 3
-Id : 515, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 514 with 284 at 3
-Id : 522, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 515 at 2,3
-Id : 525, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 522 with 8 at 2
-Id : 543, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 525 at 2,2
-Id : 39, {_}: multiply (inverse ?107) (add ?108 n1) =<= add (multiply ?108 (inverse ?107)) (inverse ?107) [108, 107] by Super 3 with 16 at 2,3
-Id : 557, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 543 with 39 at 3
-Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3
-Id : 116, {_}: ?322 =<= add (multiply ?323 (inverse ?323)) (multiply ?322 n1) [323, 322] by Demod 22 with 6 at 2
-Id : 131, {_}: ?358 =<= add (inverse n1) (multiply ?358 n1) [358] by Super 116 with 16 at 1,3
-Id : 144, {_}: add ?384 n1 =?= add (inverse n1) n1 [384] by Super 131 with 2 at 2,3
-Id : 132, {_}: add ?360 n1 =?= add (inverse n1) n1 [360] by Super 131 with 2 at 2,3
-Id : 145, {_}: add ?386 n1 =?= add ?387 n1 [387, 386] by Super 144 with 132 at 3
-Id : 730, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?1307 n1) [1307] by Super 557 with 145 at 2,3
-Id : 734, {_}: multiply (inverse n1) (inverse n1) =<= add (inverse n1) (inverse n1) [] by Super 730 with 284 at 3
-Id : 756, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 515 with 734 at 2,2
-Id : 757, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= multiply (inverse n1) (inverse n1) [] by Demod 756 with 734 at 3
-Id : 758, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (multiply (inverse n1) (inverse n1)) [] by Demod 525 with 734 at 2,3
-Id : 759, {_}: inverse n1 =<= multiply (inverse n1) (add (inverse n1) (inverse n1)) [] by Demod 758 with 3 at 3
-Id : 760, {_}: inverse n1 =<= multiply (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 759 with 734 at 2,3
-Id : 761, {_}: inverse n1 =<= multiply (inverse n1) (inverse n1) [] by Demod 757 with 760 at 2
-Id : 765, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 734 with 761 at 2
-Id : 771, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Super 24 with 765 at 1,2,2,3
-Id : 809, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Demod 771 with 765 at 1,2
-Id : 810, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (inverse n1)) [1319] by Demod 809 with 765 at 2,2,3
-Id : 859, {_}: pixley (inverse n1) n1 ?1388 =<= multiply (inverse n1) (add n1 ?1388) [1388] by Demod 810 with 40 at 3
-Id : 860, {_}: pixley (inverse n1) n1 (inverse n1) =>= multiply (inverse n1) n1 [] by Super 859 with 4 at 2,3
-Id : 885, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 860 with 8 at 2
-Id : 902, {_}: multiply n1 (add ?1409 (inverse n1)) =<= add (multiply ?1409 n1) (inverse n1) [1409] by Super 3 with 885 at 2,3
-Id : 168, {_}: multiply ?429 (multiply ?430 (add ?429 (inverse ?430))) =>= multiply ?430 (add ?429 (inverse ?430)) [430, 429] by Super 162 with 7 at 1,2
-Id : 903, {_}: multiply n1 (add (inverse n1) ?1411) =<= add (inverse n1) (multiply ?1411 n1) [1411] by Super 3 with 885 at 1,3
-Id : 118, {_}: ?328 =<= add (inverse n1) (multiply ?328 n1) [328] by Super 116 with 16 at 1,3
-Id : 1013, {_}: multiply n1 (add (inverse n1) ?1510) =>= ?1510 [1510] by Demod 903 with 118 at 3
-Id : 1014, {_}: multiply n1 n1 =>= inverse (inverse n1) [] by Super 1013 with 4 at 2,2
-Id : 1051, {_}: multiply n1 (add n1 (inverse n1)) =<= add (inverse (inverse n1)) (inverse n1) [] by Super 902 with 1014 at 1,3
-Id : 1091, {_}: multiply n1 n1 =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1051 with 4 at 2,2
-Id : 1092, {_}: inverse (inverse n1) =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1091 with 1014 at 2
-Id : 1370, {_}: multiply (inverse (inverse n1)) (multiply n1 (inverse (inverse n1))) =>= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Super 168 with 1092 at 2,2,2
-Id : 1373, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =<= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Demod 1370 with 16 at 2,2
-Id : 1374, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= multiply n1 (inverse (inverse n1)) [] by Demod 1373 with 1092 at 2,3
-Id : 1375, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= inverse (inverse n1) [] by Demod 1374 with 16 at 3
-Id : 1407, {_}: multiply (inverse (inverse n1)) (add n1 (inverse (inverse n1))) =>= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Super 40 with 1375 at 2,3
-Id : 1015, {_}: multiply n1 (add ?1513 n1) =>= n1 [1513] by Super 1013 with 145 at 2,2
-Id : 1292, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 1015 at 2
-Id : 1307, {_}: n1 =<= add n1 (inverse (inverse n1)) [] by Demod 1292 with 1014 at 2,3
-Id : 1421, {_}: multiply (inverse (inverse n1)) n1 =<= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Demod 1407 with 1307 at 2,2
-Id : 1422, {_}: multiply (inverse (inverse n1)) n1 =<= multiply (inverse (inverse n1)) (add n1 n1) [] by Demod 1421 with 284 at 3
-Id : 111, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2
-Id : 359, {_}: multiply (multiply ?774 n1) (add ?774 ?775) =<= add (multiply ?774 n1) (multiply ?775 (multiply ?774 n1)) [775, 774] by Super 14 with 111 at 1,2,2
-Id : 114, {_}: multiply ?317 (multiply ?317 n1) =>= multiply ?317 n1 [317] by Super 2 with 111 at 1,2
-Id : 364, {_}: multiply (multiply ?788 n1) (add ?788 ?788) =?= add (multiply ?788 n1) (multiply ?788 n1) [788] by Super 359 with 114 at 2,3
-Id : 390, {_}: multiply (multiply ?814 n1) (add ?814 ?814) =>= multiply n1 (add ?814 ?814) [814] by Demod 364 with 3 at 3
-Id : 391, {_}: multiply (multiply n1 n1) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Super 390 with 145 at 2,2
-Id : 1050, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Demod 391 with 1014 at 1,2
-Id : 1286, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= n1 [816] by Demod 1050 with 1015 at 3
-Id : 1423, {_}: multiply (inverse (inverse n1)) n1 =>= n1 [] by Demod 1422 with 1286 at 3
-Id : 1449, {_}: multiply n1 (add (inverse (inverse n1)) (inverse n1)) =>= add n1 (inverse n1) [] by Super 902 with 1423 at 1,3
-Id : 1452, {_}: multiply n1 (inverse (inverse n1)) =>= add n1 (inverse n1) [] by Demod 1449 with 1092 at 2,2
-Id : 1453, {_}: multiply n1 (inverse (inverse n1)) =>= n1 [] by Demod 1452 with 4 at 3
-Id : 1454, {_}: inverse (inverse n1) =>= n1 [] by Demod 1453 with 16 at 2
-Id : 1500, {_}: multiply (multiply ?2051 n1) (multiply n1 ?2051) =>= multiply (inverse (inverse n1)) ?2051 [2051] by Super 49 with 1454 at 1,2,2
-Id : 3169, {_}: multiply (multiply ?3985 n1) (multiply n1 ?3985) =>= multiply n1 ?3985 [3985] by Demod 1500 with 1454 at 1,3
-Id : 933, {_}: multiply n1 (add (inverse n1) ?1411) =>= ?1411 [1411] by Demod 903 with 118 at 3
-Id : 3175, {_}: multiply (multiply (add (inverse n1) ?3998) n1) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Super 3169 with 933 at 2,2
-Id : 1440, {_}: inverse (inverse n1) =<= add (inverse n1) n1 [] by Super 118 with 1423 at 2,3
-Id : 1591, {_}: n1 =<= add (inverse n1) n1 [] by Demod 1440 with 1454 at 2
-Id : 1602, {_}: add ?2105 n1 =>= n1 [2105] by Super 145 with 1591 at 3
-Id : 1719, {_}: multiply ?2217 n1 =<= add ?2217 (multiply n1 ?2217) [2217] by Super 14 with 1602 at 2,2
-Id : 1478, {_}: n1 =<= add n1 n1 [] by Demod 1307 with 1454 at 2,3
-Id : 1483, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) n1 [660] by Demod 297 with 1478 at 2,3
-Id : 1482, {_}: multiply (inverse ?177) n1 =<= add (inverse ?177) (inverse ?177) [177] by Demod 284 with 1478 at 2,2
-Id : 1484, {_}: multiply n1 (multiply (inverse ?660) n1) =>= multiply (inverse ?660) n1 [660] by Demod 1483 with 1482 at 2,2
-Id : 1727, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= add (multiply (inverse ?2233) n1) (multiply (inverse ?2233) n1) [2233] by Super 1719 with 1484 at 2,3
-Id : 1763, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= multiply n1 (add (inverse ?2233) (inverse ?2233)) [2233] by Demod 1727 with 3 at 3
-Id : 1764, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply n1 (multiply (inverse ?2233) n1) [2233] by Demod 1763 with 1482 at 2,3
-Id : 1765, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply (inverse ?2233) n1 [2233] by Demod 1764 with 1484 at 3
-Id : 1914, {_}: multiply (inverse ?2603) n1 =<= add (inverse n1) (multiply (inverse ?2603) n1) [2603] by Super 118 with 1765 at 2,3
-Id : 1949, {_}: multiply (inverse ?2603) n1 =>= inverse ?2603 [2603] by Demod 1914 with 118 at 3
-Id : 1994, {_}: multiply n1 (add (inverse ?2679) ?2680) =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Super 3 with 1949 at 1,3
-Id : 2422, {_}: multiply n1 (multiply n1 (add (inverse n1) ?3107)) =>= multiply ?3107 n1 [3107] by Super 933 with 1994 at 2,2
-Id : 2437, {_}: multiply n1 ?3107 =?= multiply ?3107 n1 [3107] by Demod 2422 with 933 at 2,2
-Id : 3237, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Demod 3175 with 2437 at 1,2
-Id : 3238, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= ?3998 [3998] by Demod 3237 with 933 at 3
-Id : 3239, {_}: multiply ?3998 ?3998 =>= ?3998 [3998] by Demod 3238 with 933 at 1,2
-Id : 3295, {_}: multiply ?4085 (add ?4086 ?4085) =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Super 3 with 3239 at 2,3
-Id : 3506, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= multiply ?37 (add ?38 ?37) [39, 38, 37] by Demod 13 with 3295 at 3
-Id : 4221, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 ?157)) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Demod 52 with 3506 at 2,2
-Id : 4233, {_}: multiply (add ?4966 ?4967) (multiply ?4967 (add ?4968 ?4967)) =>= multiply ?4967 (add ?4968 ?4967) [4968, 4967, 4966] by Demod 4221 with 3506 at 3
-Id : 1725, {_}: multiply (add (inverse n1) ?2230) n1 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Super 1719 with 933 at 2,3
-Id : 2746, {_}: multiply n1 (add (inverse n1) ?2230) =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 1725 with 2437 at 2
-Id : 2751, {_}: ?2230 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 2746 with 933 at 2
-Id : 4246, {_}: multiply (add ?5016 ?5017) (multiply ?5017 ?5017) =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Super 4233 with 2751 at 2,2,2
-Id : 4327, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Demod 4246 with 3239 at 2,2
-Id : 3296, {_}: multiply ?4088 (add ?4088 ?4089) =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Super 3 with 3239 at 1,3
-Id : 3736, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= multiply ?41 (add ?41 ?43) [43, 42, 41] by Demod 14 with 3296 at 3
-Id : 4328, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add ?5017 ?5017) [5017, 5016] by Demod 4327 with 3736 at 3
-Id : 4329, {_}: ?5017 =<= multiply ?5017 (add ?5017 ?5017) [5017] by Demod 4328 with 2 at 2
-Id : 3529, {_}: multiply ?4289 (add ?4290 ?4289) =<= add (multiply ?4290 ?4289) ?4289 [4290, 4289] by Super 3 with 3239 at 2,3
-Id : 3546, {_}: multiply ?4342 (add ?4342 ?4342) =>= add ?4342 ?4342 [4342] by Super 3529 with 3239 at 1,3
-Id : 4330, {_}: ?5017 =<= add ?5017 ?5017 [5017] by Demod 4329 with 3546 at 3
-Id : 4419, {_}: multiply ?5179 (add ?5180 ?5180) =>= multiply ?5180 ?5179 [5180, 5179] by Super 3 with 4330 at 3
-Id : 4472, {_}: multiply ?5179 ?5180 =?= multiply ?5180 ?5179 [5180, 5179] by Demod 4419 with 4330 at 2,2
-Id : 6559, {_}: multiply ?7216 (add ?7217 ?7218) =<= add (multiply ?7217 ?7216) (multiply ?7216 ?7218) [7218, 7217, 7216] by Super 3 with 4472 at 2,3
-Id : 4435, {_}: multiply ?5223 (add ?5224 ?5223) =<= multiply ?5223 (add ?5223 (add ?5224 ?5223)) [5224, 5223] by Super 3736 with 4330 at 2,2
-Id : 4446, {_}: multiply ?5223 (add ?5224 ?5223) =?= multiply ?5223 (add ?5223 ?5223) [5224, 5223] by Demod 4435 with 3506 at 3
-Id : 4447, {_}: multiply ?5223 (add ?5224 ?5223) =>= multiply ?5223 ?5223 [5224, 5223] by Demod 4446 with 4330 at 2,3
-Id : 4448, {_}: multiply ?5223 (add ?5224 ?5223) =>= ?5223 [5224, 5223] by Demod 4447 with 3239 at 3
-Id : 4587, {_}: multiply (add ?5347 ?5348) (add ?5349 ?5348) =<= add (multiply ?5349 (add ?5347 ?5348)) ?5348 [5349, 5348, 5347] by Super 3 with 4448 at 2,3
-Id : 13274, {_}: multiply ?16470 (add ?16471 ?16472) =<= add (multiply ?16471 ?16470) (multiply ?16470 ?16472) [16472, 16471, 16470] by Super 3 with 4472 at 2,3
-Id : 1990, {_}: inverse ?2668 =<= add (inverse n1) (inverse ?2668) [2668] by Super 118 with 1949 at 2,3
-Id : 2035, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =?= multiply ?2698 (add (inverse n1) (inverse ?2698)) [2698] by Super 168 with 1990 at 2,2,2
-Id : 2073, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =>= multiply ?2698 (inverse ?2698) [2698] by Demod 2035 with 1990 at 2,3
-Id : 3753, {_}: multiply n1 (multiply (inverse n1) (add (inverse n1) ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Super 933 with 3296 at 2,2
-Id : 3737, {_}: multiply (inverse ?110) (add n1 ?111) =<= multiply (inverse ?110) (add (inverse ?110) ?111) [111, 110] by Demod 40 with 3296 at 3
-Id : 3799, {_}: multiply n1 (multiply (inverse n1) (add n1 ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Demod 3753 with 3737 at 2,2
-Id : 811, {_}: pixley (inverse n1) n1 ?1319 =<= multiply (inverse n1) (add n1 ?1319) [1319] by Demod 810 with 40 at 3
-Id : 3800, {_}: multiply n1 (pixley (inverse n1) n1 ?4498) =>= multiply ?4498 (inverse n1) [4498] by Demod 3799 with 811 at 2,2
-Id : 1503, {_}: multiply (inverse (inverse n1)) (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Super 40 with 1454 at 2,2,3
-Id : 1564, {_}: multiply n1 (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Demod 1503 with 1454 at 1,2
-Id : 1565, {_}: multiply n1 (add n1 ?2058) =<= add n1 (multiply ?2058 n1) [2058] by Demod 1564 with 1454 at 1,3
-Id : 1981, {_}: multiply n1 (add n1 (inverse ?2643)) =>= add n1 (inverse ?2643) [2643] by Super 1565 with 1949 at 2,3
-Id : 2089, {_}: pixley n1 ?2784 n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Super 19 with 1981 at 2,3
-Id : 2096, {_}: n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Demod 2089 with 8 at 2
-Id : 2097, {_}: n1 =<= add (inverse ?2784) (add n1 (inverse ?2784)) [2784] by Demod 2096 with 16 at 1,3
-Id : 4563, {_}: ?4085 =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Demod 3295 with 4448 at 2
-Id : 4567, {_}: add ?5289 ?5290 =<= add ?5290 (add ?5289 ?5290) [5290, 5289] by Super 4563 with 4448 at 1,3
-Id : 5426, {_}: n1 =<= add n1 (inverse ?2784) [2784] by Demod 2097 with 4567 at 3
-Id : 5450, {_}: multiply n1 (multiply ?6117 n1) =<= multiply ?6117 (add n1 (inverse ?6117)) [6117] by Super 168 with 5426 at 2,2,2
-Id : 5478, {_}: multiply n1 (multiply ?6117 n1) =>= multiply ?6117 n1 [6117] by Demod 5450 with 5426 at 2,3
-Id : 2780, {_}: multiply n1 (add (inverse ?3598) ?3599) =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Super 1994 with 2437 at 2,3
-Id : 38, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 (add n1 (inverse ?104))) [105, 104] by Super 19 with 16 at 1,3
-Id : 5427, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 n1) [105, 104] by Demod 38 with 5426 at 2,2,3
-Id : 5431, {_}: pixley n1 ?104 ?105 =<= multiply n1 (add (inverse ?104) ?105) [105, 104] by Demod 5427 with 1994 at 3
-Id : 5434, {_}: pixley n1 ?3598 ?3599 =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Demod 2780 with 5431 at 2
-Id : 5505, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= add (inverse ?6141) (multiply ?6142 n1) [6142, 6141] by Super 5434 with 5478 at 2,3
-Id : 5432, {_}: pixley n1 ?2679 ?2680 =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Demod 1994 with 5431 at 2
-Id : 5574, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= pixley n1 ?6141 ?6142 [6142, 6141] by Demod 5505 with 5432 at 3
-Id : 5935, {_}: pixley n1 n1 ?6510 =>= multiply ?6510 n1 [6510] by Super 6 with 5574 at 2
-Id : 5952, {_}: ?6510 =<= multiply ?6510 n1 [6510] by Demod 5935 with 6 at 2
-Id : 5985, {_}: multiply n1 ?6117 =?= multiply ?6117 n1 [6117] by Demod 5478 with 5952 at 2,2
-Id : 5986, {_}: multiply n1 ?6117 =>= ?6117 [6117] by Demod 5985 with 5952 at 3
-Id : 5995, {_}: pixley (inverse n1) n1 ?4498 =>= multiply ?4498 (inverse n1) [4498] by Demod 3800 with 5986 at 2
-Id : 4560, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= ?37 [39, 38, 37] by Demod 3506 with 4448 at 3
-Id : 4745, {_}: multiply n1 (add ?5532 (inverse n1)) =>= add ?5532 (inverse n1) [5532] by Super 933 with 4567 at 2,2
-Id : 4852, {_}: multiply ?5678 (add ?5678 (inverse n1)) =?= multiply n1 (add ?5678 (inverse n1)) [5678] by Super 168 with 4745 at 2,2
-Id : 4888, {_}: multiply ?5678 (add ?5678 (inverse n1)) =>= add ?5678 (inverse n1) [5678] by Demod 4852 with 4745 at 3
-Id : 5026, {_}: multiply (inverse ?5768) (add n1 (inverse n1)) =>= add (inverse ?5768) (inverse n1) [5768] by Super 3737 with 4888 at 3
-Id : 5122, {_}: multiply (inverse ?5768) n1 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5026 with 4 at 2,2
-Id : 5123, {_}: multiply n1 (inverse ?5768) =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5122 with 2437 at 2
-Id : 5124, {_}: inverse ?5768 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5123 with 16 at 2
-Id : 5166, {_}: multiply (inverse n1) (add ?5860 (inverse ?5861)) =>= inverse n1 [5861, 5860] by Super 4560 with 5124 at 2,2,2
-Id : 6158, {_}: multiply ?6712 (inverse n1) =<= multiply (inverse n1) (add ?6712 (inverse (inverse n1))) [6712] by Super 168 with 5166 at 2,2
-Id : 6219, {_}: multiply ?6712 (inverse n1) =>= inverse n1 [6712] by Demod 6158 with 5166 at 3
-Id : 6251, {_}: pixley (inverse n1) n1 ?4498 =>= inverse n1 [4498] by Demod 5995 with 6219 at 3
-Id : 2037, {_}: pixley (inverse n1) ?2703 ?2704 =<= add (multiply (inverse n1) (inverse ?2703)) (multiply ?2704 (inverse ?2703)) [2704, 2703] by Super 19 with 1990 at 2,2,3
-Id : 2071, {_}: pixley (inverse n1) ?2703 ?2704 =<= multiply (inverse ?2703) (add (inverse n1) ?2704) [2704, 2703] by Demod 2037 with 3 at 3
-Id : 5976, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) ?63 [62, 63] by Demod 111 with 5952 at 2,3
-Id : 6253, {_}: ?6806 =<= add (inverse n1) ?6806 [6806] by Super 5976 with 6219 at 1,3
-Id : 6304, {_}: pixley (inverse n1) ?2703 ?2704 =>= multiply (inverse ?2703) ?2704 [2704, 2703] by Demod 2071 with 6253 at 2,3
-Id : 6308, {_}: multiply (inverse n1) ?4498 =>= inverse n1 [4498] by Demod 6251 with 6304 at 2
-Id : 6315, {_}: inverse n1 =<= multiply ?2698 (inverse ?2698) [2698] by Demod 2073 with 6308 at 2
-Id : 6591, {_}: inverse n1 =<= multiply (inverse ?7342) ?7342 [7342] by Super 6315 with 4472 at 3
-Id : 13310, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =?= add (multiply ?16624 (inverse ?16623)) (inverse n1) [16624, 16623] by Super 13274 with 6591 at 2,3
-Id : 6698, {_}: multiply ?7545 (add ?7545 (inverse ?7545)) =>= add ?7545 (inverse n1) [7545] by Super 3296 with 6591 at 2,3
-Id : 6721, {_}: multiply ?7545 n1 =<= add ?7545 (inverse n1) [7545] by Demod 6698 with 4 at 2,2
-Id : 6722, {_}: ?7545 =<= add ?7545 (inverse n1) [7545] by Demod 6721 with 5952 at 2
-Id : 13428, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =>= multiply ?16624 (inverse ?16623) [16624, 16623] by Demod 13310 with 6722 at 3
-Id : 13655, {_}: multiply (add ?17100 ?17101) (add (inverse ?17101) ?17101) =>= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Super 4587 with 13428 at 1,3
-Id : 6531, {_}: ?7094 =<= add (multiply ?7094 ?7095) ?7094 [7095, 7094] by Super 4563 with 4472 at 1,3
-Id : 6689, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =?= add (inverse n1) (multiply ?7514 ?7513) [7514, 7513] by Super 3 with 6591 at 1,3
-Id : 7566, {_}: multiply ?8615 (add (inverse ?8615) ?8616) =>= multiply ?8616 ?8615 [8616, 8615] by Demod 6689 with 6253 at 3
-Id : 7568, {_}: multiply ?8620 n1 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Super 7566 with 4 at 2,2
-Id : 7615, {_}: ?8620 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Demod 7568 with 5952 at 2
-Id : 7635, {_}: inverse (inverse ?8669) =<= add ?8669 (inverse (inverse ?8669)) [8669] by Super 6531 with 7615 at 1,3
-Id : 7710, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= add (multiply ?8783 (inverse (inverse ?8783))) (multiply ?8784 (inverse (inverse ?8783))) [8784, 8783] by Super 19 with 7635 at 2,2,3
-Id : 9183, {_}: pixley ?10684 (inverse ?10684) ?10685 =<= multiply (inverse (inverse ?10684)) (add ?10684 ?10685) [10685, 10684] by Demod 7710 with 3 at 3
-Id : 9184, {_}: pixley ?10687 (inverse ?10687) (inverse ?10687) =>= multiply (inverse (inverse ?10687)) n1 [10687] by Super 9183 with 4 at 2,3
-Id : 9239, {_}: ?10687 =<= multiply (inverse (inverse ?10687)) n1 [10687] by Demod 9184 with 7 at 2
-Id : 9240, {_}: ?10687 =<= multiply n1 (inverse (inverse ?10687)) [10687] by Demod 9239 with 4472 at 3
-Id : 9241, {_}: ?10687 =<= inverse (inverse ?10687) [10687] by Demod 9240 with 5986 at 3
-Id : 9328, {_}: add (inverse ?10804) ?10804 =>= n1 [10804] by Super 4 with 9241 at 2,2
-Id : 13791, {_}: multiply (add ?17100 ?17101) n1 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13655 with 9328 at 2,2
-Id : 13792, {_}: multiply n1 (add ?17100 ?17101) =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13791 with 4472 at 2
-Id : 14391, {_}: add ?18258 ?18259 =<= add (multiply ?18258 (inverse ?18259)) ?18259 [18259, 18258] by Demod 13792 with 5986 at 2
-Id : 6742, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =>= multiply ?7514 ?7513 [7514, 7513] by Demod 6689 with 6253 at 3
-Id : 7563, {_}: multiply (add (inverse ?8606) ?8607) ?8606 =>= multiply ?8607 ?8606 [8607, 8606] by Super 4472 with 6742 at 3
-Id : 14401, {_}: add (add (inverse (inverse ?18285)) ?18286) ?18285 =>= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Super 14391 with 7563 at 1,3
-Id : 14494, {_}: add (add ?18285 ?18286) ?18285 =<= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Demod 14401 with 9241 at 1,1,2
-Id : 13793, {_}: add ?17100 ?17101 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13792 with 5986 at 2
-Id : 14495, {_}: add (add ?18285 ?18286) ?18285 =>= add ?18286 ?18285 [18286, 18285] by Demod 14494 with 13793 at 3
-Id : 6533, {_}: multiply ?7100 (add ?7100 ?7101) =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Super 3296 with 4472 at 2,3
-Id : 7753, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= multiply (inverse (inverse ?8783)) (add ?8783 ?8784) [8784, 8783] by Demod 7710 with 3 at 3
-Id : 9278, {_}: pixley ?8783 (inverse ?8783) ?8784 =>= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 7753 with 9241 at 1,3
-Id : 7714, {_}: pixley (add ?8794 (inverse (inverse ?8794))) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Super 24 with 7635 at 1,2,2,3
-Id : 7746, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Demod 7714 with 7635 at 1,2
-Id : 7747, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (inverse (inverse ?8794))) [8795, 8794] by Demod 7746 with 4330 at 2,2,3
-Id : 7748, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= multiply (inverse (inverse ?8794)) (add (inverse (inverse ?8794)) ?8795) [8795, 8794] by Demod 7747 with 3296 at 3
-Id : 7749, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =>= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7748 with 3737 at 3
-Id : 9298, {_}: pixley ?8794 (inverse ?8794) ?8795 =?= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7749 with 9241 at 1,2
-Id : 9299, {_}: pixley ?8794 (inverse ?8794) ?8795 =>= multiply ?8794 (add n1 ?8795) [8795, 8794] by Demod 9298 with 9241 at 1,3
-Id : 9310, {_}: multiply ?8783 (add n1 ?8784) =?= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9278 with 9299 at 2
-Id : 9334, {_}: n1 =<= add n1 ?10824 [10824] by Super 5426 with 9241 at 2,3
-Id : 9392, {_}: multiply ?8783 n1 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9310 with 9334 at 2,2
-Id : 9393, {_}: ?8783 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9392 with 5952 at 2
-Id : 9397, {_}: ?7100 =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Demod 6533 with 9393 at 2
-Id : 7652, {_}: multiply ?8717 (add (inverse (inverse ?8717)) ?8718) =>= add ?8717 (multiply ?8718 ?8717) [8718, 8717] by Super 3 with 7615 at 1,3
-Id : 8997, {_}: multiply ?10489 (add (inverse (inverse ?10489)) ?10490) =>= multiply ?10489 (add ?10489 ?10490) [10490, 10489] by Demod 7652 with 3296 at 3
-Id : 9013, {_}: multiply (add (inverse (inverse ?10527)) ?10528) ?10527 =>= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Super 8997 with 4472 at 2
-Id : 11578, {_}: multiply (add ?10527 ?10528) ?10527 =?= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Demod 9013 with 9241 at 1,1,2
-Id : 11579, {_}: multiply (add ?10527 ?10528) ?10527 =>= ?10527 [10528, 10527] by Demod 11578 with 9393 at 3
-Id : 11608, {_}: add ?13907 ?13908 =<= add (add ?13907 ?13908) ?13907 [13908, 13907] by Super 9397 with 11579 at 2,3
-Id : 14496, {_}: add ?18285 ?18286 =?= add ?18286 ?18285 [18286, 18285] by Demod 14495 with 11608 at 2
-Id : 20857, {_}: multiply ?26392 (add ?26393 ?26394) =<= add (multiply ?26392 ?26394) (multiply ?26393 ?26392) [26394, 26393, 26392] by Super 6559 with 14496 at 3
-Id : 6561, {_}: multiply ?7224 (add ?7225 ?7226) =<= add (multiply ?7224 ?7225) (multiply ?7226 ?7224) [7226, 7225, 7224] by Super 3 with 4472 at 1,3
-Id : 45701, {_}: multiply ?26392 (add ?26393 ?26394) =?= multiply ?26392 (add ?26394 ?26393) [26394, 26393, 26392] by Demod 20857 with 6561 at 3
-Id : 92, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (add ?268 ?269) (inverse ?270)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Super 19 with 14 at 2,3
-Id : 88314, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Demod 92 with 4472 at 1,3
-Id : 9395, {_}: ?4088 =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Demod 3296 with 9393 at 2
-Id : 88315, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) ?269 [270, 269, 268] by Demod 88314 with 9395 at 2,3
-Id : 88452, {_}: pixley (add ?145802 ?145803) ?145804 ?145803 =<= multiply (add ?145802 ?145803) (add (inverse ?145804) ?145803) [145804, 145803, 145802] by Demod 88315 with 4587 at 3
-Id : 88455, {_}: pixley (add ?145816 ?145817) (inverse ?145818) ?145817 =>= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145818, 145817, 145816] by Super 88452 with 9241 at 1,2,3
-Id : 11, {_}: multiply (multiply ?29 (add ?30 ?31)) (multiply ?31 ?29) =>= multiply ?31 ?29 [31, 30, 29] by Super 2 with 3 at 1,2
-Id : 6691, {_}: multiply (inverse n1) (multiply ?7519 (inverse (add ?7520 ?7519))) =>= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Super 11 with 6591 at 1,2
-Id : 6741, {_}: inverse n1 =<= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Demod 6691 with 6308 at 2
-Id : 7453, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= add (inverse n1) (multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439)))) [8441, 8440, 8439] by Super 19 with 6741 at 1,3
-Id : 7492, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439))) [8441, 8440, 8439] by Demod 7453 with 6253 at 3
-Id : 98274, {_}: pixley ?163996 (add ?163997 ?163996) n1 =>= add ?163996 (inverse (add ?163997 ?163996)) [163997, 163996] by Super 5986 with 7492 at 2
-Id : 4588, {_}: multiply (add ?5351 ?5352) (add ?5352 ?5353) =<= add ?5352 (multiply ?5353 (add ?5351 ?5352)) [5353, 5352, 5351] by Super 3 with 4448 at 1,3
-Id : 13309, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =?= add (multiply ?16621 ?16620) (inverse n1) [16621, 16620] by Super 13274 with 6315 at 2,3
-Id : 13427, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =>= multiply ?16621 ?16620 [16621, 16620] by Demod 13309 with 6722 at 3
-Id : 13531, {_}: multiply (add ?17007 (inverse ?17008)) (add (inverse ?17008) ?17008) =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Super 4588 with 13427 at 2,3
-Id : 11835, {_}: add ?14300 ?14301 =<= add (add ?14300 ?14301) ?14300 [14301, 14300] by Super 9397 with 11579 at 2,3
-Id : 11844, {_}: add ?14326 (add ?14327 ?14326) =?= add (add ?14327 ?14326) ?14326 [14327, 14326] by Super 11835 with 4567 at 1,3
-Id : 11909, {_}: add ?14327 ?14326 =<= add (add ?14327 ?14326) ?14326 [14326, 14327] by Demod 11844 with 4567 at 2
-Id : 11970, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add ?69 (inverse ?70))) [71, 70, 69] by Demod 24 with 11909 at 2,2,3
-Id : 12697, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= multiply (add ?69 (inverse ?70)) (add (inverse ?70) ?71) [71, 70, 69] by Demod 11970 with 4588 at 3
-Id : 13561, {_}: pixley (add ?17007 (inverse ?17008)) ?17008 ?17008 =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Demod 13531 with 12697 at 2
-Id : 14017, {_}: add ?17647 (inverse ?17648) =<= add (inverse ?17648) (multiply ?17647 ?17648) [17648, 17647] by Demod 13561 with 7 at 2
-Id : 10227, {_}: multiply (inverse ?12001) (add ?12001 ?12002) =>= multiply ?12002 (inverse ?12001) [12002, 12001] by Super 6742 with 9241 at 1,2,2
-Id : 10243, {_}: multiply (inverse ?12047) ?12047 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Super 10227 with 9397 at 2,2
-Id : 10311, {_}: inverse n1 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Demod 10243 with 6591 at 2
-Id : 10454, {_}: inverse n1 =<= multiply (inverse ?12293) (multiply ?12293 ?12294) [12294, 12293] by Demod 10311 with 4472 at 3
-Id : 10488, {_}: inverse n1 =<= multiply ?12387 (multiply (inverse ?12387) ?12388) [12388, 12387] by Super 10454 with 9241 at 1,3
-Id : 14062, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =?= add (inverse (multiply (inverse ?17790) ?17791)) (inverse n1) [17791, 17790] by Super 14017 with 10488 at 2,3
-Id : 14147, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =>= inverse (multiply (inverse ?17790) ?17791) [17791, 17790] by Demod 14062 with 6722 at 3
-Id : 20167, {_}: add ?25476 (inverse (multiply (inverse ?25476) ?25477)) =?= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Super 11608 with 14147 at 1,3
-Id : 20309, {_}: inverse (multiply (inverse ?25476) ?25477) =<= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Demod 20167 with 14147 at 2
-Id : 98343, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =<= add ?164219 (inverse (add (inverse (multiply (inverse ?164219) ?164220)) ?164219)) [164220, 164219] by Super 98274 with 20309 at 2,2
-Id : 98565, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (inverse (inverse (multiply (inverse ?164219) ?164220))) [164220, 164219] by Demod 98343 with 20309 at 1,2,3
-Id : 98566, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (multiply (inverse ?164219) ?164220) [164220, 164219] by Demod 98565 with 9241 at 2,3
-Id : 13654, {_}: multiply (add ?17097 ?17098) (add ?17098 (inverse ?17098)) =>= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Super 4588 with 13428 at 2,3
-Id : 13794, {_}: multiply (add ?17097 ?17098) n1 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13654 with 4 at 2,2
-Id : 13795, {_}: multiply n1 (add ?17097 ?17098) =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13794 with 4472 at 2
-Id : 14561, {_}: add ?18466 ?18467 =<= add ?18467 (multiply ?18466 (inverse ?18467)) [18467, 18466] by Demod 13795 with 5986 at 2
-Id : 14565, {_}: add ?18477 ?18478 =<= add ?18478 (multiply (inverse ?18478) ?18477) [18478, 18477] by Super 14561 with 4472 at 2,3
-Id : 98567, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164220 ?164219 [164220, 164219] by Demod 98566 with 14565 at 3
-Id : 7451, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =?= add (multiply ?8433 (inverse (add ?8431 ?8432))) (inverse n1) [8433, 8432, 8431] by Super 3 with 6741 at 2,3
-Id : 7493, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =>= multiply ?8433 (inverse (add ?8431 ?8432)) [8433, 8432, 8431] by Demod 7451 with 6722 at 3
-Id : 105415, {_}: pixley (add ?172221 ?172222) (inverse (multiply ?172223 (inverse (add ?172221 ?172222)))) n1 =>= add (add ?172223 ?172222) (add ?172221 ?172222) [172223, 172222, 172221] by Super 98567 with 7493 at 1,2,2
-Id : 10242, {_}: multiply (inverse ?12044) ?12044 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12045, 12044] by Super 10227 with 9395 at 2,2
-Id : 10309, {_}: inverse n1 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12044, 12045] by Demod 10242 with 6591 at 2
-Id : 10337, {_}: inverse n1 =<= multiply (inverse ?12122) (multiply ?12123 ?12122) [12123, 12122] by Demod 10309 with 4472 at 3
-Id : 10370, {_}: inverse n1 =<= multiply ?12222 (multiply ?12223 (inverse ?12222)) [12223, 12222] by Super 10337 with 9241 at 1,3
-Id : 14061, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =?= add (inverse (multiply ?17788 (inverse ?17787))) (inverse n1) [17788, 17787] by Super 14017 with 10370 at 2,3
-Id : 14146, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =>= inverse (multiply ?17788 (inverse ?17787)) [17788, 17787] by Demod 14061 with 6722 at 3
-Id : 19953, {_}: add ?25324 (inverse (multiply ?25325 (inverse ?25324))) =?= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25325, 25324] by Super 11608 with 14146 at 1,3
-Id : 20011, {_}: inverse (multiply ?25325 (inverse ?25324)) =<= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25324, 25325] by Demod 19953 with 14146 at 2
-Id : 98342, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =<= add ?164216 (inverse (add (inverse (multiply ?164217 (inverse ?164216))) ?164216)) [164217, 164216] by Super 98274 with 20011 at 2,2
-Id : 98562, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (inverse (inverse (multiply ?164217 (inverse ?164216)))) [164217, 164216] by Demod 98342 with 20011 at 1,2,3
-Id : 98563, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (multiply ?164217 (inverse ?164216)) [164217, 164216] by Demod 98562 with 9241 at 2,3
-Id : 13796, {_}: add ?17097 ?17098 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13795 with 5986 at 2
-Id : 98564, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164217 ?164216 [164217, 164216] by Demod 98563 with 13796 at 3
-Id : 106322, {_}: add ?173840 (add ?173841 ?173842) =<= add (add ?173840 ?173842) (add ?173841 ?173842) [173842, 173841, 173840] by Demod 105415 with 98564 at 2
-Id : 106366, {_}: add ?174020 (add ?174021 (multiply ?174021 ?174022)) =?= add (add ?174020 (multiply ?174021 ?174022)) ?174021 [174022, 174021, 174020] by Super 106322 with 9397 at 2,3
-Id : 110603, {_}: add ?183991 ?183992 =<= add (add ?183991 (multiply ?183992 ?183993)) ?183992 [183993, 183992, 183991] by Demod 106366 with 9397 at 2,2
-Id : 111365, {_}: add (multiply ?185632 (inverse ?185633)) ?185634 =<= add (pixley ?185632 ?185633 ?185634) ?185634 [185634, 185633, 185632] by Super 110603 with 19 at 1,3
-Id : 5975, {_}: multiply ?143 (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Demod 49 with 5952 at 1,2
-Id : 6517, {_}: multiply ?7054 (multiply ?7054 (inverse ?7055)) =>= multiply (inverse ?7055) ?7054 [7055, 7054] by Super 5975 with 4472 at 2,2
-Id : 7244, {_}: multiply (multiply ?8105 (inverse ?8106)) ?8105 =>= multiply (inverse ?8106) ?8105 [8106, 8105] by Super 4472 with 6517 at 3
-Id : 9315, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply (inverse (inverse ?10763)) ?10762 [10763, 10762] by Super 7244 with 9241 at 2,1,2
-Id : 9383, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply ?10763 ?10762 [10763, 10762] by Demod 9315 with 9241 at 1,3
-Id : 10069, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (add (multiply (inverse ?11745) ?11746) (inverse ?11745))) [11747, 11746, 11745] by Super 19 with 9383 at 1,3
-Id : 10131, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (inverse ?11745)) [11747, 11746, 11745] by Demod 10069 with 6531 at 2,2,3
-Id : 10132, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =>= multiply (inverse ?11745) (add ?11746 ?11747) [11747, 11746, 11745] by Demod 10131 with 3 at 3
-Id : 111375, {_}: add (multiply (multiply (inverse ?185663) ?185664) (inverse ?185663)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Super 111365 with 10132 at 1,3
-Id : 111673, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Demod 111375 with 4472 at 1,2
-Id : 111674, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185664, 185663] by Demod 111673 with 4587 at 3
-Id : 9338, {_}: multiply ?10835 (multiply ?10835 ?10836) =?= multiply (inverse (inverse ?10836)) ?10835 [10836, 10835] by Super 6517 with 9241 at 2,2,2
-Id : 9347, {_}: multiply ?10835 (multiply ?10835 ?10836) =>= multiply ?10836 ?10835 [10836, 10835] by Demod 9338 with 9241 at 1,3
-Id : 111675, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185663, 185664] by Demod 111674 with 9347 at 1,2
-Id : 88316, {_}: pixley (add ?268 ?269) ?270 ?269 =<= multiply (add ?268 ?269) (add (inverse ?270) ?269) [270, 269, 268] by Demod 88315 with 4587 at 3
-Id : 111676, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= pixley (add ?185664 ?185665) ?185663 ?185665 [185665, 185663, 185664] by Demod 111675 with 88316 at 3
-Id : 111830, {_}: add (multiply ?145816 (inverse (inverse ?145818))) ?145817 =?= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 88455 with 111676 at 2
-Id : 111831, {_}: add (multiply ?145816 ?145818) ?145817 =<= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 111830 with 9241 at 2,1,2
-Id : 112319, {_}: add a (multiply b c) === add a (multiply b c) [] by Demod 112318 with 14496 at 3
-Id : 112318, {_}: add a (multiply b c) =<= add (multiply b c) a [] by Demod 112317 with 111831 at 3
-Id : 112317, {_}: add a (multiply b c) =<= multiply (add b a) (add c a) [] by Demod 112316 with 4472 at 3
-Id : 112316, {_}: add a (multiply b c) =<= multiply (add c a) (add b a) [] by Demod 112315 with 45701 at 3
-Id : 112315, {_}: add a (multiply b c) =<= multiply (add c a) (add a b) [] by Demod 112314 with 4472 at 3
-Id : 112314, {_}: add a (multiply b c) =<= multiply (add a b) (add c a) [] by Demod 1 with 45701 at 3
-Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property
-% SZS output end CNFRefutation for BOO023-1.p
-29618: solved BOO023-1.p in 25.957622 using nrkbo
-29618: status Unsatisfiable for BOO023-1.p
-NO CLASH, using fixed ground order
-29626: Facts:
-29626: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-29626: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-29626: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-29626: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-29626: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-29626: Goal:
-29626: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-29626: Order:
-29626: nrkbo
-29626: Leaf order:
-29626: a 2 0 2 1,1,2
-29626: f 2 0 2 2,1,2,2
-29626: e 2 0 2 3,1,1,2,2
-29626: b 2 0 2 3,1,2
-29626: g 2 0 2 3,3,1,2,2
-29626: c 3 0 3 1,1,1,2,2
-29626: d 3 0 3 2,1,1,2,2
-29626: inverse 4 1 2 0,2,1,2
-29626: multiply 16 3 7 0,2
-NO CLASH, using fixed ground order
-29627: Facts:
-29627: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-29627: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-29627: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-29627: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-29627: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-29627: Goal:
-29627: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-29627: Order:
-29627: kbo
-29627: Leaf order:
-29627: a 2 0 2 1,1,2
-29627: f 2 0 2 2,1,2,2
-29627: e 2 0 2 3,1,1,2,2
-29627: b 2 0 2 3,1,2
-29627: g 2 0 2 3,3,1,2,2
-29627: c 3 0 3 1,1,1,2,2
-29627: d 3 0 3 2,1,1,2,2
-29627: inverse 4 1 2 0,2,1,2
-29627: multiply 16 3 7 0,2
-NO CLASH, using fixed ground order
-29628: Facts:
-29628: Id : 2, {_}:
- multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
- =>=
- multiply ?2 ?3 (multiply ?4 ?5 ?6)
- [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-29628: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-29628: Id : 4, {_}:
- multiply ?11 ?11 ?12 =>= ?11
- [12, 11] by ternary_multiply_2 ?11 ?12
-29628: Id : 5, {_}:
- multiply (inverse ?14) ?14 ?15 =>= ?15
- [15, 14] by left_inverse ?14 ?15
-29628: Id : 6, {_}:
- multiply ?17 ?18 (inverse ?18) =>= ?17
- [18, 17] by right_inverse ?17 ?18
-29628: Goal:
-29628: Id : 1, {_}:
- multiply (multiply a (inverse a) b)
- (inverse (multiply (multiply c d e) f (multiply c d g)))
- (multiply d (multiply g f e) c)
- =>=
- b
- [] by prove_single_axiom
-29628: Order:
-29628: lpo
-29628: Leaf order:
-29628: a 2 0 2 1,1,2
-29628: f 2 0 2 2,1,2,2
-29628: e 2 0 2 3,1,1,2,2
-29628: b 2 0 2 3,1,2
-29628: g 2 0 2 3,3,1,2,2
-29628: c 3 0 3 1,1,1,2,2
-29628: d 3 0 3 2,1,1,2,2
-29628: inverse 4 1 2 0,2,1,2
-29628: multiply 16 3 7 0,2
-Statistics :
-Max weight : 24
-Found proof, 10.457305s
-% SZS status Unsatisfiable for BOO034-1.p
-% SZS output start CNFRefutation for BOO034-1.p
-Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
-Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
-Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
-Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
-Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
-Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2
-Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2
-Id : 919, {_}: multiply (multiply ?2933 ?2934 ?2935) ?2933 ?2934 =?= multiply ?2935 ?2933 (multiply ?2933 ?2934 ?2934) [2935, 2934, 2933] by Super 12 with 13 at 3
-Id : 1358, {_}: multiply (multiply ?4047 ?4048 ?4049) ?4047 ?4048 =>= multiply ?4049 ?4047 ?4048 [4049, 4048, 4047] by Demod 919 with 3 at 3,3
-Id : 518, {_}: multiply (multiply ?1782 ?1783 ?1784) ?1785 ?1783 =?= multiply ?1782 ?1783 (multiply ?1784 ?1785 ?1783) [1785, 1784, 1783, 1782] by Super 2 with 3 at 3,2
-Id : 658, {_}: multiply (multiply ?2168 ?2169 ?2170) ?2170 ?2169 =>= multiply ?2168 ?2169 ?2170 [2170, 2169, 2168] by Super 518 with 4 at 3,3
-Id : 663, {_}: multiply ?2187 (inverse ?2188) ?2188 =?= multiply ?2187 ?2188 (inverse ?2188) [2188, 2187] by Super 658 with 6 at 1,2
-Id : 700, {_}: multiply ?2187 (inverse ?2188) ?2188 =>= ?2187 [2188, 2187] by Demod 663 with 6 at 3
-Id : 1370, {_}: multiply ?4102 ?4102 (inverse ?4103) =?= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Super 1358 with 700 at 1,2
-Id : 1414, {_}: ?4102 =<= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Demod 1370 with 4 at 2
-Id : 1523, {_}: multiply ?4433 ?4434 (multiply ?4435 ?4433 (inverse ?4433)) =>= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Super 13 with 1414 at 3,3
-Id : 1537, {_}: multiply ?4433 ?4434 ?4435 =?= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Demod 1523 with 6 at 3,2
-Id : 1363, {_}: multiply ?4066 ?4066 ?4067 =?= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Super 1358 with 6 at 1,2
-Id : 1412, {_}: ?4066 =<= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Demod 1363 with 4 at 2
-Id : 1452, {_}: multiply (multiply ?4284 ?4285 (inverse ?4285)) ?4286 ?4285 =>= multiply ?4284 ?4285 ?4286 [4286, 4285, 4284] by Super 12 with 1412 at 3,3
-Id : 1474, {_}: multiply ?4284 ?4286 ?4285 =?= multiply ?4284 ?4285 ?4286 [4285, 4286, 4284] by Demod 1452 with 6 at 1,2
-Id : 726, {_}: inverse (inverse ?2325) =>= ?2325 [2325] by Super 5 with 700 at 2
-Id : 760, {_}: multiply ?2416 (inverse ?2416) ?2417 =>= ?2417 [2417, 2416] by Super 5 with 726 at 1,2
-Id : 41048, {_}: b === b [] by Demod 41047 with 700 at 2
-Id : 41047, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f e g)) =>= b [] by Demod 41046 with 1474 at 3,3,2
-Id : 41046, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f g e)) =>= b [] by Demod 41045 with 1537 at 3,3,2
-Id : 41045, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e f g)) =>= b [] by Demod 41044 with 1474 at 3,3,2
-Id : 41044, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e g f)) =>= b [] by Demod 41043 with 1537 at 3,3,2
-Id : 41043, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply g f e)) =>= b [] by Demod 41042 with 1474 at 3,2
-Id : 41042, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c (multiply g f e) d) =>= b [] by Demod 41041 with 1537 at 3,2
-Id : 41041, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply d c (multiply g f e)) =>= b [] by Demod 41040 with 1474 at 3,1,2,2
-Id : 41040, {_}: multiply b (inverse (multiply c d (multiply f g e))) (multiply d c (multiply g f e)) =>= b [] by Demod 41039 with 1474 at 2
-Id : 41039, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply c d (multiply f g e))) =>= b [] by Demod 41038 with 1537 at 2
-Id : 41038, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d c (multiply g f e)) =>= b [] by Demod 41037 with 1474 at 3,2
-Id : 41037, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d (multiply g f e) c) =>= b [] by Demod 41036 with 760 at 2,2
-Id : 41036, {_}: multiply (inverse (multiply c d (multiply f g e))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41035 with 1537 at 3,1,1,2
-Id : 41035, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41034 with 1474 at 2
-Id : 41034, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) (multiply a (inverse a) b) =>= b [] by Demod 11 with 1537 at 2
-Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2
-Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
-% SZS output end CNFRefutation for BOO034-1.p
-29626: solved BOO034-1.p in 10.42465 using nrkbo
-29626: status Unsatisfiable for BOO034-1.p
-CLASH, statistics insufficient
-29634: Facts:
-29634: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29634: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-29634: Goal:
-29634: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-29634: Order:
-29634: nrkbo
-29634: Leaf order:
-29634: s 1 0 0
-29634: k 1 0 0
-29634: f 3 1 3 0,2,1,2
-29634: g 3 1 3 0,2,2
-29634: apply 13 2 5 0,2
-CLASH, statistics insufficient
-29635: Facts:
-29635: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29635: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-29635: Goal:
-29635: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-29635: Order:
-29635: kbo
-29635: Leaf order:
-29635: s 1 0 0
-29635: k 1 0 0
-29635: f 3 1 3 0,2,1,2
-29635: g 3 1 3 0,2,2
-29635: apply 13 2 5 0,2
-CLASH, statistics insufficient
-29636: Facts:
-29636: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29636: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-29636: Goal:
-29636: Id : 1, {_}:
- apply (apply ?1 (f ?1)) (g ?1)
- =<=
- apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
- [1] by prove_u_combinator ?1
-29636: Order:
-29636: lpo
-29636: Leaf order:
-29636: s 1 0 0
-29636: k 1 0 0
-29636: f 3 1 3 0,2,1,2
-29636: g 3 1 3 0,2,2
-29636: apply 13 2 5 0,2
-% SZS status Timeout for COL004-1.p
-NO CLASH, using fixed ground order
-29663: Facts:
-29663: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-29663: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-29663: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-29663: Goal:
-29663: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-29663: Order:
-29663: nrkbo
-29663: Leaf order:
-29663: strong_fixed_point 3 0 2 1,2
-29663: fixed_pt 3 0 3 2,2
-29663: s 11 0 0
-29663: k 13 0 0
-29663: apply 32 2 3 0,2
-NO CLASH, using fixed ground order
-29664: Facts:
-29664: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-29664: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-29664: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-29664: Goal:
-29664: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-29664: Order:
-29664: kbo
-29664: Leaf order:
-29664: strong_fixed_point 3 0 2 1,2
-29664: fixed_pt 3 0 3 2,2
-29664: s 11 0 0
-29664: k 13 0 0
-29664: apply 32 2 3 0,2
-NO CLASH, using fixed ground order
-29665: Facts:
-29665: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-29665: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-29665: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply (apply s (apply k s)) k))
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- [] by strong_fixed_point
-29665: Goal:
-29665: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-29665: Order:
-29665: lpo
-29665: Leaf order:
-29665: strong_fixed_point 3 0 2 1,2
-29665: fixed_pt 3 0 3 2,2
-29665: s 11 0 0
-29665: k 13 0 0
-29665: apply 32 2 3 0,2
-% SZS status Timeout for COL006-6.p
-CLASH, statistics insufficient
-29690: Facts:
-29690: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29690: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-29690: Id : 4, {_}:
- apply (apply t ?11) ?12 =>= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-29690: Goal:
-29690: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-29690: Order:
-29690: nrkbo
-29690: Leaf order:
-29690: s 1 0 0
-29690: b 1 0 0
-29690: t 1 0 0
-29690: f 3 1 3 0,2,2
-29690: apply 17 2 3 0,2
-CLASH, statistics insufficient
-29691: Facts:
-29691: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29691: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-29691: Id : 4, {_}:
- apply (apply t ?11) ?12 =>= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-29691: Goal:
-29691: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-29691: Order:
-29691: kbo
-29691: Leaf order:
-29691: s 1 0 0
-29691: b 1 0 0
-29691: t 1 0 0
-29691: f 3 1 3 0,2,2
-29691: apply 17 2 3 0,2
-CLASH, statistics insufficient
-29692: Facts:
-29692: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-29692: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-29692: Id : 4, {_}:
- apply (apply t ?11) ?12 =?= apply ?12 ?11
- [12, 11] by t_definition ?11 ?12
-29692: Goal:
-29692: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-29692: Order:
-29692: lpo
-29692: Leaf order:
-29692: s 1 0 0
-29692: b 1 0 0
-29692: t 1 0 0
-29692: f 3 1 3 0,2,2
-29692: apply 17 2 3 0,2
-% SZS status Timeout for COL036-1.p
-CLASH, statistics insufficient
-29776: Facts:
-29776: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-29776: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-29776: Goal:
-29776: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-29776: Order:
-29776: nrkbo
-29776: Leaf order:
-29776: b 1 0 0
-29776: t 1 0 0
-29776: f 2 1 2 0,2,1,1,2
-29776: g 2 1 2 0,2,1,2
-29776: h 2 1 2 0,2,2
-29776: apply 13 2 5 0,2
-CLASH, statistics insufficient
-29777: Facts:
-29777: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-29777: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-29777: Goal:
-29777: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-29777: Order:
-29777: kbo
-29777: Leaf order:
-29777: b 1 0 0
-29777: t 1 0 0
-29777: f 2 1 2 0,2,1,1,2
-29777: g 2 1 2 0,2,1,2
-29777: h 2 1 2 0,2,2
-29777: apply 13 2 5 0,2
-CLASH, statistics insufficient
-29778: Facts:
-29778: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-29778: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-29778: Goal:
-29778: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (g ?1)) (f ?1)
- [1] by prove_f_combinator ?1
-29778: Order:
-29778: lpo
-29778: Leaf order:
-29778: b 1 0 0
-29778: t 1 0 0
-29778: f 2 1 2 0,2,1,1,2
-29778: g 2 1 2 0,2,1,2
-29778: h 2 1 2 0,2,2
-29778: apply 13 2 5 0,2
-Goal subsumed
-Statistics :
-Max weight : 100
-Found proof, 5.339173s
-% SZS status Unsatisfiable for COL063-1.p
-% SZS output start CNFRefutation for COL063-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2
-Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2
-Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
-Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
-% SZS output end CNFRefutation for COL063-1.p
-29776: solved COL063-1.p in 5.300331 using nrkbo
-29776: status Unsatisfiable for COL063-1.p
-NO CLASH, using fixed ground order
-29785: Facts:
-29785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29785: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29785: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29785: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29785: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29785: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29785: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29785: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29785: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29785: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29785: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29785: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29785: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29785: Goal:
-29785: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-29785: Order:
-29785: nrkbo
-29785: Leaf order:
-29785: a 3 0 3 2
-29785: identity 4 0 2 2,1,3
-29785: inverse 1 1 0
-29785: least_upper_bound 14 2 1 0,1,3
-29785: greatest_lower_bound 14 2 1 0,2,3
-29785: multiply 19 2 1 0,3
-NO CLASH, using fixed ground order
-29786: Facts:
-29786: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29786: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29786: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29786: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29786: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29786: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29786: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29786: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29786: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29786: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29786: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29786: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29786: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29786: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29786: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29786: Goal:
-29786: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-29786: Order:
-29786: kbo
-29786: Leaf order:
-29786: a 3 0 3 2
-29786: identity 4 0 2 2,1,3
-29786: inverse 1 1 0
-29786: least_upper_bound 14 2 1 0,1,3
-29786: greatest_lower_bound 14 2 1 0,2,3
-29786: multiply 19 2 1 0,3
-NO CLASH, using fixed ground order
-29787: Facts:
-29787: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29787: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29787: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29787: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29787: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29787: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29787: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29787: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29787: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29787: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29787: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29787: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29787: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29787: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29787: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29787: Goal:
-29787: Id : 1, {_}:
- a
- =<=
- multiply (least_upper_bound a identity)
- (greatest_lower_bound a identity)
- [] by prove_p19
-29787: Order:
-29787: lpo
-29787: Leaf order:
-29787: a 3 0 3 2
-29787: identity 4 0 2 2,1,3
-29787: inverse 1 1 0
-29787: least_upper_bound 14 2 1 0,1,3
-29787: greatest_lower_bound 14 2 1 0,2,3
-29787: multiply 19 2 1 0,3
-% SZS status Timeout for GRP167-3.p
-NO CLASH, using fixed ground order
-29831: Facts:
-29831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29831: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29831: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29831: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29831: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29831: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29831: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29831: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29831: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29831: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29831: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29831: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29831: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29831: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29831: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29831: Goal:
-29831: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =<=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-29831: Order:
-29831: nrkbo
-29831: Leaf order:
-29831: identity 2 0 0
-29831: a 2 0 2 1,1,2
-29831: b 2 0 2 2,1,2
-29831: inverse 4 1 3 0,2
-29831: least_upper_bound 14 2 1 0,1,2
-29831: greatest_lower_bound 14 2 1 0,3
-29831: multiply 18 2 0
-NO CLASH, using fixed ground order
-29832: Facts:
-29832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29832: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29832: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29832: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29832: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29832: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29832: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29832: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-NO CLASH, using fixed ground order
-29833: Facts:
-29833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29833: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29833: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29833: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29833: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29833: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29832: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29832: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29832: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29832: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29832: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29832: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29832: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29832: Goal:
-29832: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =<=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-29832: Order:
-29832: kbo
-29832: Leaf order:
-29832: identity 2 0 0
-29832: a 2 0 2 1,1,2
-29832: b 2 0 2 2,1,2
-29832: inverse 4 1 3 0,2
-29832: least_upper_bound 14 2 1 0,1,2
-29832: greatest_lower_bound 14 2 1 0,3
-29832: multiply 18 2 0
-29833: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29833: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29833: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29833: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29833: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29833: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29833: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29833: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29833: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29833: Goal:
-29833: Id : 1, {_}:
- inverse (least_upper_bound a b)
- =<=
- greatest_lower_bound (inverse a) (inverse b)
- [] by prove_p10
-29833: Order:
-29833: lpo
-29833: Leaf order:
-29833: identity 2 0 0
-29833: a 2 0 2 1,1,2
-29833: b 2 0 2 2,1,2
-29833: inverse 4 1 3 0,2
-29833: least_upper_bound 14 2 1 0,1,2
-29833: greatest_lower_bound 14 2 1 0,3
-29833: multiply 18 2 0
-% SZS status Timeout for GRP179-1.p
-NO CLASH, using fixed ground order
-29866: Facts:
-29866: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29866: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29866: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29866: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29866: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29866: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29866: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29866: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29866: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29866: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29866: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29866: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29866: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29866: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29866: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29866: Goal:
-29866: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-29866: Order:
-29866: nrkbo
-29866: Leaf order:
-29866: a 2 0 2 1,1,2
-29866: identity 4 0 2 2,2
-29866: inverse 3 1 2 0,1,2
-29866: greatest_lower_bound 14 2 1 0,1,3
-29866: least_upper_bound 14 2 1 0,2
-29866: multiply 18 2 0
-NO CLASH, using fixed ground order
-29867: Facts:
-29867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29867: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29867: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29867: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29867: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29867: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29867: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29867: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29867: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29867: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29867: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29867: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29867: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29867: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29867: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29867: Goal:
-29867: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-29867: Order:
-29867: kbo
-29867: Leaf order:
-29867: a 2 0 2 1,1,2
-29867: identity 4 0 2 2,2
-29867: inverse 3 1 2 0,1,2
-29867: greatest_lower_bound 14 2 1 0,1,3
-29867: least_upper_bound 14 2 1 0,2
-29867: multiply 18 2 0
-NO CLASH, using fixed ground order
-29868: Facts:
-29868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29868: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29868: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29868: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29868: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29868: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29868: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29868: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29868: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29868: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29868: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29868: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29868: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29868: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29868: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29868: Goal:
-29868: Id : 1, {_}:
- least_upper_bound (inverse a) identity
- =>=
- inverse (greatest_lower_bound a identity)
- [] by prove_p18
-29868: Order:
-29868: lpo
-29868: Leaf order:
-29868: a 2 0 2 1,1,2
-29868: identity 4 0 2 2,2
-29868: inverse 3 1 2 0,1,2
-29868: greatest_lower_bound 14 2 1 0,1,3
-29868: least_upper_bound 14 2 1 0,2
-29868: multiply 18 2 0
-% SZS status Timeout for GRP179-2.p
-NO CLASH, using fixed ground order
-29889: Facts:
-29889: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29889: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29889: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29889: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29889: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29889: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29889: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29889: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29889: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29889: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29889: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29889: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29889: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29889: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29889: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29889: Goal:
-29889: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-29889: Order:
-29889: nrkbo
-29889: Leaf order:
-29889: identity 2 0 0
-29889: a 3 0 3 1,2
-29889: b 3 0 3 2,1,1,2,2
-29889: inverse 2 1 1 0,1,2,2
-29889: greatest_lower_bound 14 2 1 0,1,1,2,2
-29889: least_upper_bound 14 2 1 0,3
-29889: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-29890: Facts:
-29890: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29890: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29890: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29890: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29890: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29890: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29890: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29890: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29890: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29890: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29890: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29890: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29890: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29890: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29890: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29890: Goal:
-29890: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-29890: Order:
-29890: kbo
-29890: Leaf order:
-29890: identity 2 0 0
-29890: a 3 0 3 1,2
-29890: b 3 0 3 2,1,1,2,2
-29890: inverse 2 1 1 0,1,2,2
-29890: greatest_lower_bound 14 2 1 0,1,1,2,2
-29890: least_upper_bound 14 2 1 0,3
-29890: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-29891: Facts:
-29891: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29891: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29891: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29891: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29891: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29891: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29891: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29891: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29891: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29891: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29891: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29891: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29891: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29891: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29891: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29891: Goal:
-29891: Id : 1, {_}:
- multiply a (multiply (inverse (greatest_lower_bound a b)) b)
- =>=
- least_upper_bound a b
- [] by prove_p11
-29891: Order:
-29891: lpo
-29891: Leaf order:
-29891: identity 2 0 0
-29891: a 3 0 3 1,2
-29891: b 3 0 3 2,1,1,2,2
-29891: inverse 2 1 1 0,1,2,2
-29891: greatest_lower_bound 14 2 1 0,1,1,2,2
-29891: least_upper_bound 14 2 1 0,3
-29891: multiply 20 2 2 0,2
-% SZS status Timeout for GRP180-1.p
-NO CLASH, using fixed ground order
-29925: Facts:
-29925: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29925: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29925: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29925: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29925: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29925: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29925: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29925: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29925: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29925: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29925: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29925: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29925: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29925: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29925: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29925: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-29925: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-29925: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-29925: Goal:
-29925: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-29925: Order:
-29925: nrkbo
-29925: Leaf order:
-29925: a 2 0 2 1,1,2
-29925: identity 7 0 3 2,1,2
-29925: inverse 8 1 1 0,2,2
-29925: least_upper_bound 14 2 1 0,1,2
-29925: greatest_lower_bound 15 2 2 0,2
-29925: multiply 20 2 0
-NO CLASH, using fixed ground order
-29926: Facts:
-29926: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29926: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29926: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29926: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29926: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29926: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29926: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29926: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29926: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29926: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29926: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29926: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29926: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29926: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29926: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29926: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-29926: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-29926: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-29926: Goal:
-29926: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-29926: Order:
-29926: kbo
-29926: Leaf order:
-29926: a 2 0 2 1,1,2
-29926: identity 7 0 3 2,1,2
-29926: inverse 8 1 1 0,2,2
-29926: least_upper_bound 14 2 1 0,1,2
-29926: greatest_lower_bound 15 2 2 0,2
-29926: multiply 20 2 0
-NO CLASH, using fixed ground order
-29928: Facts:
-29928: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29928: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29928: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29928: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29928: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29928: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29928: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29928: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29928: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29928: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29928: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29928: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29928: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29928: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29928: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29928: Id : 17, {_}: inverse identity =>= identity [] by p20_1
-29928: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
-29928: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p20_3 ?53 ?54
-29928: Goal:
-29928: Id : 1, {_}:
- greatest_lower_bound (least_upper_bound a identity)
- (inverse (greatest_lower_bound a identity))
- =>=
- identity
- [] by prove_p20
-29928: Order:
-29928: lpo
-29928: Leaf order:
-29928: a 2 0 2 1,1,2
-29928: identity 7 0 3 2,1,2
-29928: inverse 8 1 1 0,2,2
-29928: least_upper_bound 14 2 1 0,1,2
-29928: greatest_lower_bound 15 2 2 0,2
-29928: multiply 20 2 0
-% SZS status Timeout for GRP183-2.p
-NO CLASH, using fixed ground order
-29950: Facts:
-29950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29950: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29950: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29950: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29950: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29950: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29950: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29950: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29950: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29950: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29950: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29950: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29950: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29950: Goal:
-29950: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-29950: Order:
-29950: nrkbo
-29950: Leaf order:
-29950: b 2 0 2 2,1,2
-29950: identity 3 0 1 2,2
-29950: a 3 0 3 1,1,2
-29950: inverse 3 1 2 0,2,3
-29950: greatest_lower_bound 14 2 1 0,1,2,3
-29950: least_upper_bound 14 2 1 0,2
-29950: multiply 20 2 2 0,1,2
-NO CLASH, using fixed ground order
-29951: Facts:
-29951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29951: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29951: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29951: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29951: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29951: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29951: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29951: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29951: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29951: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29951: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29951: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29951: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29951: Goal:
-29951: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-29951: Order:
-29951: kbo
-29951: Leaf order:
-29951: b 2 0 2 2,1,2
-29951: identity 3 0 1 2,2
-29951: a 3 0 3 1,1,2
-29951: inverse 3 1 2 0,2,3
-29951: greatest_lower_bound 14 2 1 0,1,2,3
-29951: least_upper_bound 14 2 1 0,2
-29951: multiply 20 2 2 0,1,2
-NO CLASH, using fixed ground order
-29952: Facts:
-29952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-29952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-29952: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-29952: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-29952: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-29952: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-29952: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-29952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-29952: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-29952: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-29952: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-29952: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-29952: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-29952: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-29952: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-29952: Goal:
-29952: Id : 1, {_}:
- least_upper_bound (multiply a b) identity
- =<=
- multiply a (inverse (greatest_lower_bound a (inverse b)))
- [] by prove_p23
-29952: Order:
-29952: lpo
-29952: Leaf order:
-29952: b 2 0 2 2,1,2
-29952: identity 3 0 1 2,2
-29952: a 3 0 3 1,1,2
-29952: inverse 3 1 2 0,2,3
-29952: greatest_lower_bound 14 2 1 0,1,2,3
-29952: least_upper_bound 14 2 1 0,2
-29952: multiply 20 2 2 0,1,2
-% SZS status Timeout for GRP186-1.p
-NO CLASH, using fixed ground order
-29976: Facts:
-29976: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-29976: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-29976: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-29976: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-29976: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-29976: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-29976: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-29976: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-29976: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-29976: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-29976: Goal:
-29976: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-29976: Order:
-29976: nrkbo
-29976: Leaf order:
-29976: n0 1 0 0
-29976: n1 2 0 1 3
-29976: b 4 0 4 1,2,1,2,1,2,2
-29976: a 7 0 7 1,2
-29976: complement 15 1 6 0,1,1,2,2
-29976: meet 14 2 5 0,1,2,2
-29976: join 17 2 5 0,2
-NO CLASH, using fixed ground order
-29977: Facts:
-29977: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-29977: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-29977: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-29977: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-29977: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-29977: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-29977: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-29977: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-29977: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-29977: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-29977: Goal:
-29977: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-29977: Order:
-29977: kbo
-29977: Leaf order:
-29977: n0 1 0 0
-29977: n1 2 0 1 3
-29977: b 4 0 4 1,2,1,2,1,2,2
-29977: a 7 0 7 1,2
-29977: complement 15 1 6 0,1,1,2,2
-29977: meet 14 2 5 0,1,2,2
-29977: join 17 2 5 0,2
-NO CLASH, using fixed ground order
-29978: Facts:
-29978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-29978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-29978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-29978: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-29978: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-29978: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-29978: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-29978: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-29978: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-29978: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-29978: Goal:
-29978: Id : 1, {_}:
- join a
- (join
- (meet (complement a) (meet (join a (complement b)) (join a b)))
- (meet (complement a)
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))))
- =>=
- n1
- [] by prove_e2
-29978: Order:
-29978: lpo
-29978: Leaf order:
-29978: n0 1 0 0
-29978: n1 2 0 1 3
-29978: b 4 0 4 1,2,1,2,1,2,2
-29978: a 7 0 7 1,2
-29978: complement 15 1 6 0,1,1,2,2
-29978: meet 14 2 5 0,1,2,2
-29978: join 17 2 5 0,2
-% SZS status Timeout for LAT017-1.p
-NO CLASH, using fixed ground order
-30001: Facts:
-30001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-30001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-30001: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-30001: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-30001: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-30001: Id : 7, {_}:
- join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-30001: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-30001: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-30001: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =<=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-30001: Goal:
-30001: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-30001: Order:
-30001: nrkbo
-30001: Leaf order:
-30001: b 2 0 2 1,2,2
-30001: c 2 0 2 2,2,2
-30001: a 3 0 3 1,2
-30001: join 20 2 2 0,2,2
-30001: meet 21 2 3 0,2
-NO CLASH, using fixed ground order
-30002: Facts:
-30002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-30002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-30002: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-30002: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-30002: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-30002: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-30002: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-30002: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-30002: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =<=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-30002: Goal:
-30002: Id : 1, {_}:
- meet a (join b c) =<= join (meet a b) (meet a c)
- [] by prove_distributivity
-30002: Order:
-30002: kbo
-30002: Leaf order:
-30002: b 2 0 2 1,2,2
-30002: c 2 0 2 2,2,2
-30002: a 3 0 3 1,2
-30002: join 20 2 2 0,2,2
-30002: meet 21 2 3 0,2
-NO CLASH, using fixed ground order
-30003: Facts:
-30003: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-30003: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-30003: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
-30003: Id : 5, {_}:
- join ?9 ?10 =?= join ?10 ?9
- [10, 9] by commutativity_of_join ?9 ?10
-30003: Id : 6, {_}:
- meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
- [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
-30003: Id : 7, {_}:
- join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
- [18, 17, 16] by associativity_of_join ?16 ?17 ?18
-30003: Id : 8, {_}:
- join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
- =>=
- meet ?20 (join ?21 ?22)
- [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
-30003: Id : 9, {_}:
- meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
- =>=
- join ?24 (meet ?25 ?26)
- [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
-30003: Id : 10, {_}:
- join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
- =<=
- meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
- [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
-30003: Goal:
-30003: Id : 1, {_}:
- meet a (join b c) =>= join (meet a b) (meet a c)
- [] by prove_distributivity
-30003: Order:
-30003: lpo
-30003: Leaf order:
-30003: b 2 0 2 1,2,2
-30003: c 2 0 2 2,2,2
-30003: a 3 0 3 1,2
-30003: join 20 2 2 0,2,2
-30003: meet 21 2 3 0,2
-% SZS status Timeout for LAT020-1.p
-NO CLASH, using fixed ground order
-30025: Facts:
-30025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30025: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30025: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30025: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30025: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30025: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30025: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30025: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30025: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30025: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30025: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30025: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30025: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30025: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30025: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30025: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30025: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30025: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30025: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30025: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30025: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30025: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30025: Goal:
-30025: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-30025: Order:
-30025: nrkbo
-30025: Leaf order:
-30025: x 2 0 2 1,1,2
-30025: y 2 0 2 2,1,2
-30025: z 2 0 2 3,1,2
-30025: additive_identity 9 0 1 3
-30025: additive_inverse 22 1 0
-30025: commutator 1 2 0
-30025: add 25 2 1 0,2
-30025: multiply 40 2 0
-30025: associator 3 3 2 0,1,2
-NO CLASH, using fixed ground order
-30026: Facts:
-30026: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30026: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30026: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30026: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30026: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30026: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30026: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30026: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30026: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30026: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30026: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30026: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30026: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30026: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30026: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30026: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30026: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30026: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30026: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30026: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30026: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30026: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30026: Goal:
-30026: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-30026: Order:
-30026: kbo
-30026: Leaf order:
-30026: x 2 0 2 1,1,2
-30026: y 2 0 2 2,1,2
-30026: z 2 0 2 3,1,2
-30026: additive_identity 9 0 1 3
-30026: additive_inverse 22 1 0
-30026: commutator 1 2 0
-30026: add 25 2 1 0,2
-30026: multiply 40 2 0
-30026: associator 3 3 2 0,1,2
-NO CLASH, using fixed ground order
-30027: Facts:
-30027: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30027: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30027: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30027: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30027: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30027: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30027: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30027: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30027: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30027: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30027: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30027: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30027: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30027: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30027: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30027: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30027: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30027: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30027: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30027: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30027: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30027: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30027: Goal:
-30027: Id : 1, {_}:
- add (associator x y z) (associator x z y) =>= additive_identity
- [] by prove_equation
-30027: Order:
-30027: lpo
-30027: Leaf order:
-30027: x 2 0 2 1,1,2
-30027: y 2 0 2 2,1,2
-30027: z 2 0 2 3,1,2
-30027: additive_identity 9 0 1 3
-30027: additive_inverse 22 1 0
-30027: commutator 1 2 0
-30027: add 25 2 1 0,2
-30027: multiply 40 2 0
-30027: associator 3 3 2 0,1,2
-% SZS status Timeout for RNG025-5.p
-NO CLASH, using fixed ground order
-30048: Facts:
-30048: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30048: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30048: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30048: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30048: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30048: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30048: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30048: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30048: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30048: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30048: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30048: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30048: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30048: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30048: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30048: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30048: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30048: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30048: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30048: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30048: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30048: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30048: Goal:
-30048: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-30048: Order:
-30048: nrkbo
-30048: Leaf order:
-30048: y 1 0 1 2,2
-30048: x 2 0 2 1,2
-30048: additive_identity 9 0 1 3
-30048: additive_inverse 22 1 0
-30048: commutator 1 2 0
-30048: add 24 2 0
-30048: multiply 40 2 0
-30048: associator 2 3 1 0,2
-NO CLASH, using fixed ground order
-30049: Facts:
-30049: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30049: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30049: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30049: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30049: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30049: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30049: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30049: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30049: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30049: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30049: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30049: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30049: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30049: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30049: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30049: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30049: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30049: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30049: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30049: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30049: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30049: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30049: Goal:
-30049: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-30049: Order:
-30049: kbo
-30049: Leaf order:
-30049: y 1 0 1 2,2
-30049: x 2 0 2 1,2
-30049: additive_identity 9 0 1 3
-30049: additive_inverse 22 1 0
-30049: commutator 1 2 0
-30049: add 24 2 0
-30049: multiply 40 2 0
-30049: associator 2 3 1 0,2
-NO CLASH, using fixed ground order
-30050: Facts:
-30050: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-30050: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-30050: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-30050: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-30050: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-30050: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-30050: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-30050: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-30050: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-30050: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-30050: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-30050: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-30050: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-30050: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-30050: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-30050: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-30050: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-30050: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-30050: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-30050: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-30050: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-30050: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-30050: Goal:
-30050: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
-30050: Order:
-30050: lpo
-30050: Leaf order:
-30050: y 1 0 1 2,2
-30050: x 2 0 2 1,2
-30050: additive_identity 9 0 1 3
-30050: additive_inverse 22 1 0
-30050: commutator 1 2 0
-30050: add 24 2 0
-30050: multiply 40 2 0
-30050: associator 2 3 1 0,2
-% SZS status Timeout for RNG025-7.p
-CLASH, statistics insufficient
-30088: Facts:
-30088: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-30088: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-30088: Goal:
-30088: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-30088: Order:
-30088: nrkbo
-30088: Leaf order:
-30088: s 1 0 0
-30088: k 1 0 0
-30088: f 3 1 3 0,2,2
-30088: apply 11 2 3 0,2
-CLASH, statistics insufficient
-30089: Facts:
-30089: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-30089: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-30089: Goal:
-30089: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-30089: Order:
-30089: kbo
-30089: Leaf order:
-30089: s 1 0 0
-30089: k 1 0 0
-30089: f 3 1 3 0,2,2
-30089: apply 11 2 3 0,2
-CLASH, statistics insufficient
-30090: Facts:
-30090: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-30090: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
-30090: Goal:
-30090: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-30090: Order:
-30090: lpo
-30090: Leaf order:
-30090: s 1 0 0
-30090: k 1 0 0
-30090: f 3 1 3 0,2,2
-30090: apply 11 2 3 0,2
-% SZS status Timeout for COL006-1.p
-NO CLASH, using fixed ground order
-30176: Facts:
-30176: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30176: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30176: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-30176: Goal:
-30176: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30176: Order:
-30176: nrkbo
-30176: Leaf order:
-30176: strong_fixed_point 3 0 2 1,2
-30176: fixed_pt 3 0 3 2,2
-30176: k 10 0 0
-30176: s 11 0 0
-30176: apply 29 2 3 0,2
-NO CLASH, using fixed ground order
-30177: Facts:
-30177: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30177: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30177: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-30177: Goal:
-30177: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30177: Order:
-30177: kbo
-30177: Leaf order:
-30177: strong_fixed_point 3 0 2 1,2
-30177: fixed_pt 3 0 3 2,2
-30177: k 10 0 0
-30177: s 11 0 0
-30177: apply 29 2 3 0,2
-NO CLASH, using fixed ground order
-30178: Facts:
-30178: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30178: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30178: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
- (apply (apply s (apply k (apply (apply s s) (apply s k))))
- (apply (apply s (apply k s)) k))
- [] by strong_fixed_point
-30178: Goal:
-30178: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30178: Order:
-30178: lpo
-30178: Leaf order:
-30178: strong_fixed_point 3 0 2 1,2
-30178: fixed_pt 3 0 3 2,2
-30178: k 10 0 0
-30178: s 11 0 0
-30178: apply 29 2 3 0,2
-% SZS status Timeout for COL006-5.p
-NO CLASH, using fixed ground order
-30201: Facts:
-30201: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30201: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30201: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-30201: Goal:
-30201: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30201: Order:
-30201: nrkbo
-30201: Leaf order:
-30201: strong_fixed_point 3 0 2 1,2
-30201: fixed_pt 3 0 3 2,2
-30201: k 7 0 0
-30201: s 10 0 0
-30201: apply 25 2 3 0,2
-NO CLASH, using fixed ground order
-30202: Facts:
-30202: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30202: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30202: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-30202: Goal:
-30202: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30202: Order:
-30202: kbo
-30202: Leaf order:
-30202: strong_fixed_point 3 0 2 1,2
-30202: fixed_pt 3 0 3 2,2
-30202: k 7 0 0
-30202: s 10 0 0
-30202: apply 25 2 3 0,2
-NO CLASH, using fixed ground order
-30203: Facts:
-30203: Id : 2, {_}:
- apply (apply (apply s ?2) ?3) ?4
- =?=
- apply (apply ?2 ?4) (apply ?3 ?4)
- [4, 3, 2] by s_definition ?2 ?3 ?4
-30203: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
-30203: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply s
- (apply k
- (apply (apply (apply s s) (apply (apply s k) k))
- (apply (apply s s) (apply s k)))))
- (apply (apply s (apply k s)) k)
- [] by strong_fixed_point
-30203: Goal:
-30203: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30203: Order:
-30203: lpo
-30203: Leaf order:
-30203: strong_fixed_point 3 0 2 1,2
-30203: fixed_pt 3 0 3 2,2
-30203: k 7 0 0
-30203: s 10 0 0
-30203: apply 25 2 3 0,2
-% SZS status Timeout for COL006-7.p
-NO CLASH, using fixed ground order
-30224: Facts:
-30224: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30224: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-NO CLASH, using fixed ground order
-30225: Facts:
-30225: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30225: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-30225: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-30225: Goal:
-30225: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30225: Order:
-30225: kbo
-30225: Leaf order:
-30225: strong_fixed_point 3 0 2 1,2
-30225: fixed_pt 3 0 3 2,2
-30225: n 6 0 0
-30225: b 9 0 0
-30225: apply 26 2 3 0,2
-NO CLASH, using fixed ground order
-30226: Facts:
-30226: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30226: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-30226: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-30226: Goal:
-30226: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30226: Order:
-30226: lpo
-30226: Leaf order:
-30226: strong_fixed_point 3 0 2 1,2
-30226: fixed_pt 3 0 3 2,2
-30226: n 6 0 0
-30226: b 9 0 0
-30226: apply 26 2 3 0,2
-30224: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
- [] by strong_fixed_point
-30224: Goal:
-30224: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30224: Order:
-30224: nrkbo
-30224: Leaf order:
-30224: strong_fixed_point 3 0 2 1,2
-30224: fixed_pt 3 0 3 2,2
-30224: n 6 0 0
-30224: b 9 0 0
-30224: apply 26 2 3 0,2
-% SZS status Timeout for COL044-6.p
-NO CLASH, using fixed ground order
-30249: Facts:
-30249: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30249: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-30249: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-30249: Goal:
-30249: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30249: Order:
-30249: nrkbo
-30249: Leaf order:
-30249: strong_fixed_point 3 0 2 1,2
-30249: fixed_pt 3 0 3 2,2
-30249: n 6 0 0
-30249: b 9 0 0
-30249: apply 26 2 3 0,2
-NO CLASH, using fixed ground order
-30250: Facts:
-30250: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30250: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-30250: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-30250: Goal:
-30250: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30250: Order:
-30250: kbo
-30250: Leaf order:
-30250: strong_fixed_point 3 0 2 1,2
-30250: fixed_pt 3 0 3 2,2
-30250: n 6 0 0
-30250: b 9 0 0
-30250: apply 26 2 3 0,2
-NO CLASH, using fixed ground order
-30251: Facts:
-30251: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-30251: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-30251: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply (apply b b)
- (apply (apply n (apply n (apply b b))) n))) n)) b)) b
- [] by strong_fixed_point
-30251: Goal:
-30251: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-30251: Order:
-30251: lpo
-30251: Leaf order:
-30251: strong_fixed_point 3 0 2 1,2
-30251: fixed_pt 3 0 3 2,2
-30251: n 6 0 0
-30251: b 9 0 0
-30251: apply 26 2 3 0,2
-% SZS status Timeout for COL044-7.p
-CLASH, statistics insufficient
-30275: Facts:
-30275: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30275: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30275: Goal:
-30275: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-30275: Order:
-30275: nrkbo
-30275: Leaf order:
-30275: b 1 0 0
-30275: t 1 0 0
-30275: f 2 1 2 0,2,1,1,2
-30275: g 2 1 2 0,2,1,2
-30275: h 2 1 2 0,2,2
-30275: apply 13 2 5 0,2
-CLASH, statistics insufficient
-30276: Facts:
-30276: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30276: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30276: Goal:
-30276: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-30276: Order:
-30276: kbo
-30276: Leaf order:
-30276: b 1 0 0
-30276: t 1 0 0
-30276: f 2 1 2 0,2,1,1,2
-30276: g 2 1 2 0,2,1,2
-30276: h 2 1 2 0,2,2
-30276: apply 13 2 5 0,2
-CLASH, statistics insufficient
-30277: Facts:
-30277: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30277: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30277: Goal:
-30277: Id : 1, {_}:
- apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (h ?1) (f ?1)) (g ?1)
- [1] by prove_v_combinator ?1
-30277: Order:
-30277: lpo
-30277: Leaf order:
-30277: b 1 0 0
-30277: t 1 0 0
-30277: f 2 1 2 0,2,1,1,2
-30277: g 2 1 2 0,2,1,2
-30277: h 2 1 2 0,2,2
-30277: apply 13 2 5 0,2
-Goal subsumed
-Statistics :
-Max weight : 124
-Found proof, 34.381663s
-% SZS status Unsatisfiable for COL064-1.p
-% SZS output start CNFRefutation for COL064-1.p
-Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
-Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
-Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2
-Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2
-Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2
-Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2
-Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
-Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
-Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
-Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
-Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
-Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
-Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
-% SZS output end CNFRefutation for COL064-1.p
-30275: solved COL064-1.p in 34.366147 using nrkbo
-30275: status Unsatisfiable for COL064-1.p
-CLASH, statistics insufficient
-30288: Facts:
-30288: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30288: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30288: Goal:
-30288: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-30288: Order:
-30288: nrkbo
-30288: Leaf order:
-30288: b 1 0 0
-30288: t 1 0 0
-30288: f 2 1 2 0,2,1,1,1,2
-30288: g 2 1 2 0,2,1,1,2
-30288: h 2 1 2 0,2,1,2
-30288: i 2 1 2 0,2,2
-30288: apply 15 2 7 0,2
-CLASH, statistics insufficient
-30289: Facts:
-30289: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30289: Id : 3, {_}:
- apply (apply t ?7) ?8 =>= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30289: Goal:
-30289: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-30289: Order:
-30289: kbo
-30289: Leaf order:
-30289: b 1 0 0
-30289: t 1 0 0
-30289: f 2 1 2 0,2,1,1,1,2
-30289: g 2 1 2 0,2,1,1,2
-30289: h 2 1 2 0,2,1,2
-30289: i 2 1 2 0,2,2
-30289: apply 15 2 7 0,2
-CLASH, statistics insufficient
-30290: Facts:
-30290: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-30290: Id : 3, {_}:
- apply (apply t ?7) ?8 =?= apply ?8 ?7
- [8, 7] by t_definition ?7 ?8
-30290: Goal:
-30290: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
- =>=
- apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
- [1] by prove_g_combinator ?1
-30290: Order:
-30290: lpo
-30290: Leaf order:
-30290: b 1 0 0
-30290: t 1 0 0
-30290: f 2 1 2 0,2,1,1,1,2
-30290: g 2 1 2 0,2,1,1,2
-30290: h 2 1 2 0,2,1,2
-30290: i 2 1 2 0,2,2
-30290: apply 15 2 7 0,2
-% SZS status Timeout for COL065-1.p
-CLASH, statistics insufficient
-30319: Facts:
-30319: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30319: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30319: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30319: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30319: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30319: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30319: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30319: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30319: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30319: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30319: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30319: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30319: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30319: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30319: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30319: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-30319: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-30319: Goal:
-30319: Id : 1, {_}: a =>= b [] by prove_p12
-30319: Order:
-30319: nrkbo
-30319: Leaf order:
-30319: identity 2 0 0
-30319: a 3 0 1 2
-30319: b 3 0 1 3
-30319: c 4 0 0
-30319: inverse 1 1 0
-30319: greatest_lower_bound 15 2 0
-30319: least_upper_bound 15 2 0
-30319: multiply 18 2 0
-CLASH, statistics insufficient
-30320: Facts:
-30320: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30320: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30320: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30320: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30320: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30320: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30320: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30320: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30320: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30320: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30320: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30320: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30320: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30320: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30320: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30320: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-30320: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-30320: Goal:
-30320: Id : 1, {_}: a =>= b [] by prove_p12
-30320: Order:
-30320: kbo
-30320: Leaf order:
-30320: identity 2 0 0
-30320: a 3 0 1 2
-30320: b 3 0 1 3
-30320: c 4 0 0
-30320: inverse 1 1 0
-30320: greatest_lower_bound 15 2 0
-30320: least_upper_bound 15 2 0
-30320: multiply 18 2 0
-CLASH, statistics insufficient
-30321: Facts:
-30321: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30321: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30321: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30321: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30321: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30321: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30321: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30321: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30321: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30321: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30321: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30321: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30321: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30321: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30321: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30321: Id : 17, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_1
-30321: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
-30321: Goal:
-30321: Id : 1, {_}: a =>= b [] by prove_p12
-30321: Order:
-30321: lpo
-30321: Leaf order:
-30321: identity 2 0 0
-30321: a 3 0 1 2
-30321: b 3 0 1 3
-30321: c 4 0 0
-30321: inverse 1 1 0
-30321: greatest_lower_bound 15 2 0
-30321: least_upper_bound 15 2 0
-30321: multiply 18 2 0
-% SZS status Timeout for GRP181-1.p
-CLASH, statistics insufficient
-30347: Facts:
-30347: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30347: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30347: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30347: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30347: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30347: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30347: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30347: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30347: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30347: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30347: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30347: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30347: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30347: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30347: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30347: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-30347: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-30347: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-30347: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-30347: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-30347: Goal:
-30347: Id : 1, {_}: a =>= b [] by prove_p12
-30347: Order:
-30347: nrkbo
-30347: Leaf order:
-30347: a 3 0 1 2
-30347: b 3 0 1 3
-30347: identity 4 0 0
-30347: c 4 0 0
-30347: inverse 7 1 0
-30347: greatest_lower_bound 15 2 0
-30347: least_upper_bound 15 2 0
-30347: multiply 20 2 0
-CLASH, statistics insufficient
-30348: Facts:
-30348: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30348: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30348: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30348: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30348: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30348: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30348: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30348: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30348: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30348: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30348: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30348: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30348: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30348: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30348: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30348: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-30348: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-30348: Id : 19, {_}:
- inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-30348: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-30348: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-30348: Goal:
-30348: Id : 1, {_}: a =>= b [] by prove_p12
-30348: Order:
-30348: kbo
-30348: Leaf order:
-30348: a 3 0 1 2
-30348: b 3 0 1 3
-30348: identity 4 0 0
-30348: c 4 0 0
-30348: inverse 7 1 0
-30348: greatest_lower_bound 15 2 0
-30348: least_upper_bound 15 2 0
-30348: multiply 20 2 0
-CLASH, statistics insufficient
-30349: Facts:
-30349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30349: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30349: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30349: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30349: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30349: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30349: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30349: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30349: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30349: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30349: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30349: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30349: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30349: Id : 17, {_}: inverse identity =>= identity [] by p12_1
-30349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
-30349: Id : 19, {_}:
- inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
- [54, 53] by p12_3 ?53 ?54
-30349: Id : 20, {_}:
- greatest_lower_bound a c =>= greatest_lower_bound b c
- [] by p12_4
-30349: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
-30349: Goal:
-30349: Id : 1, {_}: a =>= b [] by prove_p12
-30349: Order:
-30349: lpo
-30349: Leaf order:
-30349: a 3 0 1 2
-30349: b 3 0 1 3
-30349: identity 4 0 0
-30349: c 4 0 0
-30349: inverse 7 1 0
-30349: greatest_lower_bound 15 2 0
-30349: least_upper_bound 15 2 0
-30349: multiply 20 2 0
-% SZS status Timeout for GRP181-2.p
-NO CLASH, using fixed ground order
-30391: Facts:
-30391: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30391: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30391: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30391: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30391: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30391: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30391: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30391: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30391: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30391: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30391: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30391: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30391: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30391: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30391: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30391: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-30391: Goal:
-30391: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
-30391: Order:
-30391: nrkbo
-30391: Leaf order:
-30391: identity 3 0 0
-30391: a 4 0 2 1,2
-30391: b 4 0 2 2,2
-30391: inverse 3 1 0
-30391: greatest_lower_bound 14 2 0
-30391: least_upper_bound 15 2 0
-30391: multiply 20 2 2 0,2
-NO CLASH, using fixed ground order
-30392: Facts:
-30392: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30392: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30392: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30392: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30392: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30392: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30392: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30392: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30392: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30392: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-NO CLASH, using fixed ground order
-30393: Facts:
-30393: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-30393: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-30393: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-30393: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-30393: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-30393: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-30393: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-30393: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-30393: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-30393: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-30393: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30393: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30393: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30393: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30393: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30393: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-30393: Goal:
-30393: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
-30393: Order:
-30393: lpo
-30393: Leaf order:
-30393: identity 3 0 0
-30393: a 4 0 2 1,2
-30393: b 4 0 2 2,2
-30393: inverse 3 1 0
-30393: greatest_lower_bound 14 2 0
-30393: least_upper_bound 15 2 0
-30393: multiply 20 2 2 0,2
-30392: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-30392: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-30392: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-30392: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-30392: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-30392: Id : 17, {_}:
- greatest_lower_bound (least_upper_bound a (inverse a))
- (least_upper_bound b (inverse b))
- =>=
- identity
- [] by p33_1
-30392: Goal:
-30392: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
-30392: Order:
-30392: kbo
-30392: Leaf order:
-30392: identity 3 0 0
-30392: a 4 0 2 1,2
-30392: b 4 0 2 2,2
-30392: inverse 3 1 0
-30392: greatest_lower_bound 14 2 0
-30392: least_upper_bound 15 2 0
-30392: multiply 20 2 2 0,2
-% SZS status Timeout for GRP187-1.p
-NO CLASH, using fixed ground order
-30417: Facts:
-30417: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30417: Goal:
-30417: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-30417: Order:
-30417: nrkbo
-30417: Leaf order:
-30417: a1 2 0 2 1,1,2
-30417: b1 2 0 2 1,1,3
-30417: inverse 9 1 2 0,1,2
-30417: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-30418: Facts:
-30418: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30418: Goal:
-30418: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-30418: Order:
-30418: kbo
-30418: Leaf order:
-30418: a1 2 0 2 1,1,2
-30418: b1 2 0 2 1,1,3
-30418: inverse 9 1 2 0,1,2
-30418: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-30419: Facts:
-30419: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30419: Goal:
-30419: Id : 1, {_}:
- multiply (inverse a1) a1 =<= multiply (inverse b1) b1
- [] by prove_these_axioms_1
-30419: Order:
-30419: lpo
-30419: Leaf order:
-30419: a1 2 0 2 1,1,2
-30419: b1 2 0 2 1,1,3
-30419: inverse 9 1 2 0,1,2
-30419: multiply 12 2 2 0,2
-% SZS status Timeout for GRP505-1.p
-NO CLASH, using fixed ground order
-30445: Facts:
-30445: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30445: Goal:
-30445: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-30445: Order:
-30445: nrkbo
-30445: Leaf order:
-30445: a3 2 0 2 1,1,2
-30445: b3 2 0 2 2,1,2
-30445: c3 2 0 2 2,2
-30445: inverse 7 1 0
-30445: multiply 14 2 4 0,2
-NO CLASH, using fixed ground order
-30446: Facts:
-30446: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30446: Goal:
-30446: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-30446: Order:
-30446: kbo
-30446: Leaf order:
-30446: a3 2 0 2 1,1,2
-30446: b3 2 0 2 2,1,2
-30446: c3 2 0 2 2,2
-30446: inverse 7 1 0
-30446: multiply 14 2 4 0,2
-NO CLASH, using fixed ground order
-30447: Facts:
-30447: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30447: Goal:
-30447: Id : 1, {_}:
- multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
- [] by prove_these_axioms_3
-30447: Order:
-30447: lpo
-30447: Leaf order:
-30447: a3 2 0 2 1,1,2
-30447: b3 2 0 2 2,1,2
-30447: c3 2 0 2 2,2
-30447: inverse 7 1 0
-30447: multiply 14 2 4 0,2
-% SZS status Timeout for GRP507-1.p
-NO CLASH, using fixed ground order
-30481: Facts:
-30481: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30481: Goal:
-30481: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
-30481: Order:
-30481: nrkbo
-30481: Leaf order:
-30481: a 2 0 2 1,2
-30481: b 2 0 2 2,2
-30481: inverse 7 1 0
-30481: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-30482: Facts:
-30482: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30482: Goal:
-30482: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
-30482: Order:
-30482: kbo
-30482: Leaf order:
-30482: a 2 0 2 1,2
-30482: b 2 0 2 2,2
-30482: inverse 7 1 0
-30482: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-30483: Facts:
-30483: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-30483: Goal:
-30483: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
-30483: Order:
-30483: lpo
-30483: Leaf order:
-30483: a 2 0 2 1,2
-30483: b 2 0 2 2,2
-30483: inverse 7 1 0
-30483: multiply 12 2 2 0,2
-% SZS status Timeout for GRP508-1.p
-NO CLASH, using fixed ground order
-31468: Facts:
-31468: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31468: Goal:
-31468: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-31468: Order:
-31468: nrkbo
-31468: Leaf order:
-31468: a 3 0 3 1,2
-31468: meet 19 2 1 0,2
-31468: join 20 2 0
-NO CLASH, using fixed ground order
-31469: Facts:
-31469: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31469: Goal:
-31469: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-31469: Order:
-31469: kbo
-31469: Leaf order:
-31469: a 3 0 3 1,2
-31469: meet 19 2 1 0,2
-31469: join 20 2 0
-NO CLASH, using fixed ground order
-31470: Facts:
-31470: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31470: Goal:
-31470: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
-31470: Order:
-31470: lpo
-31470: Leaf order:
-31470: a 3 0 3 1,2
-31470: meet 19 2 1 0,2
-31470: join 20 2 0
-% SZS status Timeout for LAT080-1.p
-NO CLASH, using fixed ground order
-31492: Facts:
-31492: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31492: Goal:
-31492: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-31492: Order:
-31492: nrkbo
-31492: Leaf order:
-31492: a 3 0 3 1,2
-31492: meet 18 2 0
-31492: join 21 2 1 0,2
-NO CLASH, using fixed ground order
-31493: Facts:
-31493: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31493: Goal:
-31493: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-31493: Order:
-31493: kbo
-31493: Leaf order:
-31493: a 3 0 3 1,2
-31493: meet 18 2 0
-31493: join 21 2 1 0,2
-NO CLASH, using fixed ground order
-31494: Facts:
-31494: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-31494: Goal:
-31494: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
-31494: Order:
-31494: lpo
-31494: Leaf order:
-31494: a 3 0 3 1,2
-31494: meet 18 2 0
-31494: join 21 2 1 0,2
-% SZS status Timeout for LAT083-1.p
-NO CLASH, using fixed ground order
-31519: Facts:
-31519: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31519: Goal:
-31519: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-31519: Order:
-31519: nrkbo
-31519: Leaf order:
-31519: a 3 0 3 1,2
-31519: join 18 2 0
-31519: meet 19 2 1 0,2
-NO CLASH, using fixed ground order
-31521: Facts:
-31521: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31521: Goal:
-31521: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-31521: Order:
-31521: lpo
-31521: Leaf order:
-31521: a 3 0 3 1,2
-31521: join 18 2 0
-31521: meet 19 2 1 0,2
-NO CLASH, using fixed ground order
-31520: Facts:
-31520: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31520: Goal:
-31520: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
-31520: Order:
-31520: kbo
-31520: Leaf order:
-31520: a 3 0 3 1,2
-31520: join 18 2 0
-31520: meet 19 2 1 0,2
-% SZS status Timeout for LAT092-1.p
-NO CLASH, using fixed ground order
-31546: Facts:
-31546: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31546: Goal:
-31546: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
-31546: Order:
-31546: nrkbo
-31546: Leaf order:
-31546: b 2 0 2 1,2
-31546: a 2 0 2 2,2
-31546: join 18 2 0
-31546: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-31547: Facts:
-31547: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31547: Goal:
-31547: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
-31547: Order:
-31547: kbo
-31547: Leaf order:
-31547: b 2 0 2 1,2
-31547: a 2 0 2 2,2
-31547: join 18 2 0
-31547: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-31548: Facts:
-31548: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31548: Goal:
-31548: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
-31548: Order:
-31548: lpo
-31548: Leaf order:
-31548: b 2 0 2 1,2
-31548: a 2 0 2 2,2
-31548: join 18 2 0
-31548: meet 20 2 2 0,2
-% SZS status Timeout for LAT093-1.p
-NO CLASH, using fixed ground order
-31571: Facts:
-31571: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31571: Goal:
-31571: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-31571: Order:
-31571: nrkbo
-31571: Leaf order:
-31571: a 3 0 3 1,2
-31571: meet 18 2 0
-31571: join 19 2 1 0,2
-NO CLASH, using fixed ground order
-31572: Facts:
-31572: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31572: Goal:
-31572: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-31572: Order:
-31572: kbo
-31572: Leaf order:
-31572: a 3 0 3 1,2
-31572: meet 18 2 0
-31572: join 19 2 1 0,2
-NO CLASH, using fixed ground order
-31573: Facts:
-31573: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31573: Goal:
-31573: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
-31573: Order:
-31573: lpo
-31573: Leaf order:
-31573: a 3 0 3 1,2
-31573: meet 18 2 0
-31573: join 19 2 1 0,2
-% SZS status Timeout for LAT094-1.p
-NO CLASH, using fixed ground order
-31595: Facts:
-31595: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31595: Goal:
-31595: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
-31595: Order:
-31595: nrkbo
-31595: Leaf order:
-31595: b 2 0 2 1,2
-31595: a 2 0 2 2,2
-31595: meet 18 2 0
-31595: join 20 2 2 0,2
-NO CLASH, using fixed ground order
-31596: Facts:
-31596: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31596: Goal:
-31596: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
-31596: Order:
-31596: kbo
-31596: Leaf order:
-31596: b 2 0 2 1,2
-31596: a 2 0 2 2,2
-31596: meet 18 2 0
-31596: join 20 2 2 0,2
-NO CLASH, using fixed ground order
-31597: Facts:
-31597: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31597: Goal:
-31597: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
-31597: Order:
-31597: lpo
-31597: Leaf order:
-31597: b 2 0 2 1,2
-31597: a 2 0 2 2,2
-31597: meet 18 2 0
-31597: join 20 2 2 0,2
-% SZS status Timeout for LAT095-1.p
-NO CLASH, using fixed ground order
-31621: Facts:
-31621: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31621: Goal:
-31621: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-31621: Order:
-31621: nrkbo
-31621: Leaf order:
-31621: a 1 0 1 1,1,1,2
-31621: c 1 0 1 1,2,1,2
-31621: b 4 0 4 2,1,1,2
-31621: join 20 2 2 0,1,1,2
-31621: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-31622: Facts:
-31622: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31622: Goal:
-31622: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-31622: Order:
-31622: kbo
-31622: Leaf order:
-31622: a 1 0 1 1,1,1,2
-31622: c 1 0 1 1,2,1,2
-31622: b 4 0 4 2,1,1,2
-31622: join 20 2 2 0,1,1,2
-31622: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-31623: Facts:
-31623: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31623: Goal:
-31623: Id : 1, {_}:
- meet (meet (join a b) (join c b)) b =>= b
- [] by prove_wal_axioms_5
-31623: Order:
-31623: lpo
-31623: Leaf order:
-31623: a 1 0 1 1,1,1,2
-31623: c 1 0 1 1,2,1,2
-31623: b 4 0 4 2,1,1,2
-31623: join 20 2 2 0,1,1,2
-31623: meet 20 2 2 0,2
-% SZS status Timeout for LAT096-1.p
-NO CLASH, using fixed ground order
-31646: Facts:
-31646: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31646: Goal:
-31646: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-31646: Order:
-31646: nrkbo
-31646: Leaf order:
-31646: a 1 0 1 1,1,1,2
-31646: c 1 0 1 1,2,1,2
-31646: b 4 0 4 2,1,1,2
-31646: meet 20 2 2 0,1,1,2
-31646: join 20 2 2 0,2
-NO CLASH, using fixed ground order
-31647: Facts:
-31647: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31647: Goal:
-31647: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-31647: Order:
-31647: kbo
-31647: Leaf order:
-31647: a 1 0 1 1,1,1,2
-31647: c 1 0 1 1,2,1,2
-31647: b 4 0 4 2,1,1,2
-31647: meet 20 2 2 0,1,1,2
-31647: join 20 2 2 0,2
-NO CLASH, using fixed ground order
-31648: Facts:
-31648: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
- (meet
- (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
- (meet ?7
- (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
- (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-31648: Goal:
-31648: Id : 1, {_}:
- join (join (meet a b) (meet c b)) b =>= b
- [] by prove_wal_axioms_6
-31648: Order:
-31648: lpo
-31648: Leaf order:
-31648: a 1 0 1 1,1,1,2
-31648: c 1 0 1 1,2,1,2
-31648: b 4 0 4 2,1,1,2
-31648: meet 20 2 2 0,1,1,2
-31648: join 20 2 2 0,2
-% SZS status Timeout for LAT097-1.p
-NO CLASH, using fixed ground order
-31673: Facts:
-31673: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31673: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31673: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31673: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31673: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31673: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31673: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31673: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31673: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31673: Goal:
-31673: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-31673: Order:
-31673: nrkbo
-31673: Leaf order:
-31673: c 2 0 2 1,2,2,2,2
-31673: b 3 0 3 1,2,2
-31673: d 3 0 3 2,2,2,2,2
-31673: a 4 0 4 1,2
-31673: join 16 2 3 0,2,2
-31673: meet 21 2 7 0,2
-NO CLASH, using fixed ground order
-31675: Facts:
-31675: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31675: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31675: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31675: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31675: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31675: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31675: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31675: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31675: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31675: Goal:
-31675: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-31675: Order:
-31675: lpo
-31675: Leaf order:
-31675: c 2 0 2 1,2,2,2,2
-31675: b 3 0 3 1,2,2
-31675: d 3 0 3 2,2,2,2,2
-31675: a 4 0 4 1,2
-31675: join 16 2 3 0,2,2
-31675: meet 21 2 7 0,2
-NO CLASH, using fixed ground order
-31674: Facts:
-31674: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31674: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31674: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31674: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31674: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31674: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31674: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31674: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31674: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31674: Goal:
-31674: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (meet d (join a (meet b d)))))
- [] by prove_H28
-31674: Order:
-31674: kbo
-31674: Leaf order:
-31674: c 2 0 2 1,2,2,2,2
-31674: b 3 0 3 1,2,2
-31674: d 3 0 3 2,2,2,2,2
-31674: a 4 0 4 1,2
-31674: join 16 2 3 0,2,2
-31674: meet 21 2 7 0,2
-% SZS status Timeout for LAT146-1.p
-NO CLASH, using fixed ground order
-31717: Facts:
-31717: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31717: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31717: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31717: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31717: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31717: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31717: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31717: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31717: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31717: Goal:
-31717: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-31717: Order:
-31717: nrkbo
-31717: Leaf order:
-31717: c 2 0 2 2,2,2,2
-31717: b 4 0 4 1,2,2
-31717: a 6 0 6 1,2
-31717: join 17 2 4 0,2,2
-31717: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-31718: Facts:
-31718: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31718: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31718: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31718: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31718: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31718: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31718: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31718: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31718: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31718: Goal:
-31718: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-31718: Order:
-31718: kbo
-31718: Leaf order:
-31718: c 2 0 2 2,2,2,2
-31718: b 4 0 4 1,2,2
-31718: a 6 0 6 1,2
-31718: join 17 2 4 0,2,2
-31718: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-31719: Facts:
-31719: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31719: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31719: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31719: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31719: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31719: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31719: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31719: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31719: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-31719: Goal:
-31719: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-31719: Order:
-31719: lpo
-31719: Leaf order:
-31719: c 2 0 2 2,2,2,2
-31719: b 4 0 4 1,2,2
-31719: a 6 0 6 1,2
-31719: join 17 2 4 0,2,2
-31719: meet 20 2 6 0,2
-% SZS status Timeout for LAT148-1.p
-NO CLASH, using fixed ground order
-31740: Facts:
-31740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31740: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31740: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31740: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31740: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31740: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-31740: Goal:
-31740: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-31740: Order:
-31740: nrkbo
-31740: Leaf order:
-31740: b 3 0 3 1,2,2
-31740: c 3 0 3 2,2,2,2
-31740: a 6 0 6 1,2
-31740: join 18 2 4 0,2,2
-31740: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-31741: Facts:
-31741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31741: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31741: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31741: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31741: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31741: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-31741: Goal:
-31741: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-31741: Order:
-31741: kbo
-31741: Leaf order:
-31741: b 3 0 3 1,2,2
-31741: c 3 0 3 2,2,2,2
-31741: a 6 0 6 1,2
-31741: join 18 2 4 0,2,2
-31741: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-31742: Facts:
-31742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31742: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31742: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31742: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31742: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31742: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-31742: Goal:
-31742: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-31742: Order:
-31742: lpo
-31742: Leaf order:
-31742: b 3 0 3 1,2,2
-31742: c 3 0 3 2,2,2,2
-31742: a 6 0 6 1,2
-31742: join 18 2 4 0,2,2
-31742: meet 20 2 6 0,2
-% SZS status Timeout for LAT156-1.p
-NO CLASH, using fixed ground order
-31822: Facts:
-31822: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31822: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31822: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31822: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31822: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31822: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31822: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31822: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31822: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-31822: Goal:
-31822: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-31822: Order:
-31822: nrkbo
-31822: Leaf order:
-31822: b 2 0 2 1,2,2
-31822: d 2 0 2 2,2,2,2,2
-31822: c 3 0 3 1,2,2,2
-31822: a 4 0 4 1,2
-31822: join 18 2 4 0,2,2
-31822: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-31823: Facts:
-31823: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31823: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31823: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31823: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31823: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31823: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31823: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31823: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31823: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-31823: Goal:
-31823: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-31823: Order:
-31823: kbo
-31823: Leaf order:
-31823: b 2 0 2 1,2,2
-31823: d 2 0 2 2,2,2,2,2
-31823: c 3 0 3 1,2,2,2
-31823: a 4 0 4 1,2
-31823: join 18 2 4 0,2,2
-31823: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-31824: Facts:
-31824: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-31824: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-31824: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-31824: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-31824: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-31824: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-31824: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-31824: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-31824: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
-31824: Goal:
-31824: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c d)))
- [] by prove_H51
-31824: Order:
-31824: lpo
-31824: Leaf order:
-31824: b 2 0 2 1,2,2
-31824: d 2 0 2 2,2,2,2,2
-31824: c 3 0 3 1,2,2,2
-31824: a 4 0 4 1,2
-31824: join 18 2 4 0,2,2
-31824: meet 19 2 5 0,2
-% SZS status Timeout for LAT160-1.p
-NO CLASH, using fixed ground order
-31846: Facts:
-31846: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-31846: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-31846: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-31846: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-31846: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-31846: Id : 7, {_}:
- or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-31846: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-31846: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-31846: Id : 10, {_}:
- and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-31846: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-31846: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-31846: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-31846: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-31846: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-31846: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-31846: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-31846: Goal:
-31846: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =<=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-31846: Order:
-31846: nrkbo
-31846: Leaf order:
-31846: falsehood 1 0 0
-31846: x 3 0 3 2,1,1,1,2
-31846: y 3 0 3 2,1,1,2
-31846: truth 8 0 4 1,1,1,1,2
-31846: not 12 1 0
-31846: xor 7 2 4 0,1,2
-31846: and 9 2 0
-31846: or 10 2 0
-31846: and_star 11 2 4 0,2
-31846: implies 14 2 0
-NO CLASH, using fixed ground order
-31847: Facts:
-31847: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-31847: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-31847: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-31847: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-31847: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-31847: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-31847: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-31847: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-31847: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-31847: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-31847: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-31847: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-31847: Id : 14, {_}:
- and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-31847: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-31847: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-31847: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-31847: Goal:
-31847: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =?=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-31847: Order:
-31847: kbo
-31847: Leaf order:
-31847: falsehood 1 0 0
-31847: x 3 0 3 2,1,1,1,2
-31847: y 3 0 3 2,1,1,2
-31847: truth 8 0 4 1,1,1,1,2
-31847: not 12 1 0
-31847: xor 7 2 4 0,1,2
-31847: and 9 2 0
-31847: or 10 2 0
-31847: and_star 11 2 4 0,2
-31847: implies 14 2 0
-NO CLASH, using fixed ground order
-31848: Facts:
-31848: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
-31848: Id : 3, {_}:
- implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
- =>=
- truth
- [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
-31848: Id : 4, {_}:
- implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
- [9, 8] by wajsberg_3 ?8 ?9
-31848: Id : 5, {_}:
- implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
- [12, 11] by wajsberg_4 ?11 ?12
-31848: Id : 6, {_}:
- or ?14 ?15 =<= implies (not ?14) ?15
- [15, 14] by or_definition ?14 ?15
-31848: Id : 7, {_}:
- or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
- [19, 18, 17] by or_associativity ?17 ?18 ?19
-31848: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
-31848: Id : 9, {_}:
- and ?24 ?25 =<= not (or (not ?24) (not ?25))
- [25, 24] by and_definition ?24 ?25
-31848: Id : 10, {_}:
- and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
- [29, 28, 27] by and_associativity ?27 ?28 ?29
-31848: Id : 11, {_}:
- and ?31 ?32 =?= and ?32 ?31
- [32, 31] by and_commutativity ?31 ?32
-31848: Id : 12, {_}:
- xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
- [35, 34] by xor_definition ?34 ?35
-31848: Id : 13, {_}:
- xor ?37 ?38 =?= xor ?38 ?37
- [38, 37] by xor_commutativity ?37 ?38
-31848: Id : 14, {_}:
- and_star ?40 ?41 =>= not (or (not ?40) (not ?41))
- [41, 40] by and_star_definition ?40 ?41
-31848: Id : 15, {_}:
- and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
- [45, 44, 43] by and_star_associativity ?43 ?44 ?45
-31848: Id : 16, {_}:
- and_star ?47 ?48 =?= and_star ?48 ?47
- [48, 47] by and_star_commutativity ?47 ?48
-31848: Id : 17, {_}: not truth =>= falsehood [] by false_definition
-31848: Goal:
-31848: Id : 1, {_}:
- and_star (xor (and_star (xor truth x) y) truth) y
- =<=
- and_star (xor (and_star (xor truth y) x) truth) x
- [] by prove_alternative_wajsberg_axiom
-31848: Order:
-31848: lpo
-31848: Leaf order:
-31848: falsehood 1 0 0
-31848: x 3 0 3 2,1,1,1,2
-31848: y 3 0 3 2,1,1,2
-31848: truth 8 0 4 1,1,1,1,2
-31848: not 12 1 0
-31848: xor 7 2 4 0,1,2
-31848: and 9 2 0
-31848: or 10 2 0
-31848: and_star 11 2 4 0,2
-31848: implies 14 2 0
-% SZS status Timeout for LCL160-1.p
-NO CLASH, using fixed ground order
-31871: Facts:
-31871: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-31871: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-31871: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-31871: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =<=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-31871: Id : 6, {_}:
- add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-31871: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-31871: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-31871: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-31871: Goal:
-31871: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
-31871: Order:
-31871: nrkbo
-31871: Leaf order:
-31871: additive_identity 2 0 0
-31871: a 2 0 2 1,2
-31871: b 2 0 2 2,2
-31871: additive_inverse 1 1 0
-31871: add 12 2 0
-31871: multiply 14 2 2 0,2
-NO CLASH, using fixed ground order
-31872: Facts:
-31872: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-31872: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-31872: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-31872: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =<=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-31872: Id : 6, {_}:
- add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-31872: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-31872: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-31872: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-31872: Goal:
-31872: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
-31872: Order:
-31872: kbo
-31872: Leaf order:
-31872: additive_identity 2 0 0
-31872: a 2 0 2 1,2
-31872: b 2 0 2 2,2
-31872: additive_inverse 1 1 0
-31872: add 12 2 0
-31872: multiply 14 2 2 0,2
-NO CLASH, using fixed ground order
-31873: Facts:
-31873: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
-31873: Id : 3, {_}:
- add ?4 (additive_inverse ?4) =>= additive_identity
- [4] by right_additive_inverse ?4
-31873: Id : 4, {_}:
- multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8)
- [8, 7, 6] by distribute1 ?6 ?7 ?8
-31873: Id : 5, {_}:
- multiply (add ?10 ?11) ?12
- =>=
- add (multiply ?10 ?12) (multiply ?11 ?12)
- [12, 11, 10] by distribute2 ?10 ?11 ?12
-31873: Id : 6, {_}:
- add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
- [16, 15, 14] by associative_addition ?14 ?15 ?16
-31873: Id : 7, {_}:
- add ?18 ?19 =?= add ?19 ?18
- [19, 18] by commutative_addition ?18 ?19
-31873: Id : 8, {_}:
- multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
- [23, 22, 21] by associative_multiplication ?21 ?22 ?23
-31873: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
-31873: Goal:
-31873: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
-31873: Order:
-31873: lpo
-31873: Leaf order:
-31873: additive_identity 2 0 0
-31873: a 2 0 2 1,2
-31873: b 2 0 2 2,2
-31873: additive_inverse 1 1 0
-31873: add 12 2 0
-31873: multiply 14 2 2 0,2
-% SZS status Timeout for RNG009-5.p
-NO CLASH, using fixed ground order
-31898: Facts:
-31898: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31898: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31898: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-31898: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-31898: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-31898: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-31898: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-31898: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-31898: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-31898: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-31898: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-31898: Goal:
-31898: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-31898: Order:
-31898: nrkbo
-31898: Leaf order:
-31898: b 2 0 1 1,2
-31898: a 2 0 1 2,2
-31898: c 2 0 1 3
-31898: additive_identity 4 0 0
-31898: additive_inverse 2 1 0
-31898: add 14 2 0
-31898: multiply 14 2 1 0,2
-NO CLASH, using fixed ground order
-31899: Facts:
-31899: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31899: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31899: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-31899: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-31899: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-31899: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-31899: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-31899: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-31899: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-31899: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-31899: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-31899: Goal:
-31899: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-31899: Order:
-31899: kbo
-31899: Leaf order:
-31899: b 2 0 1 1,2
-31899: a 2 0 1 2,2
-31899: c 2 0 1 3
-31899: additive_identity 4 0 0
-31899: additive_inverse 2 1 0
-31899: add 14 2 0
-31899: multiply 14 2 1 0,2
-NO CLASH, using fixed ground order
-31900: Facts:
-31900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31900: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31900: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-31900: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-31900: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-31900: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-31900: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-31900: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-31900: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-31900: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
-31900: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-31900: Goal:
-31900: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-31900: Order:
-31900: lpo
-31900: Leaf order:
-31900: b 2 0 1 1,2
-31900: a 2 0 1 2,2
-31900: c 2 0 1 3
-31900: additive_identity 4 0 0
-31900: additive_inverse 2 1 0
-31900: add 14 2 0
-31900: multiply 14 2 1 0,2
-% SZS status Timeout for RNG009-7.p
-NO CLASH, using fixed ground order
-31923: Facts:
-31923: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31923: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31923: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31923: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31923: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31923: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31923: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31923: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31923: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31923: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31923: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31923: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31923: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31923: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31923: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31923: Goal:
-31923: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31923: Order:
-31923: nrkbo
-31923: Leaf order:
-31923: a 5 0 5 1,1,1,1,2
-31923: b 5 0 5 2,1,1,1,2
-31923: c 5 0 5 2,1,1,2
-31923: d 5 0 5 3,1,1,2
-31923: additive_identity 9 0 1 3
-31923: additive_inverse 7 1 1 0,2,2
-31923: commutator 1 2 0
-31923: add 20 2 4 0,2
-31923: multiply 27 2 5 0,1,1,1,2
-31923: associator 6 3 5 0,1,1,2
-NO CLASH, using fixed ground order
-31924: Facts:
-31924: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31924: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31924: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31924: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31924: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31924: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31924: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31924: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31924: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31924: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31924: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31924: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31924: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31924: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31924: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31924: Goal:
-31924: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31924: Order:
-31924: kbo
-31924: Leaf order:
-31924: a 5 0 5 1,1,1,1,2
-31924: b 5 0 5 2,1,1,1,2
-31924: c 5 0 5 2,1,1,2
-31924: d 5 0 5 3,1,1,2
-31924: additive_identity 9 0 1 3
-31924: additive_inverse 7 1 1 0,2,2
-31924: commutator 1 2 0
-31924: add 20 2 4 0,2
-31924: multiply 27 2 5 0,1,1,1,2
-31924: associator 6 3 5 0,1,1,2
-NO CLASH, using fixed ground order
-31925: Facts:
-31925: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31925: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31925: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31925: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31925: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31925: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31925: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31925: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31925: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31925: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31925: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31925: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31925: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31925: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31925: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31925: Goal:
-31925: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31925: Order:
-31925: lpo
-31925: Leaf order:
-31925: a 5 0 5 1,1,1,1,2
-31925: b 5 0 5 2,1,1,1,2
-31925: c 5 0 5 2,1,1,2
-31925: d 5 0 5 3,1,1,2
-31925: additive_identity 9 0 1 3
-31925: additive_inverse 7 1 1 0,2,2
-31925: commutator 1 2 0
-31925: add 20 2 4 0,2
-31925: multiply 27 2 5 0,1,1,1,2
-31925: associator 6 3 5 0,1,1,2
-% SZS status Timeout for RNG026-6.p
-NO CLASH, using fixed ground order
-31946: Facts:
-31946: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31946: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31946: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31946: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31946: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31946: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31946: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31946: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31946: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31946: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31946: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31946: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31946: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31946: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31946: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31946: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-31946: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-31946: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-31946: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-31946: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-31946: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-31946: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-31946: Goal:
-31946: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31946: Order:
-31946: nrkbo
-31946: Leaf order:
-31946: a 5 0 5 1,1,1,1,2
-31946: b 5 0 5 2,1,1,1,2
-31946: c 5 0 5 2,1,1,2
-31946: d 5 0 5 3,1,1,2
-31946: additive_identity 9 0 1 3
-31946: additive_inverse 23 1 1 0,2,2
-31946: commutator 1 2 0
-31946: add 28 2 4 0,2
-31946: multiply 45 2 5 0,1,1,1,2
-31946: associator 6 3 5 0,1,1,2
-NO CLASH, using fixed ground order
-31947: Facts:
-31947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31947: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31947: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31947: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31947: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31947: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31947: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31947: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31947: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31947: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31947: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31947: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31947: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31947: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31947: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31947: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-31947: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-31947: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-31947: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-31947: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-31947: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-31947: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-31947: Goal:
-31947: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31947: Order:
-31947: kbo
-31947: Leaf order:
-31947: a 5 0 5 1,1,1,1,2
-31947: b 5 0 5 2,1,1,1,2
-31947: c 5 0 5 2,1,1,2
-31947: d 5 0 5 3,1,1,2
-31947: additive_identity 9 0 1 3
-31947: additive_inverse 23 1 1 0,2,2
-31947: commutator 1 2 0
-31947: add 28 2 4 0,2
-31947: multiply 45 2 5 0,1,1,1,2
-31947: associator 6 3 5 0,1,1,2
-NO CLASH, using fixed ground order
-31948: Facts:
-31948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-31948: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-31948: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-31948: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-31948: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-31948: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-31948: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-31948: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-31948: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-31948: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-31948: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-31948: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-31948: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-31948: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-31948: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-31948: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-31948: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-31948: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-31948: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-31948: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-31948: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-31948: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-31948: Goal:
-31948: Id : 1, {_}:
- add
- (add (associator (multiply a b) c d)
- (associator a b (multiply c d)))
- (additive_inverse
- (add
- (add (associator a (multiply b c) d)
- (multiply a (associator b c d)))
- (multiply (associator a b c) d)))
- =>=
- additive_identity
- [] by prove_teichmuller_identity
-31948: Order:
-31948: lpo
-31948: Leaf order:
-31948: a 5 0 5 1,1,1,1,2
-31948: b 5 0 5 2,1,1,1,2
-31948: c 5 0 5 2,1,1,2
-31948: d 5 0 5 3,1,1,2
-31948: additive_identity 9 0 1 3
-31948: additive_inverse 23 1 1 0,2,2
-31948: commutator 1 2 0
-31948: add 28 2 4 0,2
-31948: multiply 45 2 5 0,1,1,1,2
-31948: associator 6 3 5 0,1,1,2
-% SZS status Timeout for RNG026-7.p
-NO CLASH, using fixed ground order
-31979: Facts:
-31979: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-31979: Goal:
-31979: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-31979: Order:
-31979: nrkbo
-31979: Leaf order:
-31979: c 2 0 2 2,2,2,2
-31979: a 3 0 3 1,2
-31979: b 3 0 3 1,2,2
-31979: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-31980: Facts:
-31980: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-31980: Goal:
-31980: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-31980: Order:
-31980: kbo
-31980: Leaf order:
-31980: c 2 0 2 2,2,2,2
-31980: a 3 0 3 1,2
-31980: b 3 0 3 1,2,2
-31980: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-31981: Facts:
-31981: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by sh_1 ?2 ?3 ?4
-31981: Goal:
-31981: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-31981: Order:
-31981: lpo
-31981: Leaf order:
-31981: c 2 0 2 2,2,2,2
-31981: a 3 0 3 1,2
-31981: b 3 0 3 1,2,2
-31981: nand 12 2 6 0,2
-% SZS status Timeout for BOO076-1.p
-CLASH, statistics insufficient
-32007: Facts:
-32007: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32007: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-32007: Goal:
-32007: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-32007: Order:
-32007: nrkbo
-32007: Leaf order:
-32007: b 1 0 0
-32007: w 1 0 0
-32007: f 3 1 3 0,2,2
-32007: apply 12 2 3 0,2
-CLASH, statistics insufficient
-32008: Facts:
-32008: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32008: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-32008: Goal:
-32008: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-32008: Order:
-32008: kbo
-32008: Leaf order:
-32008: b 1 0 0
-32008: w 1 0 0
-32008: f 3 1 3 0,2,2
-32008: apply 12 2 3 0,2
-CLASH, statistics insufficient
-32009: Facts:
-32009: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32009: Id : 3, {_}:
- apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
- [8, 7] by w_definition ?7 ?8
-32009: Goal:
-32009: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_strong_fixed_point ?1
-32009: Order:
-32009: lpo
-32009: Leaf order:
-32009: b 1 0 0
-32009: w 1 0 0
-32009: f 3 1 3 0,2,2
-32009: apply 12 2 3 0,2
-% SZS status Timeout for COL003-1.p
-CLASH, statistics insufficient
-32036: Facts:
-32036: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-CLASH, statistics insufficient
-32037: Facts:
-32037: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32037: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-32037: Goal:
-32037: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32037: Order:
-32037: kbo
-32037: Leaf order:
-32037: b 1 0 0
-32037: w1 1 0 0
-32037: f 3 1 3 0,2,2
-32037: apply 12 2 3 0,2
-32036: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-32036: Goal:
-32036: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32036: Order:
-32036: nrkbo
-32036: Leaf order:
-32036: b 1 0 0
-32036: w1 1 0 0
-32036: f 3 1 3 0,2,2
-32036: apply 12 2 3 0,2
-CLASH, statistics insufficient
-32038: Facts:
-32038: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32038: Id : 3, {_}:
- apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
- [8, 7] by w1_definition ?7 ?8
-32038: Goal:
-32038: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32038: Order:
-32038: lpo
-32038: Leaf order:
-32038: b 1 0 0
-32038: w1 1 0 0
-32038: f 3 1 3 0,2,2
-32038: apply 12 2 3 0,2
-% SZS status Timeout for COL042-1.p
-NO CLASH, using fixed ground order
-32071: Facts:
-32071: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32071: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-32071: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-32071: Goal:
-32071: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32071: Order:
-32071: nrkbo
-32071: Leaf order:
-32071: strong_fixed_point 3 0 2 1,2
-32071: fixed_pt 3 0 3 2,2
-32071: h 6 0 0
-32071: b 12 0 0
-32071: apply 29 2 3 0,2
-NO CLASH, using fixed ground order
-32072: Facts:
-32072: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32072: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-32072: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-32072: Goal:
-32072: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32072: Order:
-32072: kbo
-32072: Leaf order:
-32072: strong_fixed_point 3 0 2 1,2
-32072: fixed_pt 3 0 3 2,2
-32072: h 6 0 0
-32072: b 12 0 0
-32072: apply 29 2 3 0,2
-NO CLASH, using fixed ground order
-32073: Facts:
-32073: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32073: Id : 3, {_}:
- apply (apply (apply h ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?7) ?8) ?7
- [8, 7, 6] by h_definition ?6 ?7 ?8
-32073: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply h
- (apply (apply b (apply (apply b h) (apply b b)))
- (apply h (apply (apply b h) (apply b b))))) h)) b)) b
- [] by strong_fixed_point
-32073: Goal:
-32073: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32073: Order:
-32073: lpo
-32073: Leaf order:
-32073: strong_fixed_point 3 0 2 1,2
-32073: fixed_pt 3 0 3 2,2
-32073: h 6 0 0
-32073: b 12 0 0
-32073: apply 29 2 3 0,2
-% SZS status Timeout for COL043-3.p
-NO CLASH, using fixed ground order
-32095: Facts:
-NO CLASH, using fixed ground order
-32096: Facts:
-32096: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32096: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32096: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-32096: Goal:
-32096: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32096: Order:
-32096: kbo
-32096: Leaf order:
-32096: strong_fixed_point 3 0 2 1,2
-32096: fixed_pt 3 0 3 2,2
-32096: n 6 0 0
-32096: b 10 0 0
-32096: apply 27 2 3 0,2
-NO CLASH, using fixed ground order
-32097: Facts:
-32097: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32097: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32097: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-32097: Goal:
-32097: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32097: Order:
-32097: lpo
-32097: Leaf order:
-32097: strong_fixed_point 3 0 2 1,2
-32097: fixed_pt 3 0 3 2,2
-32097: n 6 0 0
-32097: b 10 0 0
-32097: apply 27 2 3 0,2
-32095: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32095: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32095: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply (apply b b) n))))) n)) b)) b
- [] by strong_fixed_point
-32095: Goal:
-32095: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32095: Order:
-32095: nrkbo
-32095: Leaf order:
-32095: strong_fixed_point 3 0 2 1,2
-32095: fixed_pt 3 0 3 2,2
-32095: n 6 0 0
-32095: b 10 0 0
-32095: apply 27 2 3 0,2
-% SZS status Timeout for COL044-8.p
-NO CLASH, using fixed ground order
-32149: Facts:
-32149: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32149: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32149: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-32149: Goal:
-32149: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32149: Order:
-32149: nrkbo
-32149: Leaf order:
-32149: strong_fixed_point 3 0 2 1,2
-32149: fixed_pt 3 0 3 2,2
-32149: n 6 0 0
-32149: b 10 0 0
-32149: apply 27 2 3 0,2
-NO CLASH, using fixed ground order
-32150: Facts:
-32150: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32150: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32150: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-32150: Goal:
-32150: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32150: Order:
-32150: kbo
-32150: Leaf order:
-32150: strong_fixed_point 3 0 2 1,2
-32150: fixed_pt 3 0 3 2,2
-32150: n 6 0 0
-32150: b 10 0 0
-32150: apply 27 2 3 0,2
-NO CLASH, using fixed ground order
-32151: Facts:
-32151: Id : 2, {_}:
- apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
- [4, 3, 2] by b_definition ?2 ?3 ?4
-32151: Id : 3, {_}:
- apply (apply (apply n ?6) ?7) ?8
- =?=
- apply (apply (apply ?6 ?8) ?7) ?8
- [8, 7, 6] by n_definition ?6 ?7 ?8
-32151: Id : 4, {_}:
- strong_fixed_point
- =<=
- apply
- (apply b
- (apply
- (apply b
- (apply
- (apply n
- (apply n
- (apply (apply b (apply b b))
- (apply n (apply n (apply b b)))))) n)) b)) b
- [] by strong_fixed_point
-32151: Goal:
-32151: Id : 1, {_}:
- apply strong_fixed_point fixed_pt
- =<=
- apply fixed_pt (apply strong_fixed_point fixed_pt)
- [] by prove_strong_fixed_point
-32151: Order:
-32151: lpo
-32151: Leaf order:
-32151: strong_fixed_point 3 0 2 1,2
-32151: fixed_pt 3 0 3 2,2
-32151: n 6 0 0
-32151: b 10 0 0
-32151: apply 27 2 3 0,2
-% SZS status Timeout for COL044-9.p
-NO CLASH, using fixed ground order
-32174: Facts:
-32174: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-32174: Goal:
-32174: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-32174: Order:
-32174: nrkbo
-32174: Leaf order:
-32174: b2 2 0 2 1,1,1,2
-32174: a2 2 0 2 2,2
-32174: inverse 8 1 1 0,1,1,2
-32174: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-32175: Facts:
-32175: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-32175: Goal:
-32175: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-32175: Order:
-32175: kbo
-32175: Leaf order:
-32175: b2 2 0 2 1,1,1,2
-32175: a2 2 0 2 2,2
-32175: inverse 8 1 1 0,1,1,2
-32175: multiply 12 2 2 0,2
-NO CLASH, using fixed ground order
-32176: Facts:
-32176: Id : 2, {_}:
- multiply
- (inverse
- (multiply
- (inverse
- (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
- (multiply (inverse (multiply ?4 ?5))
- (multiply ?4
- (inverse
- (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
- ?7
- =>=
- ?6
- [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
-32176: Goal:
-32176: Id : 1, {_}:
- multiply (multiply (inverse b2) b2) a2 =>= a2
- [] by prove_these_axioms_2
-32176: Order:
-32176: lpo
-32176: Leaf order:
-32176: b2 2 0 2 1,1,1,2
-32176: a2 2 0 2 2,2
-32176: inverse 8 1 1 0,1,1,2
-32176: multiply 12 2 2 0,2
-% SZS status Timeout for GRP506-1.p
-NO CLASH, using fixed ground order
-32197: Facts:
-32197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-NO CLASH, using fixed ground order
-32198: Facts:
-32198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32198: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32198: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32198: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32198: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32198: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-32198: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-32198: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-32198: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-32198: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-32197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32197: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32197: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32197: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32197: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32197: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-NO CLASH, using fixed ground order
-32197: Id : 11, {_}:
- complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-32197: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-32197: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-32197: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-32197: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-32197: Goal:
-32197: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-32197: Order:
-32197: nrkbo
-32197: Leaf order:
-32197: n0 1 0 0
-32197: n1 2 0 0
-32197: b 3 0 3 1,2,2
-32197: a 7 0 7 1,2
-32197: complement 14 1 2 0,1,2,2,2,2
-32197: join 18 2 3 0,2,2
-32197: meet 19 2 5 0,2
-32199: Facts:
-32199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32199: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32199: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32199: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32199: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32199: Id : 10, {_}:
- complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
- [27, 26] by compatibility1 ?26 ?27
-32199: Id : 11, {_}:
- complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
- [30, 29] by compatibility2 ?29 ?30
-32199: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
-32199: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
-32199: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
-32199: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-32199: Goal:
-32199: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-32199: Order:
-32199: lpo
-32199: Leaf order:
-32199: n0 1 0 0
-32199: n1 2 0 0
-32199: b 3 0 3 1,2,2
-32199: a 7 0 7 1,2
-32199: complement 14 1 2 0,1,2,2,2,2
-32199: join 18 2 3 0,2,2
-32199: meet 19 2 5 0,2
-32198: Id : 15, {_}:
- join (meet (complement ?38) (join ?38 ?39))
- (join (complement ?39) (meet ?38 ?39))
- =>=
- n1
- [39, 38] by megill ?38 ?39
-32198: Goal:
-32198: Id : 1, {_}:
- meet a (join b (meet a (join (complement a) (meet a b))))
- =>=
- meet a (join (complement a) (meet a b))
- [] by prove_this
-32198: Order:
-32198: kbo
-32198: Leaf order:
-32198: n0 1 0 0
-32198: n1 2 0 0
-32198: b 3 0 3 1,2,2
-32198: a 7 0 7 1,2
-32198: complement 14 1 2 0,1,2,2,2,2
-32198: join 18 2 3 0,2,2
-32198: meet 19 2 5 0,2
-% SZS status Timeout for LAT053-1.p
-NO CLASH, using fixed ground order
-32222: Facts:
-32222: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32222: Goal:
-32222: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
-32222: Order:
-32222: nrkbo
-32222: Leaf order:
-32222: a 2 0 2 1,2
-32222: b 2 0 2 2,2
-32222: join 20 2 0
-32222: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-32223: Facts:
-32223: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32223: Goal:
-32223: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
-32223: Order:
-32223: kbo
-32223: Leaf order:
-32223: a 2 0 2 1,2
-32223: b 2 0 2 2,2
-32223: join 20 2 0
-32223: meet 20 2 2 0,2
-NO CLASH, using fixed ground order
-32224: Facts:
-32224: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32224: Goal:
-32224: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
-32224: Order:
-32224: lpo
-32224: Leaf order:
-32224: a 2 0 2 1,2
-32224: b 2 0 2 2,2
-32224: join 20 2 0
-32224: meet 20 2 2 0,2
-% SZS status Timeout for LAT081-1.p
-NO CLASH, using fixed ground order
-32257: Facts:
-32257: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32257: Goal:
-32257: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
-32257: Order:
-32257: nrkbo
-32257: Leaf order:
-32257: a 2 0 2 1,2
-32257: b 2 0 2 2,2
-32257: meet 18 2 0
-32257: join 22 2 2 0,2
-NO CLASH, using fixed ground order
-32258: Facts:
-32258: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32258: Goal:
-32258: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
-32258: Order:
-32258: kbo
-32258: Leaf order:
-32258: a 2 0 2 1,2
-32258: b 2 0 2 2,2
-32258: meet 18 2 0
-32258: join 22 2 2 0,2
-NO CLASH, using fixed ground order
-32259: Facts:
-32259: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32259: Goal:
-32259: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
-32259: Order:
-32259: lpo
-32259: Leaf order:
-32259: a 2 0 2 1,2
-32259: b 2 0 2 2,2
-32259: meet 18 2 0
-32259: join 22 2 2 0,2
-% SZS status Timeout for LAT084-1.p
-NO CLASH, using fixed ground order
-32283: Facts:
-32283: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32283: Goal:
-32283: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-32283: Order:
-32283: nrkbo
-32283: Leaf order:
-32283: b 1 0 1 2,2,2
-32283: a 3 0 3 1,2
-32283: meet 19 2 1 0,2
-32283: join 21 2 1 0,2,2
-NO CLASH, using fixed ground order
-32284: Facts:
-32284: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32284: Goal:
-32284: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-32284: Order:
-32284: kbo
-32284: Leaf order:
-32284: b 1 0 1 2,2,2
-32284: a 3 0 3 1,2
-32284: meet 19 2 1 0,2
-32284: join 21 2 1 0,2,2
-NO CLASH, using fixed ground order
-32285: Facts:
-32285: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32285: Goal:
-32285: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
-32285: Order:
-32285: lpo
-32285: Leaf order:
-32285: b 1 0 1 2,2,2
-32285: a 3 0 3 1,2
-32285: meet 19 2 1 0,2
-32285: join 21 2 1 0,2,2
-% SZS status Timeout for LAT086-1.p
-NO CLASH, using fixed ground order
-32311: Facts:
-32311: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32311: Goal:
-32311: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-32311: Order:
-32311: nrkbo
-32311: Leaf order:
-32311: b 1 0 1 2,2,2
-32311: a 3 0 3 1,2
-32311: meet 19 2 1 0,2,2
-32311: join 21 2 1 0,2
-NO CLASH, using fixed ground order
-32312: Facts:
-32312: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32312: Goal:
-32312: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-32312: Order:
-32312: kbo
-32312: Leaf order:
-32312: b 1 0 1 2,2,2
-32312: a 3 0 3 1,2
-32312: meet 19 2 1 0,2,2
-32312: join 21 2 1 0,2
-NO CLASH, using fixed ground order
-32313: Facts:
-32313: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-32313: Goal:
-32313: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
-32313: Order:
-32313: lpo
-32313: Leaf order:
-32313: b 1 0 1 2,2,2
-32313: a 3 0 3 1,2
-32313: meet 19 2 1 0,2,2
-32313: join 21 2 1 0,2
-% SZS status Timeout for LAT087-1.p
-NO CLASH, using fixed ground order
-32355: Facts:
-32355: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32355: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32355: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32355: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32355: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32355: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32355: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32355: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32355: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-32355: Goal:
-32355: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32355: Order:
-32355: nrkbo
-32355: Leaf order:
-32355: a 4 0 4 1,2
-32355: b 4 0 4 1,2,2
-32355: c 4 0 4 2,2,2,2
-32355: join 17 2 4 0,2,2
-32355: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-32356: Facts:
-32356: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32356: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32356: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32356: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32356: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32356: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32356: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32356: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32356: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-32356: Goal:
-32356: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32356: Order:
-32356: kbo
-32356: Leaf order:
-32356: a 4 0 4 1,2
-32356: b 4 0 4 1,2,2
-32356: c 4 0 4 2,2,2,2
-32356: join 17 2 4 0,2,2
-32356: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-32357: Facts:
-32357: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32357: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32357: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32357: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32357: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32357: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32357: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32357: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32357: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H3 ?26 ?27 ?28
-32357: Goal:
-32357: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32357: Order:
-32357: lpo
-32357: Leaf order:
-32357: a 4 0 4 1,2
-32357: b 4 0 4 1,2,2
-32357: c 4 0 4 2,2,2,2
-32357: join 17 2 4 0,2,2
-32357: meet 21 2 6 0,2
-% SZS status Timeout for LAT099-1.p
-NO CLASH, using fixed ground order
-32378: Facts:
-32378: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32378: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32378: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32378: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32378: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32378: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32378: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32378: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32378: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-32378: Goal:
-32378: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-32378: Order:
-32378: nrkbo
-32378: Leaf order:
-32378: d 2 0 2 2,2,2,2,2
-32378: b 3 0 3 1,2,2
-32378: c 3 0 3 1,2,2,2
-32378: a 4 0 4 1,2
-32378: meet 19 2 5 0,2
-32378: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-32379: Facts:
-32379: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32379: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32379: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32379: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32379: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32379: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32379: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32379: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32379: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-32379: Goal:
-32379: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-32379: Order:
-32379: kbo
-32379: Leaf order:
-32379: d 2 0 2 2,2,2,2,2
-32379: b 3 0 3 1,2,2
-32379: c 3 0 3 1,2,2,2
-32379: a 4 0 4 1,2
-32379: meet 19 2 5 0,2
-32379: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-32380: Facts:
-32380: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32380: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32380: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32380: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32380: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32380: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32380: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32380: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32380: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-32380: Goal:
-32380: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-32380: Order:
-32380: lpo
-32380: Leaf order:
-32380: d 2 0 2 2,2,2,2,2
-32380: b 3 0 3 1,2,2
-32380: c 3 0 3 1,2,2,2
-32380: a 4 0 4 1,2
-32380: meet 19 2 5 0,2
-32380: join 19 2 5 0,2,2
-% SZS status Timeout for LAT110-1.p
-NO CLASH, using fixed ground order
-32414: Facts:
-32414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32414: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32414: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32414: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32414: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32414: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-32414: Goal:
-32414: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-32414: Order:
-32414: nrkbo
-32414: Leaf order:
-32414: b 3 0 3 1,2,2
-32414: c 3 0 3 2,2,2
-32414: a 5 0 5 1,2
-32414: join 17 2 4 0,2,2
-32414: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-32415: Facts:
-32415: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32415: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32415: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32415: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32415: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32415: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32415: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32415: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32415: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-32415: Goal:
-32415: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-32415: Order:
-32415: kbo
-32415: Leaf order:
-32415: b 3 0 3 1,2,2
-32415: c 3 0 3 2,2,2
-32415: a 5 0 5 1,2
-32415: join 17 2 4 0,2,2
-32415: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-32416: Facts:
-32416: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32416: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32416: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32416: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32416: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32416: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32416: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32416: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32416: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
- [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
-32416: Goal:
-32416: Id : 1, {_}:
- meet a (join b c)
- =<=
- join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
- [] by prove_H69
-32416: Order:
-32416: lpo
-32416: Leaf order:
-32416: b 3 0 3 1,2,2
-32416: c 3 0 3 2,2,2
-32416: a 5 0 5 1,2
-32416: join 17 2 4 0,2,2
-32416: meet 20 2 5 0,2
-% SZS status Timeout for LAT118-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-32445: Facts:
-32445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32445: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32445: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32445: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32445: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32445: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-32445: Goal:
-32445: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32445: Order:
-32445: kbo
-32445: Leaf order:
-32445: b 3 0 3 1,2,2
-32445: c 3 0 3 2,2,2,2
-32445: a 6 0 6 1,2
-32445: join 17 2 4 0,2,2
-32445: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-32446: Facts:
-32446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32446: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32446: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32446: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32446: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32446: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-32446: Goal:
-32446: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32446: Order:
-32446: lpo
-32446: Leaf order:
-32446: b 3 0 3 1,2,2
-32446: c 3 0 3 2,2,2,2
-32446: a 6 0 6 1,2
-32446: join 17 2 4 0,2,2
-32446: meet 21 2 6 0,2
-32444: Facts:
-32444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32444: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32444: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32444: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32444: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32444: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?28 (meet ?26 ?27)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H22 ?26 ?27 ?28
-32444: Goal:
-32444: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32444: Order:
-32444: nrkbo
-32444: Leaf order:
-32444: b 3 0 3 1,2,2
-32444: c 3 0 3 2,2,2,2
-32444: a 6 0 6 1,2
-32444: join 17 2 4 0,2,2
-32444: meet 21 2 6 0,2
-% SZS status Timeout for LAT142-1.p
-NO CLASH, using fixed ground order
-32541: Facts:
-32541: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32541: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32541: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32541: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32541: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32541: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32541: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32541: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32541: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-32541: Goal:
-32541: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =<=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-32541: Order:
-32541: nrkbo
-32541: Leaf order:
-32541: d 2 0 2 2,2,2,2,2
-32541: b 3 0 3 1,2,2
-32541: c 3 0 3 1,2,2,2
-32541: a 4 0 4 1,2
-32541: join 16 2 3 0,2,2,2
-32541: meet 21 2 7 0,2
-NO CLASH, using fixed ground order
-32542: Facts:
-32542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32542: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32542: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32542: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32542: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32542: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-32542: Goal:
-32542: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =<=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-32542: Order:
-32542: kbo
-32542: Leaf order:
-32542: d 2 0 2 2,2,2,2,2
-32542: b 3 0 3 1,2,2
-32542: c 3 0 3 1,2,2,2
-32542: a 4 0 4 1,2
-32542: join 16 2 3 0,2,2,2
-32542: meet 21 2 7 0,2
-NO CLASH, using fixed ground order
-32543: Facts:
-32543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32543: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32543: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32543: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32543: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32543: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 ?29))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
- [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
-32543: Goal:
-32543: Id : 1, {_}:
- meet a (meet b (join c (meet a d)))
- =>=
- meet a (meet b (join c (meet d (join a (meet b c)))))
- [] by prove_H45
-32543: Order:
-32543: lpo
-32543: Leaf order:
-32543: d 2 0 2 2,2,2,2,2
-32543: b 3 0 3 1,2,2
-32543: c 3 0 3 1,2,2,2
-32543: a 4 0 4 1,2
-32543: join 16 2 3 0,2,2,2
-32543: meet 21 2 7 0,2
-% SZS status Timeout for LAT147-1.p
-NO CLASH, using fixed ground order
-32564: Facts:
-32564: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32564: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32564: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32564: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32564: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32564: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32564: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32564: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32564: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-32564: Goal:
-32564: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32564: Order:
-32564: nrkbo
-32564: Leaf order:
-32564: b 3 0 3 1,2,2
-32564: c 3 0 3 2,2,2,2
-32564: a 6 0 6 1,2
-32564: join 18 2 4 0,2,2
-32564: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-32565: Facts:
-32565: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32565: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32565: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32565: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32565: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32565: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32565: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32565: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32565: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-32565: Goal:
-32565: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32565: Order:
-32565: kbo
-32565: Leaf order:
-32565: b 3 0 3 1,2,2
-32565: c 3 0 3 2,2,2,2
-32565: a 6 0 6 1,2
-32565: join 18 2 4 0,2,2
-32565: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-32566: Facts:
-32566: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32566: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32566: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32566: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32566: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32566: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32566: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32566: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32566: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
- [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
-32566: Goal:
-32566: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-32566: Order:
-32566: lpo
-32566: Leaf order:
-32566: b 3 0 3 1,2,2
-32566: c 3 0 3 2,2,2,2
-32566: a 6 0 6 1,2
-32566: join 18 2 4 0,2,2
-32566: meet 20 2 6 0,2
-% SZS status Timeout for LAT154-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-32589: Facts:
-32589: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32589: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32589: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32589: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32589: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32589: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32589: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32589: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32589: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-32589: Goal:
-32589: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32589: Order:
-32589: kbo
-32589: Leaf order:
-32589: a 4 0 4 1,2
-32589: b 4 0 4 1,2,2
-32589: c 4 0 4 2,2,2,2
-32589: join 18 2 4 0,2,2
-32589: meet 20 2 6 0,2
-32588: Facts:
-32588: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32588: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32588: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32588: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32588: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32588: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32588: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32588: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32588: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-32588: Goal:
-32588: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32588: Order:
-32588: nrkbo
-32588: Leaf order:
-32588: a 4 0 4 1,2
-32588: b 4 0 4 1,2,2
-32588: c 4 0 4 2,2,2,2
-32588: join 18 2 4 0,2,2
-32588: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-32590: Facts:
-32590: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32590: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32590: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32590: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32590: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32590: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32590: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32590: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32590: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
- [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
-32590: Goal:
-32590: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-32590: Order:
-32590: lpo
-32590: Leaf order:
-32590: a 4 0 4 1,2
-32590: b 4 0 4 1,2,2
-32590: c 4 0 4 2,2,2,2
-32590: join 18 2 4 0,2,2
-32590: meet 20 2 6 0,2
-% SZS status Timeout for LAT155-1.p
-NO CLASH, using fixed ground order
-32615: Facts:
-32615: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32615: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32615: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32615: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32615: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32615: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32615: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32615: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32615: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-32615: Goal:
-32615: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-32615: Order:
-32615: nrkbo
-32615: Leaf order:
-32615: c 2 0 2 2,2,2
-32615: a 4 0 4 1,2
-32615: b 4 0 4 1,2,2
-32615: meet 18 2 4 0,2
-32615: join 18 2 4 0,2,2
-NO CLASH, using fixed ground order
-32616: Facts:
-32616: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32616: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32616: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32616: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32616: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32616: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32616: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32616: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32616: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-32616: Goal:
-32616: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-32616: Order:
-32616: kbo
-32616: Leaf order:
-32616: c 2 0 2 2,2,2
-32616: a 4 0 4 1,2
-32616: b 4 0 4 1,2,2
-32616: meet 18 2 4 0,2
-32616: join 18 2 4 0,2,2
-NO CLASH, using fixed ground order
-32617: Facts:
-32617: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-32617: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-32617: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-32617: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-32617: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-32617: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-32617: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-32617: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-32617: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
-32617: Goal:
-32617: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-32617: Order:
-32617: lpo
-32617: Leaf order:
-32617: c 2 0 2 2,2,2
-32617: a 4 0 4 1,2
-32617: b 4 0 4 1,2,2
-32617: meet 18 2 4 0,2
-32617: join 18 2 4 0,2,2
-% SZS status Timeout for LAT170-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-32640: Facts:
-32640: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-32640: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-32640: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-32640: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-32640: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-32640: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-32640: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-32640: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-32640: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-32640: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-32640: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-32640: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-32640: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-NO CLASH, using fixed ground order
-32641: Facts:
-32641: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-32641: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-32641: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-32641: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-32641: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-32641: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-32641: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-32641: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-32641: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-32641: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-32641: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-32641: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-32641: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-32641: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-32641: Goal:
-32641: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32641: Order:
-32641: lpo
-32641: Leaf order:
-32641: y 4 0 4 3,1,1,1,2
-32641: additive_identity 9 0 1 3
-32641: x 9 0 9 1,1,1,1,2
-32641: additive_inverse 6 1 0
-32641: commutator 1 2 0
-32641: add 16 2 0
-32641: multiply 22 2 4 0,2
-32641: associator 5 3 4 0,1,1,1,2
-32639: Facts:
-32639: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-32639: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-32639: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-32639: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-32639: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-32639: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-32639: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-32639: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-32639: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-32639: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-32639: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-32639: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-32639: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-32639: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-32639: Goal:
-32639: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32639: Order:
-32639: nrkbo
-32639: Leaf order:
-32639: y 4 0 4 3,1,1,1,2
-32639: additive_identity 9 0 1 3
-32639: x 9 0 9 1,1,1,1,2
-32639: additive_inverse 6 1 0
-32639: commutator 1 2 0
-32639: add 16 2 0
-32639: multiply 22 2 4 0,2
-32639: associator 5 3 4 0,1,1,1,2
-32640: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-32640: Goal:
-32640: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32640: Order:
-32640: kbo
-32640: Leaf order:
-32640: y 4 0 4 3,1,1,1,2
-32640: additive_identity 9 0 1 3
-32640: x 9 0 9 1,1,1,1,2
-32640: additive_inverse 6 1 0
-32640: commutator 1 2 0
-32640: add 16 2 0
-32640: multiply 22 2 4 0,2
-32640: associator 5 3 4 0,1,1,1,2
-% SZS status Timeout for RNG031-6.p
-NO CLASH, using fixed ground order
-32666: Facts:
-32666: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-32666: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-32666: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-32666: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-32666: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-32666: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-32666: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-32666: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-32666: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-32666: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-32666: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-32666: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-32666: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-32666: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-32666: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-32666: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-32666: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-32666: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-32666: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-32666: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-32666: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-32666: Goal:
-32666: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32666: Order:
-32666: nrkbo
-32666: Leaf order:
-32666: y 4 0 4 3,1,1,1,2
-32666: additive_identity 9 0 1 3
-32666: x 9 0 9 1,1,1,1,2
-32666: additive_inverse 22 1 0
-32666: commutator 1 2 0
-32666: add 24 2 0
-32666: multiply 40 2 4 0,2add
-32666: associator 5 3 4 0,1,1,1,2
-NO CLASH, using fixed ground order
-32667: Facts:
-32667: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-32667: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-32667: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-32667: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-32667: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-32667: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-32667: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-32667: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-32667: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-32667: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-32667: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-32667: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-32667: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-32667: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-32667: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-32667: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-32667: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-32667: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-32667: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-32667: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-32667: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-32667: Goal:
-32667: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32667: Order:
-32667: kbo
-32667: Leaf order:
-32667: y 4 0 4 3,1,1,1,2
-32667: additive_identity 9 0 1 3
-32667: x 9 0 9 1,1,1,1,2
-32667: additive_inverse 22 1 0
-32667: commutator 1 2 0
-32667: add 24 2 0
-32667: multiply 40 2 4 0,2add
-32667: associator 5 3 4 0,1,1,1,2
-NO CLASH, using fixed ground order
-32668: Facts:
-32668: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-32668: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-32668: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-32668: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-32668: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-32668: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-32668: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-32668: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-32668: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-32668: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-32668: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-32668: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-32668: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-32668: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-32668: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-32668: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-32668: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-32668: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-32668: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-32668: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-32668: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-32668: Goal:
-32668: Id : 1, {_}:
- multiply
- (multiply (multiply (associator x x y) (associator x x y)) x)
- (multiply (associator x x y) (associator x x y))
- =>=
- additive_identity
- [] by prove_conjecture_2
-32668: Order:
-32668: lpo
-32668: Leaf order:
-32668: y 4 0 4 3,1,1,1,2
-32668: additive_identity 9 0 1 3
-32668: x 9 0 9 1,1,1,1,2
-32668: additive_inverse 22 1 0
-32668: commutator 1 2 0
-32668: add 24 2 0
-32668: multiply 40 2 4 0,2add
-32668: associator 5 3 4 0,1,1,1,2
-% SZS status Timeout for RNG031-7.p
-NO CLASH, using fixed ground order
-32691: Facts:
-32691: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-32691: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-32691: Goal:
-32691: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
-32691: Order:
-32691: nrkbo
-32691: Leaf order:
-32691: f 2 1 0
-32691: g1 2 1 1 0,2
-32691: g2 2 1 1 0,3
-NO CLASH, using fixed ground order
-32692: Facts:
-32692: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-32692: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-32692: Goal:
-32692: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
-32692: Order:
-32692: kbo
-32692: Leaf order:
-32692: f 2 1 0
-32692: g1 2 1 1 0,2
-32692: g2 2 1 1 0,3
-NO CLASH, using fixed ground order
-32693: Facts:
-32693: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
-32693: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
-32693: Goal:
-32693: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
-32693: Order:
-32693: lpo
-32693: Leaf order:
-32693: f 2 1 0
-32693: g1 2 1 1 0,2
-32693: g2 2 1 1 0,3
-32691: status GaveUp for SYN305-1.p
-32693: status GaveUp for SYN305-1.p
-32692: status GaveUp for SYN305-1.p
-% SZS status Timeout for SYN305-1.p
-CLASH, statistics insufficient
-32698: Facts:
-32698: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32698: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-32698: Goal:
-32698: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32698: Order:
-32698: nrkbo
-32698: Leaf order:
-32698: b 1 0 0
-32698: h 1 0 0
-32698: f 3 1 3 0,2,2
-32698: apply 14 2 3 0,2
-CLASH, statistics insufficient
-32699: Facts:
-32699: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32699: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-32699: Goal:
-32699: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32699: Order:
-32699: kbo
-32699: Leaf order:
-32699: b 1 0 0
-32699: h 1 0 0
-32699: f 3 1 3 0,2,2
-32699: apply 14 2 3 0,2
-CLASH, statistics insufficient
-32700: Facts:
-32700: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32700: Id : 3, {_}:
- apply (apply (apply h ?7) ?8) ?9
- =?=
- apply (apply (apply ?7 ?8) ?9) ?8
- [9, 8, 7] by h_definition ?7 ?8 ?9
-32700: Goal:
-32700: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-32700: Order:
-32700: lpo
-32700: Leaf order:
-32700: b 1 0 0
-32700: h 1 0 0
-32700: f 3 1 3 0,2,2
-32700: apply 14 2 3 0,2
-% SZS status Timeout for COL043-1.p
-CLASH, statistics insufficient
-32721: Facts:
-32721: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32721: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-32721: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-32721: Goal:
-32721: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =<=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-32721: Order:
-32721: nrkbo
-32721: Leaf order:
-32721: b 1 0 0
-32721: q 1 0 0
-32721: w 1 0 0
-32721: h 2 1 2 0,2,2
-32721: f 3 1 3 0,2,1,1,1,2
-32721: g 4 1 4 0,2,1,1,2
-32721: apply 22 2 8 0,2
-CLASH, statistics insufficient
-32722: Facts:
-32722: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32722: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-32722: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-32722: Goal:
-32722: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =<=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-32722: Order:
-32722: kbo
-32722: Leaf order:
-32722: b 1 0 0
-32722: q 1 0 0
-32722: w 1 0 0
-32722: h 2 1 2 0,2,2
-32722: f 3 1 3 0,2,1,1,1,2
-32722: g 4 1 4 0,2,1,1,2
-32722: apply 22 2 8 0,2
-CLASH, statistics insufficient
-32723: Facts:
-32723: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-32723: Id : 3, {_}:
- apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
- [9, 8, 7] by q_definition ?7 ?8 ?9
-32723: Id : 4, {_}:
- apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
- [12, 11] by w_definition ?11 ?12
-32723: Goal:
-32723: Id : 1, {_}:
- apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
- =>=
- apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
- [1] by prove_p_combinator ?1
-32723: Order:
-32723: lpo
-32723: Leaf order:
-32723: b 1 0 0
-32723: q 1 0 0
-32723: w 1 0 0
-32723: h 2 1 2 0,2,2
-32723: f 3 1 3 0,2,1,1,1,2
-32723: g 4 1 4 0,2,1,1,2
-32723: apply 22 2 8 0,2
-% SZS status Timeout for COL066-1.p
-NO CLASH, using fixed ground order
-32745: Facts:
-32745: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-32745: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-32745: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-32745: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-32745: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-32745: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-32745: Id : 8, {_}:
- join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-32745: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-32745: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-32745: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-32745: Goal:
-32745: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-32745: Order:
-32745: nrkbo
-32745: Leaf order:
-32745: n0 1 0 0
-32745: n1 2 0 1 3
-32745: b 4 0 4 2,1,1,1,1,2
-32745: a 5 0 5 1,1,1,1,1,1,2
-32745: complement 15 1 6 0,1,2
-32745: meet 12 2 3 0,1,1,1,1,2
-32745: join 17 2 5 0,2
-NO CLASH, using fixed ground order
-32746: Facts:
-32746: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-32746: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-32746: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-32746: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-32746: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-32746: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-32746: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-32746: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-32746: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-NO CLASH, using fixed ground order
-32747: Facts:
-32747: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
-32747: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
-32747: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
-32747: Id : 5, {_}:
- meet ?9 ?10 =?= meet ?10 ?9
- [10, 9] by commutativity_of_meet ?9 ?10
-32747: Id : 6, {_}:
- join ?12 ?13 =?= join ?13 ?12
- [13, 12] by commutativity_of_join ?12 ?13
-32747: Id : 7, {_}:
- meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
- [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
-32747: Id : 8, {_}:
- join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
- [21, 20, 19] by associativity_of_join ?19 ?20 ?21
-32747: Id : 9, {_}:
- complement (complement ?23) =>= ?23
- [23] by complement_involution ?23
-32747: Id : 10, {_}:
- join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
- [26, 25] by join_complement ?25 ?26
-32747: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-32747: Goal:
-32747: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-32747: Order:
-32747: lpo
-32747: Leaf order:
-32747: n0 1 0 0
-32747: n1 2 0 1 3
-32747: b 4 0 4 2,1,1,1,1,2
-32747: a 5 0 5 1,1,1,1,1,1,2
-32747: complement 15 1 6 0,1,2
-32747: meet 12 2 3 0,1,1,1,1,2
-32747: join 17 2 5 0,2
-32746: Id : 11, {_}:
- meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
- [29, 28] by meet_complement ?28 ?29
-32746: Goal:
-32746: Id : 1, {_}:
- join
- (complement
- (join
- (join (meet (complement a) b)
- (meet (complement a) (complement b)))
- (meet a (join (complement a) b)))) (join (complement a) b)
- =>=
- n1
- [] by prove_e3
-32746: Order:
-32746: kbo
-32746: Leaf order:
-32746: n0 1 0 0
-32746: n1 2 0 1 3
-32746: b 4 0 4 2,1,1,1,1,2
-32746: a 5 0 5 1,1,1,1,1,1,2
-32746: complement 15 1 6 0,1,2
-32746: meet 12 2 3 0,1,1,1,1,2
-32746: join 17 2 5 0,2
-% SZS status Timeout for LAT018-1.p
-NO CLASH, using fixed ground order
-301: Facts:
-301: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-301: Goal:
-301: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-301: Order:
-301: nrkbo
-301: Leaf order:
-301: a 2 0 2 1,1,2
-301: b 2 0 2 2,1,2
-301: c 2 0 2 2,2
-301: join 20 2 0
-301: meet 22 2 4 0,2
-NO CLASH, using fixed ground order
-302: Facts:
-302: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-302: Goal:
-302: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-302: Order:
-302: kbo
-302: Leaf order:
-302: a 2 0 2 1,1,2
-302: b 2 0 2 2,1,2
-302: c 2 0 2 2,2
-302: join 20 2 0
-302: meet 22 2 4 0,2
-NO CLASH, using fixed ground order
-303: Facts:
-303: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-303: Goal:
-303: Id : 1, {_}:
- meet (meet a b) c =>= meet a (meet b c)
- [] by prove_normal_axioms_3
-303: Order:
-303: lpo
-303: Leaf order:
-303: a 2 0 2 1,1,2
-303: b 2 0 2 2,1,2
-303: c 2 0 2 2,2
-303: join 20 2 0
-303: meet 22 2 4 0,2
-% SZS status Timeout for LAT082-1.p
-NO CLASH, using fixed ground order
-337: Facts:
-337: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-337: Goal:
-337: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-337: Order:
-337: nrkbo
-337: Leaf order:
-337: a 2 0 2 1,1,2
-337: b 2 0 2 2,1,2
-337: c 2 0 2 2,2
-337: meet 18 2 0
-337: join 24 2 4 0,2
-NO CLASH, using fixed ground order
-338: Facts:
-338: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-338: Goal:
-338: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-338: Order:
-338: kbo
-338: Leaf order:
-338: a 2 0 2 1,1,2
-338: b 2 0 2 2,1,2
-338: c 2 0 2 2,2
-338: meet 18 2 0
-338: join 24 2 4 0,2
-NO CLASH, using fixed ground order
-339: Facts:
-339: Id : 2, {_}:
- join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
- (meet
- (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
- (meet
- (join
- (meet ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
- (meet ?8
- (join ?3
- (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
- (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
- (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
- =>=
- ?3
- [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
-339: Goal:
-339: Id : 1, {_}:
- join (join a b) c =>= join a (join b c)
- [] by prove_normal_axioms_6
-339: Order:
-339: lpo
-339: Leaf order:
-339: a 2 0 2 1,1,2
-339: b 2 0 2 2,1,2
-339: c 2 0 2 2,2
-339: meet 18 2 0
-339: join 24 2 4 0,2
-% SZS status Timeout for LAT085-1.p
-NO CLASH, using fixed ground order
-1422: Facts:
-1422: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1422: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1422: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1422: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1422: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1422: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1422: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1422: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1422: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-1422: Goal:
-1422: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-1422: Order:
-1422: nrkbo
-1422: Leaf order:
-1422: a 4 0 4 1,2
-1422: b 4 0 4 1,2,2
-1422: c 4 0 4 2,2,2,2
-1422: join 16 2 4 0,2,2
-1422: meet 22 2 6 0,2
-NO CLASH, using fixed ground order
-1423: Facts:
-1423: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1423: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1423: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1423: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1423: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1423: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1423: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1423: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1423: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-1423: Goal:
-1423: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-1423: Order:
-1423: kbo
-1423: Leaf order:
-1423: a 4 0 4 1,2
-1423: b 4 0 4 1,2,2
-1423: c 4 0 4 2,2,2,2
-1423: join 16 2 4 0,2,2
-1423: meet 22 2 6 0,2
-NO CLASH, using fixed ground order
-1424: Facts:
-1424: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1424: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1424: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1424: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1424: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1424: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1424: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1424: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1424: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-1424: Goal:
-1424: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-1424: Order:
-1424: lpo
-1424: Leaf order:
-1424: a 4 0 4 1,2
-1424: b 4 0 4 1,2,2
-1424: c 4 0 4 2,2,2,2
-1424: join 16 2 4 0,2,2
-1424: meet 22 2 6 0,2
-% SZS status Timeout for LAT144-1.p
-NO CLASH, using fixed ground order
-1797: Facts:
-1797: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1797: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1797: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1797: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1797: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1797: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1797: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1797: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1797: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-1797: Goal:
-1797: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-1797: Order:
-1797: nrkbo
-1797: Leaf order:
-1797: d 2 0 2 2,2,2,2,2
-1797: b 3 0 3 1,2,2
-1797: c 3 0 3 1,2,2,2
-1797: a 4 0 4 1,2
-1797: join 18 2 5 0,2,2
-1797: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-1798: Facts:
-1798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1798: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1798: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1798: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1798: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1798: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-1798: Goal:
-1798: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-1798: Order:
-1798: kbo
-1798: Leaf order:
-1798: d 2 0 2 2,2,2,2,2
-1798: b 3 0 3 1,2,2
-1798: c 3 0 3 1,2,2,2
-1798: a 4 0 4 1,2
-1798: join 18 2 5 0,2,2
-1798: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-1799: Facts:
-1799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-1799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-1799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-1799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-1799: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-1799: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-1799: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-1799: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-1799: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-1799: Goal:
-1799: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-1799: Order:
-1799: lpo
-1799: Leaf order:
-1799: d 2 0 2 2,2,2,2,2
-1799: b 3 0 3 1,2,2
-1799: c 3 0 3 1,2,2,2
-1799: a 4 0 4 1,2
-1799: join 18 2 5 0,2,2
-1799: meet 19 2 5 0,2
-% SZS status Timeout for LAT150-1.p
-NO CLASH, using fixed ground order
-3353: Facts:
-3353: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-3353: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-3353: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-3353: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-3353: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-3353: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-3353: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-3353: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-3353: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-3353: Goal:
-3353: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-3353: Order:
-3353: nrkbo
-3353: Leaf order:
-3353: d 2 0 2 2,2,2,2,2
-3353: b 3 0 3 1,2,2
-3353: c 3 0 3 1,2,2,2
-3353: a 4 0 4 1,2
-3353: join 18 2 5 0,2,2
-3353: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-3358: Facts:
-3358: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-3358: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-3358: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-3358: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-3358: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-3358: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-3358: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-3358: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-3358: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-3358: Goal:
-3358: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-3358: Order:
-3358: kbo
-3358: Leaf order:
-3358: d 2 0 2 2,2,2,2,2
-3358: b 3 0 3 1,2,2
-3358: c 3 0 3 1,2,2,2
-3358: a 4 0 4 1,2
-3358: join 18 2 5 0,2,2
-3358: meet 19 2 5 0,2
-NO CLASH, using fixed ground order
-3361: Facts:
-3361: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-3361: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-3361: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-3361: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-3361: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-3361: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-3361: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-3361: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-3361: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
- [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
-3361: Goal:
-3361: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-3361: Order:
-3361: lpo
-3361: Leaf order:
-3361: d 2 0 2 2,2,2,2,2
-3361: b 3 0 3 1,2,2
-3361: c 3 0 3 1,2,2,2
-3361: a 4 0 4 1,2
-3361: join 18 2 5 0,2,2
-3361: meet 19 2 5 0,2
-% SZS status Timeout for LAT151-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-4534: Facts:
-4534: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-4534: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-4534: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-4534: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-4534: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-4534: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-4534: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-4534: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-4534: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-4534: Goal:
-4534: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-4534: Order:
-4534: kbo
-4534: Leaf order:
-4534: b 3 0 3 1,2,2
-4534: c 3 0 3 2,2,2,2
-4534: a 6 0 6 1,2
-4534: join 18 2 4 0,2,2
-4534: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-4537: Facts:
-4537: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-4537: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-4537: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-4537: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-4537: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-4537: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-4537: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-4537: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-4537: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-4537: Goal:
-4537: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-4537: Order:
-4537: lpo
-4537: Leaf order:
-4537: b 3 0 3 1,2,2
-4537: c 3 0 3 2,2,2,2
-4537: a 6 0 6 1,2
-4537: join 18 2 4 0,2,2
-4537: meet 20 2 6 0,2
-4533: Facts:
-4533: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-4533: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-4533: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-4533: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-4533: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-4533: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-4533: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-4533: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-4533: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-4533: Goal:
-4533: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-4533: Order:
-4533: nrkbo
-4533: Leaf order:
-4533: b 3 0 3 1,2,2
-4533: c 3 0 3 2,2,2,2
-4533: a 6 0 6 1,2
-4533: join 18 2 4 0,2,2
-4533: meet 20 2 6 0,2
-% SZS status Timeout for LAT152-1.p
-NO CLASH, using fixed ground order
-5952: Facts:
-5952: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-5952: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-5952: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-5952: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-5952: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-5952: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-5952: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-5952: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-5952: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-5952: Goal:
-5952: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-5952: Order:
-5952: nrkbo
-5952: Leaf order:
-5952: c 2 0 2 2,2,2,2
-5952: b 4 0 4 1,2,2
-5952: a 6 0 6 1,2
-5952: join 18 2 4 0,2,2
-5952: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-5958: Facts:
-5958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-5958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-5958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-5958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-5958: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-5958: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-5958: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-5958: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-5958: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-5958: Goal:
-5958: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-5958: Order:
-5958: kbo
-5958: Leaf order:
-5958: c 2 0 2 2,2,2,2
-5958: b 4 0 4 1,2,2
-5958: a 6 0 6 1,2
-5958: join 18 2 4 0,2,2
-5958: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-5959: Facts:
-5959: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-5959: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-5959: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-5959: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-5959: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-5959: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-5959: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-5959: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-5959: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-5959: Goal:
-5959: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-5959: Order:
-5959: lpo
-5959: Leaf order:
-5959: c 2 0 2 2,2,2,2
-5959: b 4 0 4 1,2,2
-5959: a 6 0 6 1,2
-5959: join 18 2 4 0,2,2
-5959: meet 20 2 6 0,2
-% SZS status Timeout for LAT159-1.p
-NO CLASH, using fixed ground order
-7548: Facts:
-7548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-7548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-7548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-7548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-7548: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-7548: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-7548: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-7548: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-7548: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-7548: Goal:
-7548: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-7548: Order:
-7548: nrkbo
-7548: Leaf order:
-7548: d 2 0 2 2,2,2,2
-7548: a 3 0 3 1,2
-7548: b 3 0 3 1,2,2
-7548: c 3 0 3 1,2,2,2
-7548: join 15 2 3 0,2,2,2
-7548: meet 19 2 6 0,2
-NO CLASH, using fixed ground order
-7549: Facts:
-7549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-7549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-7549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-7549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-7549: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-7549: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-7549: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-7549: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-7549: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-7549: Goal:
-7549: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-7549: Order:
-7549: kbo
-7549: Leaf order:
-7549: d 2 0 2 2,2,2,2
-7549: a 3 0 3 1,2
-7549: b 3 0 3 1,2,2
-7549: c 3 0 3 1,2,2,2
-7549: join 15 2 3 0,2,2,2
-7549: meet 19 2 6 0,2
-NO CLASH, using fixed ground order
-7552: Facts:
-7552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-7552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-7552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-7552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-7552: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-7552: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-7552: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-7552: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-7552: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H68 ?26 ?27 ?28
-7552: Goal:
-7552: Id : 1, {_}:
- meet a (meet b (join c d))
- =<=
- meet a (meet b (join c (meet a (join d (meet b c)))))
- [] by prove_H73
-7552: Order:
-7552: lpo
-7552: Leaf order:
-7552: d 2 0 2 2,2,2,2
-7552: a 3 0 3 1,2
-7552: b 3 0 3 1,2,2
-7552: c 3 0 3 1,2,2,2
-7552: join 15 2 3 0,2,2,2
-7552: meet 19 2 6 0,2
-% SZS status Timeout for LAT162-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-8627: Facts:
-8627: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-8627: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-8627: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-8627: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-8627: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-8627: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-8627: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-8627: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-8627: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-8627: Goal:
-8627: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-8627: Order:
-8627: kbo
-8627: Leaf order:
-8627: b 3 0 3 1,2,2
-8627: c 3 0 3 2,2,2,2
-8627: a 6 0 6 1,2
-8627: join 17 2 4 0,2,2
-8627: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-8628: Facts:
-8628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-8628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-8628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-8628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-8628: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-8628: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-8628: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-8628: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-8628: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-8628: Goal:
-8628: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-8628: Order:
-8628: lpo
-8628: Leaf order:
-8628: b 3 0 3 1,2,2
-8628: c 3 0 3 2,2,2,2
-8628: a 6 0 6 1,2
-8628: join 17 2 4 0,2,2
-8628: meet 20 2 6 0,2
-8626: Facts:
-8626: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-8626: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-8626: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-8626: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-8626: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-8626: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-8626: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-8626: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-8626: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-8626: Goal:
-8626: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-8626: Order:
-8626: nrkbo
-8626: Leaf order:
-8626: b 3 0 3 1,2,2
-8626: c 3 0 3 2,2,2,2
-8626: a 6 0 6 1,2
-8626: join 17 2 4 0,2,2
-8626: meet 20 2 6 0,2
-% SZS status Timeout for LAT164-1.p
-NO CLASH, using fixed ground order
-10913: Facts:
-10913: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-10913: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-10913: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-10913: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-10913: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-10913: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-10913: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-10913: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-10913: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-10913: Goal:
-10913: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-10913: Order:
-10913: nrkbo
-10913: Leaf order:
-10913: c 2 0 2 2,2,2
-10913: a 4 0 4 1,2
-10913: b 4 0 4 1,2,2
-10913: meet 17 2 4 0,2
-10913: join 19 2 4 0,2,2
-NO CLASH, using fixed ground order
-10920: Facts:
-10920: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-10920: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-10920: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-10920: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-10920: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-10920: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-10920: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-10920: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-10920: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-10920: Goal:
-10920: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-10920: Order:
-10920: kbo
-10920: Leaf order:
-10920: c 2 0 2 2,2,2
-10920: a 4 0 4 1,2
-10920: b 4 0 4 1,2,2
-10920: meet 17 2 4 0,2
-10920: join 19 2 4 0,2,2
-NO CLASH, using fixed ground order
-10926: Facts:
-10926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-10926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-10926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-10926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-10926: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-10926: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-10926: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-10926: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-10926: Id : 10, {_}:
- meet (join ?26 ?27) (join ?26 ?28)
- =<=
- join ?26
- (meet (join ?27 (meet ?26 (join ?27 ?28)))
- (join ?28 (meet ?26 ?27)))
- [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
-10926: Goal:
-10926: Id : 1, {_}:
- meet a (join b c)
- =<=
- meet a (join b (meet (join a b) (join c (meet a b))))
- [] by prove_H58
-10926: Order:
-10926: lpo
-10926: Leaf order:
-10926: c 2 0 2 2,2,2
-10926: a 4 0 4 1,2
-10926: b 4 0 4 1,2,2
-10926: meet 17 2 4 0,2
-10926: join 19 2 4 0,2,2
-% SZS status Timeout for LAT169-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-11323: Facts:
-11323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11323: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11323: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11323: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11323: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11323: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-11323: Goal:
-11323: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-11323: Order:
-11323: kbo
-11323: Leaf order:
-11323: b 3 0 3 1,2,2
-11323: c 3 0 3 2,2,2,2
-11323: a 6 0 6 1,2
-11323: join 18 2 4 0,2,2
-11323: meet 19 2 6 0,2
-NO CLASH, using fixed ground order
-11324: Facts:
-11324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11324: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11324: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11324: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11324: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11324: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-11324: Goal:
-11324: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-11324: Order:
-11324: lpo
-11324: Leaf order:
-11324: b 3 0 3 1,2,2
-11324: c 3 0 3 2,2,2,2
-11324: a 6 0 6 1,2
-11324: join 18 2 4 0,2,2
-11324: meet 19 2 6 0,2
-11322: Facts:
-11322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11322: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11322: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11322: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11322: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11322: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-11322: Goal:
-11322: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-11322: Order:
-11322: nrkbo
-11322: Leaf order:
-11322: b 3 0 3 1,2,2
-11322: c 3 0 3 2,2,2,2
-11322: a 6 0 6 1,2
-11322: join 18 2 4 0,2,2
-11322: meet 19 2 6 0,2
-% SZS status Timeout for LAT174-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-11474: Facts:
-11474: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11474: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11474: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11474: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11474: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11474: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11474: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11474: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11474: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11474: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11474: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11474: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11474: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11474: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11474: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11474: Goal:
-11474: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-11474: Order:
-11474: kbo
-11474: Leaf order:
-11474: cz 2 0 2 1,2
-11474: cy 2 0 2 1,2,2,2
-11474: cx 4 0 4 1,2,2
-11474: additive_identity 8 0 0
-11474: additive_inverse 6 1 0
-11474: commutator 1 2 0
-11474: add 16 2 0
-11474: multiply 28 2 6 0,2
-11474: associator 1 3 0
-NO CLASH, using fixed ground order
-11475: Facts:
-11475: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11475: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11475: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11475: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11475: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11475: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11475: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11475: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11475: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11475: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11475: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11475: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11475: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11475: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11475: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11475: Goal:
-11475: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-11475: Order:
-11475: lpo
-11475: Leaf order:
-11475: cz 2 0 2 1,2
-11475: cy 2 0 2 1,2,2,2
-11475: cx 4 0 4 1,2,2
-11475: additive_identity 8 0 0
-11475: additive_inverse 6 1 0
-11475: commutator 1 2 0
-11475: add 16 2 0
-11475: multiply 28 2 6 0,2
-11475: associator 1 3 0
-11473: Facts:
-11473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-11473: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-11473: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-11473: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-11473: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-11473: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-11473: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-11473: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-11473: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-11473: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-11473: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-11473: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-11473: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-11473: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-11473: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-11473: Goal:
-11473: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-11473: Order:
-11473: nrkbo
-11473: Leaf order:
-11473: cz 2 0 2 1,2
-11473: cy 2 0 2 1,2,2,2
-11473: cx 4 0 4 1,2,2
-11473: additive_identity 8 0 0
-11473: additive_inverse 6 1 0
-11473: commutator 1 2 0
-11473: add 16 2 0
-11473: multiply 28 2 6 0,2
-11473: associator 1 3 0
-% SZS status Timeout for RNG027-5.p
-NO CLASH, using fixed ground order
-12546: Facts:
-12546: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-12546: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-12546: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-12546: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-12546: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-12546: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-12546: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-12546: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-12546: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-12546: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-12546: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-12546: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-12546: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-12546: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-NO CLASH, using fixed ground order
-12546: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-12546: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-12546: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-12546: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-12546: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-12546: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-12547: Facts:
-12546: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-12546: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-12546: Goal:
-12546: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-12546: Order:
-12546: nrkbo
-12546: Leaf order:
-12546: cz 2 0 2 1,2
-12546: cy 2 0 2 1,2,2,2
-12546: cx 4 0 4 1,2,2
-12546: additive_identity 8 0 0
-12546: additive_inverse 22 1 0
-12546: commutator 1 2 0
-12546: add 24 2 0
-12546: multiply 46 2 6 0,2
-12547: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-12547: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-12547: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-12547: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-12547: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-12547: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-12547: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-12546: associator 1 3 0
-12547: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-12547: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-12547: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-12547: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-12547: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-12547: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-12547: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-12547: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-12547: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-12547: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-12547: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-12547: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-12547: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-12547: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-12547: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-12547: Goal:
-12547: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-12547: Order:
-12547: kbo
-12547: Leaf order:
-12547: cz 2 0 2 1,2
-12547: cy 2 0 2 1,2,2,2
-12547: cx 4 0 4 1,2,2
-12547: additive_identity 8 0 0
-12547: additive_inverse 22 1 0
-12547: commutator 1 2 0
-12547: add 24 2 0
-12547: multiply 46 2 6 0,2
-12547: associator 1 3 0
-NO CLASH, using fixed ground order
-12548: Facts:
-12548: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-12548: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-12548: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-12548: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-12548: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-12548: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-12548: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-12548: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-12548: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-12548: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-12548: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-12548: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-12548: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-12548: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-12548: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-12548: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-12548: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-12548: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-12548: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-12548: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-12548: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-12548: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-12548: Goal:
-12548: Id : 1, {_}:
- multiply cz (multiply cx (multiply cy cx))
- =<=
- multiply (multiply (multiply cz cx) cy) cx
- [] by prove_right_moufang
-12548: Order:
-12548: lpo
-12548: Leaf order:
-12548: cz 2 0 2 1,2
-12548: cy 2 0 2 1,2,2,2
-12548: cx 4 0 4 1,2,2
-12548: additive_identity 8 0 0
-12548: additive_inverse 22 1 0
-12548: commutator 1 2 0
-12548: add 24 2 0
-12548: multiply 46 2 6 0,2
-12548: associator 1 3 0
-% SZS status Timeout for RNG027-7.p
-NO CLASH, using fixed ground order
-14022: Facts:
-14022: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-14022: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-14022: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-14022: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-14022: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-14022: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-14022: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-14022: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-NO CLASH, using fixed ground order
-14022: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-14022: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-14022: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-14022: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-14022: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-14022: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-14022: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-14022: Goal:
-14022: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-14022: Order:
-14022: nrkbo
-14022: Leaf order:
-14022: y 2 0 2 2,2,2
-14022: z 2 0 2 3,2
-14022: x 4 0 4 1,2
-14022: additive_identity 8 0 0
-14022: additive_inverse 6 1 0
-14022: commutator 1 2 0
-14022: add 16 2 0
-14022: multiply 24 2 2 0,2,2
-14022: associator 3 3 2 0,2
-14023: Facts:
-14023: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-14023: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-14023: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-14023: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-14023: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-14023: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-14023: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-14023: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-14023: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-14023: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-14023: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-14023: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-14023: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-14023: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-14023: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-14023: Goal:
-14023: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-14023: Order:
-14023: kbo
-14023: Leaf order:
-14023: y 2 0 2 2,2,2
-14023: z 2 0 2 3,2
-14023: x 4 0 4 1,2
-14023: additive_identity 8 0 0
-14023: additive_inverse 6 1 0
-14023: commutator 1 2 0
-14023: add 16 2 0
-14023: multiply 24 2 2 0,2,2
-14023: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-14025: Facts:
-14025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-14025: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-14025: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-14025: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-14025: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-14025: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-14025: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-14025: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-14025: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-14025: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-14025: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-14025: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-14025: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-14025: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-14025: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-14025: Goal:
-14025: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-14025: Order:
-14025: lpo
-14025: Leaf order:
-14025: y 2 0 2 2,2,2
-14025: z 2 0 2 3,2
-14025: x 4 0 4 1,2
-14025: additive_identity 8 0 0
-14025: additive_inverse 6 1 0
-14025: commutator 1 2 0
-14025: add 16 2 0
-14025: multiply 24 2 2 0,2,2
-14025: associator 3 3 2 0,2
-% SZS status Timeout for RNG027-8.p
-NO CLASH, using fixed ground order
-15720: Facts:
-15720: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-15720: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-15720: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-15720: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-15720: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-15720: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-15720: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-15720: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-15720: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-15720: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-15720: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-15720: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-15720: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-15720: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-15720: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-15720: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-15720: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-15720: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-15720: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-15720: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-15720: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-15720: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-15720: Goal:
-15720: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-15720: Order:
-15720: nrkbo
-15720: Leaf order:
-15720: y 2 0 2 2,2,2
-15720: z 2 0 2 3,2
-15720: x 4 0 4 1,2
-15720: additive_identity 8 0 0
-15720: additive_inverse 22 1 0
-15720: commutator 1 2 0
-15720: add 24 2 0
-15720: multiply 42 2 2 0,2,2
-15720: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-15721: Facts:
-15721: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-15721: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-15721: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-15721: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-15721: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-15721: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-15721: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-15721: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-15721: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-15721: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-15721: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-15721: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-15721: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-15721: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-15721: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-15721: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-15721: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-15721: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-15721: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-15721: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-15721: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-15721: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-15721: Goal:
-15721: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-15721: Order:
-15721: kbo
-15721: Leaf order:
-15721: y 2 0 2 2,2,2
-15721: z 2 0 2 3,2
-15721: x 4 0 4 1,2
-15721: additive_identity 8 0 0
-15721: additive_inverse 22 1 0
-15721: commutator 1 2 0
-15721: add 24 2 0
-15721: multiply 42 2 2 0,2,2
-15721: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-15722: Facts:
-15722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-15722: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-15722: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-15722: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-15722: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-15722: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-15722: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-15722: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-15722: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-15722: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-15722: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-15722: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-15722: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-15722: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-15722: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-15722: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-15722: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-15722: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-15722: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-15722: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-15722: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-15722: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-15722: Goal:
-15722: Id : 1, {_}:
- associator x (multiply x y) z =>= multiply (associator x y z) x
- [] by prove_right_moufang
-15722: Order:
-15722: lpo
-15722: Leaf order:
-15722: y 2 0 2 2,2,2
-15722: z 2 0 2 3,2
-15722: x 4 0 4 1,2
-15722: additive_identity 8 0 0
-15722: additive_inverse 22 1 0
-15722: commutator 1 2 0
-15722: add 24 2 0
-15722: multiply 42 2 2 0,2,2
-15722: associator 3 3 2 0,2
-% SZS status Timeout for RNG027-9.p
-NO CLASH, using fixed ground order
-16372: Facts:
-16372: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-16372: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-16372: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-16372: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-16372: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-16372: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-16372: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-16372: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-16372: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-16372: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-16372: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-16372: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-16372: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-16372: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-16372: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-16372: Goal:
-16372: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-16372: Order:
-16372: nrkbo
-16372: Leaf order:
-16372: cy 2 0 2 1,2,1,2
-16372: cz 2 0 2 2,2
-16372: cx 4 0 4 1,1,2
-16372: additive_identity 8 0 0
-16372: additive_inverse 6 1 0
-16372: commutator 1 2 0
-16372: add 16 2 0
-16372: multiply 28 2 6 0,2
-16372: associator 1 3 0
-NO CLASH, using fixed ground order
-16373: Facts:
-16373: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-16373: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-16373: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-16373: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-16373: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-16373: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-16373: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-16373: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-16373: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-NO CLASH, using fixed ground order
-16374: Facts:
-16374: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-16374: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-16374: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-16374: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-16374: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-16374: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-16374: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-16374: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-16374: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-16373: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-16373: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-16373: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-16373: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-16373: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-16373: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-16373: Goal:
-16373: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-16373: Order:
-16373: kbo
-16373: Leaf order:
-16373: cy 2 0 2 1,2,1,2
-16373: cz 2 0 2 2,2
-16373: cx 4 0 4 1,1,2
-16373: additive_identity 8 0 0
-16373: additive_inverse 6 1 0
-16373: commutator 1 2 0
-16373: add 16 2 0
-16373: multiply 28 2 6 0,2
-16373: associator 1 3 0
-16374: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-16374: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-16374: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-16374: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-16374: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-16374: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-16374: Goal:
-16374: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-16374: Order:
-16374: lpo
-16374: Leaf order:
-16374: cy 2 0 2 1,2,1,2
-16374: cz 2 0 2 2,2
-16374: cx 4 0 4 1,1,2
-16374: additive_identity 8 0 0
-16374: additive_inverse 6 1 0
-16374: commutator 1 2 0
-16374: add 16 2 0
-16374: multiply 28 2 6 0,2
-16374: associator 1 3 0
-% SZS status Timeout for RNG028-5.p
-NO CLASH, using fixed ground order
-18637: Facts:
-18637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-18637: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-18637: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-18637: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-18637: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-18637: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-18637: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-18637: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-18637: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-18637: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-18637: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-18637: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-18637: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-18637: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-18637: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-18637: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-18637: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-18637: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-18637: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-18637: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-18637: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-18637: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-18637: Goal:
-18637: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-18637: Order:
-18637: nrkbo
-18637: Leaf order:
-18637: cy 2 0 2 1,2,1,2
-18637: cz 2 0 2 2,2
-18637: cx 4 0 4 1,1,2
-18637: additive_identity 8 0 0
-18637: additive_inverse 22 1 0
-18637: commutator 1 2 0
-18637: add 24 2 0
-18637: multiply 46 2 6 0,2
-18637: associator 1 3 0
-NO CLASH, using fixed ground order
-18660: Facts:
-18660: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-18660: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-18660: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-18660: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-18660: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-18660: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-18660: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-18660: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-18660: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-18660: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-18660: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-18660: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-18660: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-18660: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-18660: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-18660: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-18660: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-18660: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-18660: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-18660: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-18660: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-18660: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-18660: Goal:
-18660: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-18660: Order:
-18660: kbo
-18660: Leaf order:
-18660: cy 2 0 2 1,2,1,2
-18660: cz 2 0 2 2,2
-18660: cx 4 0 4 1,1,2
-18660: additive_identity 8 0 0
-18660: additive_inverse 22 1 0
-18660: commutator 1 2 0
-18660: add 24 2 0
-18660: multiply 46 2 6 0,2
-18660: associator 1 3 0
-NO CLASH, using fixed ground order
-18670: Facts:
-18670: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-18670: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-18670: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-18670: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-18670: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-18670: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-18670: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-18670: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-18670: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-18670: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-18670: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-18670: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-18670: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-18670: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-18670: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-18670: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-18670: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-18670: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-18670: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-18670: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-18670: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-18670: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-18670: Goal:
-18670: Id : 1, {_}:
- multiply (multiply cx (multiply cy cx)) cz
- =>=
- multiply cx (multiply cy (multiply cx cz))
- [] by prove_left_moufang
-18670: Order:
-18670: lpo
-18670: Leaf order:
-18670: cy 2 0 2 1,2,1,2
-18670: cz 2 0 2 2,2
-18670: cx 4 0 4 1,1,2
-18670: additive_identity 8 0 0
-18670: additive_inverse 22 1 0
-18670: commutator 1 2 0
-18670: add 24 2 0
-18670: multiply 46 2 6 0,2
-18670: associator 1 3 0
-% SZS status Timeout for RNG028-7.p
-NO CLASH, using fixed ground order
-20636: Facts:
-20636: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20636: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20636: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20636: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20636: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20636: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20636: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20636: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20636: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20636: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20636: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20636: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20636: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20636: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20636: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20636: Goal:
-20636: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-20636: Order:
-20636: nrkbo
-20636: Leaf order:
-20636: y 2 0 2 1,2,2
-20636: z 2 0 2 3,2
-20636: x 4 0 4 1,2
-20636: additive_identity 8 0 0
-20636: additive_inverse 6 1 0
-20636: commutator 1 2 0
-20636: add 16 2 0
-20636: multiply 24 2 2 0,2,2
-20636: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-20637: Facts:
-20637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20637: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20637: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20637: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20637: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20637: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20637: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20637: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20637: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20637: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20637: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20637: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20637: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20637: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20637: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20637: Goal:
-20637: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-20637: Order:
-20637: kbo
-20637: Leaf order:
-20637: y 2 0 2 1,2,2
-20637: z 2 0 2 3,2
-20637: x 4 0 4 1,2
-20637: additive_identity 8 0 0
-20637: additive_inverse 6 1 0
-20637: commutator 1 2 0
-20637: add 16 2 0
-20637: multiply 24 2 2 0,2,2
-20637: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-20638: Facts:
-20638: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-20638: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-20638: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-20638: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-20638: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-20638: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-20638: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-20638: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-20638: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-20638: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-20638: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-20638: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-20638: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-20638: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-20638: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-20638: Goal:
-20638: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-20638: Order:
-20638: lpo
-20638: Leaf order:
-20638: y 2 0 2 1,2,2
-20638: z 2 0 2 3,2
-20638: x 4 0 4 1,2
-20638: additive_identity 8 0 0
-20638: additive_inverse 6 1 0
-20638: commutator 1 2 0
-20638: add 16 2 0
-20638: multiply 24 2 2 0,2,2
-20638: associator 3 3 2 0,2
-% SZS status Timeout for RNG028-8.p
-NO CLASH, using fixed ground order
-22095: Facts:
-22095: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22095: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22095: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22095: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22095: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22095: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22095: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22095: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22095: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22095: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22095: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22095: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22095: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22095: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22095: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22095: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22095: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22095: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22095: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22095: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22095: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22095: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22095: Goal:
-22095: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-22095: Order:
-22095: nrkbo
-22095: Leaf order:
-22095: y 2 0 2 1,2,2
-22095: z 2 0 2 3,2
-22095: x 4 0 4 1,2
-22095: additive_identity 8 0 0
-22095: additive_inverse 22 1 0
-22095: commutator 1 2 0
-22095: add 24 2 0
-22095: multiply 42 2 2 0,2,2
-22095: associator 3 3 2 0,2
-NO CLASH, using fixed ground order
-22098: Facts:
-NO CLASH, using fixed ground order
-22098: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22098: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22098: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22098: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22098: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22098: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22098: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22098: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22098: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22098: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22098: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22098: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22098: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22098: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22098: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22098: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22098: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22098: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22098: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22098: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22098: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22098: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22098: Goal:
-22098: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-22098: Order:
-22098: kbo
-22098: Leaf order:
-22098: y 2 0 2 1,2,2
-22098: z 2 0 2 3,2
-22098: x 4 0 4 1,2
-22098: additive_identity 8 0 0
-22098: additive_inverse 22 1 0
-22098: commutator 1 2 0
-22098: add 24 2 0
-22098: multiply 42 2 2 0,2,2
-22098: associator 3 3 2 0,2
-22100: Facts:
-22100: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-22100: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-22100: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-22100: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-22100: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-22100: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-22100: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-22100: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-22100: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-22100: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-22100: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-22100: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-22100: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-22100: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-22100: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-22100: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-22100: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-22100: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-22100: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-22100: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-22100: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-22100: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-22100: Goal:
-22100: Id : 1, {_}:
- associator x (multiply y x) z =>= multiply x (associator x y z)
- [] by prove_left_moufang
-22100: Order:
-22100: lpo
-22100: Leaf order:
-22100: y 2 0 2 1,2,2
-22100: z 2 0 2 3,2
-22100: x 4 0 4 1,2
-22100: additive_identity 8 0 0
-22100: additive_inverse 22 1 0
-22100: commutator 1 2 0
-22100: add 24 2 0
-22100: multiply 42 2 2 0,2,2
-22100: associator 3 3 2 0,2
-% SZS status Timeout for RNG028-9.p
-NO CLASH, using fixed ground order
-23750: Facts:
-23750: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23750: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23750: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-23750: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-23750: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-23750: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-23750: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-23750: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-23750: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-23750: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-23750: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-23750: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-23750: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-23750: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-23750: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-23750: Goal:
-23750: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-23750: Order:
-23750: nrkbo
-23750: Leaf order:
-23750: cz 2 0 2 1,2,2
-23750: cy 2 0 2 2,1,2
-23750: cx 4 0 4 1,1,2
-23750: additive_identity 8 0 0
-23750: additive_inverse 6 1 0
-23750: commutator 1 2 0
-23750: add 16 2 0
-23750: multiply 28 2 6 0,2
-23750: associator 1 3 0
-NO CLASH, using fixed ground order
-23751: Facts:
-23751: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23751: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23751: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-23751: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-23751: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-23751: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-23751: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-23751: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-23751: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-23751: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-23751: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-23751: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-23751: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-23751: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-23751: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-23751: Goal:
-23751: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-23751: Order:
-23751: kbo
-23751: Leaf order:
-23751: cz 2 0 2 1,2,2
-23751: cy 2 0 2 2,1,2
-23751: cx 4 0 4 1,1,2
-23751: additive_identity 8 0 0
-23751: additive_inverse 6 1 0
-23751: commutator 1 2 0
-23751: add 16 2 0
-23751: multiply 28 2 6 0,2
-23751: associator 1 3 0
-NO CLASH, using fixed ground order
-23752: Facts:
-23752: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23752: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23752: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-23752: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-23752: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-23752: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-23752: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-23752: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-23752: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-23752: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-23752: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-23752: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-23752: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-23752: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-23752: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-23752: Goal:
-23752: Id : 1, {_}:
- multiply (multiply cx cy) (multiply cz cx)
- =>=
- multiply cx (multiply (multiply cy cz) cx)
- [] by prove_middle_law
-23752: Order:
-23752: lpo
-23752: Leaf order:
-23752: cz 2 0 2 1,2,2
-23752: cy 2 0 2 2,1,2
-23752: cx 4 0 4 1,1,2
-23752: additive_identity 8 0 0
-23752: additive_inverse 6 1 0
-23752: commutator 1 2 0
-23752: add 16 2 0
-23752: multiply 28 2 6 0,2
-23752: associator 1 3 0
-% SZS status Timeout for RNG029-5.p
-NO CLASH, using fixed ground order
-24862: Facts:
-24862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24862: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24862: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24862: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24862: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24862: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24862: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24862: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24862: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24862: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24862: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24862: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24862: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24862: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24862: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24862: Goal:
-24862: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-24862: Order:
-24862: nrkbo
-24862: Leaf order:
-24862: z 2 0 2 1,2,2
-24862: y 2 0 2 2,1,2
-24862: x 4 0 4 1,1,2
-24862: additive_identity 8 0 0
-24862: additive_inverse 6 1 0
-24862: commutator 1 2 0
-24862: add 16 2 0
-24862: multiply 28 2 6 0,2
-24862: associator 1 3 0
-NO CLASH, using fixed ground order
-24863: Facts:
-24863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24863: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24863: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24863: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24863: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24863: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24863: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24863: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24863: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24863: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24863: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24863: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24863: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24863: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24863: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24863: Goal:
-24863: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-24863: Order:
-24863: kbo
-24863: Leaf order:
-24863: z 2 0 2 1,2,2
-24863: y 2 0 2 2,1,2
-24863: x 4 0 4 1,1,2
-24863: additive_identity 8 0 0
-24863: additive_inverse 6 1 0
-24863: commutator 1 2 0
-24863: add 16 2 0
-24863: multiply 28 2 6 0,2
-24863: associator 1 3 0
-NO CLASH, using fixed ground order
-24864: Facts:
-24864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-24864: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-24864: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-24864: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-24864: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-24864: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-24864: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-24864: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-24864: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-24864: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-24864: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-24864: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-24864: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-24864: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-24864: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-24864: Goal:
-24864: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-24864: Order:
-24864: lpo
-24864: Leaf order:
-24864: z 2 0 2 1,2,2
-24864: y 2 0 2 2,1,2
-24864: x 4 0 4 1,1,2
-24864: additive_identity 8 0 0
-24864: additive_inverse 6 1 0
-24864: commutator 1 2 0
-24864: add 16 2 0
-24864: multiply 28 2 6 0,2
-24864: associator 1 3 0
-% SZS status Timeout for RNG029-6.p
-NO CLASH, using fixed ground order
-26436: Facts:
-26436: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26436: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26436: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26436: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26436: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26436: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26436: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26436: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26436: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26436: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26436: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26436: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26436: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26436: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26436: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26436: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26436: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26436: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26436: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26436: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26436: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26436: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26436: Goal:
-26436: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-26436: Order:
-26436: nrkbo
-26436: Leaf order:
-26436: z 2 0 2 1,2,2
-26436: y 2 0 2 2,1,2
-26436: x 4 0 4 1,1,2
-26436: additive_identity 8 0 0
-26436: additive_inverse 22 1 0
-26436: commutator 1 2 0
-26436: add 24 2 0
-26436: multiply 46 2 6 0,2
-26436: associator 1 3 0
-NO CLASH, using fixed ground order
-26437: Facts:
-26437: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26437: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26437: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26437: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26437: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26437: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-NO CLASH, using fixed ground order
-26438: Facts:
-26438: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26438: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26438: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26438: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26438: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26438: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26438: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26438: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26438: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26438: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26438: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26438: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26438: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26438: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26438: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26438: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26438: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26438: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26438: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26438: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26438: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26438: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26438: Goal:
-26438: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-26438: Order:
-26438: lpo
-26438: Leaf order:
-26438: z 2 0 2 1,2,2
-26438: y 2 0 2 2,1,2
-26438: x 4 0 4 1,1,2
-26438: additive_identity 8 0 0
-26438: additive_inverse 22 1 0
-26438: commutator 1 2 0
-26438: add 24 2 0
-26438: multiply 46 2 6 0,2
-26438: associator 1 3 0
-26437: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26437: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26437: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26437: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26437: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26437: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26437: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26437: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26437: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26437: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26437: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26437: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26437: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26437: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26437: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26437: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26437: Goal:
-26437: Id : 1, {_}:
- multiply (multiply x y) (multiply z x)
- =<=
- multiply (multiply x (multiply y z)) x
- [] by prove_middle_moufang
-26437: Order:
-26437: kbo
-26437: Leaf order:
-26437: z 2 0 2 1,2,2
-26437: y 2 0 2 2,1,2
-26437: x 4 0 4 1,1,2
-26437: additive_identity 8 0 0
-26437: additive_inverse 22 1 0
-26437: commutator 1 2 0
-26437: add 24 2 0
-26437: multiply 46 2 6 0,2
-26437: associator 1 3 0
-% SZS status Timeout for RNG029-7.p
-NO CLASH, using fixed ground order
-28162: Facts:
-28162: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-28162: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-28162: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-28162: Id : 5, {_}: add c d =>= d [] by absorbtion
-28162: Goal:
-28162: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-28162: Order:
-28162: nrkbo
-28162: Leaf order:
-28162: c 1 0 0
-28162: d 2 0 0
-28162: a 2 0 2 1,1,1,2
-28162: b 3 0 3 1,2,1,1,2
-28162: negate 9 1 5 0,1,2
-28162: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-28167: Facts:
-28167: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-28167: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-28167: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-28167: Id : 5, {_}: add c d =>= d [] by absorbtion
-28167: Goal:
-28167: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-28167: Order:
-28167: kbo
-28167: Leaf order:
-28167: c 1 0 0
-28167: d 2 0 0
-28167: a 2 0 2 1,1,1,2
-28167: b 3 0 3 1,2,1,1,2
-28167: negate 9 1 5 0,1,2
-28167: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-28168: Facts:
-28168: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-28168: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-28168: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-28168: Id : 5, {_}: add c d =>= d [] by absorbtion
-28168: Goal:
-28168: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-28168: Order:
-28168: lpo
-28168: Leaf order:
-28168: c 1 0 0
-28168: d 2 0 0
-28168: a 2 0 2 1,1,1,2
-28168: b 3 0 3 1,2,1,1,2
-28168: negate 9 1 5 0,1,2
-28168: add 13 2 3 0,2
-% SZS status Timeout for ROB006-1.p
-NO CLASH, using fixed ground order
-30020: Facts:
-30020: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30020: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30020: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30020: Id : 5, {_}: add c d =>= d [] by absorbtion
-30020: Goal:
-30020: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30020: Order:
-30020: nrkbo
-30020: Leaf order:
-30020: c 1 0 0
-30020: d 2 0 0
-30020: negate 4 1 0
-30020: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-30021: Facts:
-30021: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30021: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30021: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30021: Id : 5, {_}: add c d =>= d [] by absorbtion
-30021: Goal:
-30021: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30021: Order:
-30021: kbo
-30021: Leaf order:
-30021: c 1 0 0
-30021: d 2 0 0
-30021: negate 4 1 0
-30021: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-30022: Facts:
-30022: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-30022: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-30022: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-30022: Id : 5, {_}: add c d =>= d [] by absorbtion
-30022: Goal:
-30022: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-30022: Order:
-30022: lpo
-30022: Leaf order:
-30022: c 1 0 0
-30022: d 2 0 0
-30022: negate 4 1 0
-30022: add 11 2 1 0,2
-% SZS status Timeout for ROB006-2.p
-NO CLASH, using fixed ground order
-31074: Facts:
-31074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-31074: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-31074: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-31074: Id : 5, {_}: add c d =>= c [] by identity_constant
-31074: Goal:
-31074: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-31074: Order:
-31074: nrkbo
-31074: Leaf order:
-31074: d 1 0 0
-31074: c 2 0 0
-31074: a 2 0 2 1,1,1,2
-31074: b 3 0 3 1,2,1,1,2
-31074: negate 9 1 5 0,1,2
-31074: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-31075: Facts:
-31075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-31075: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-31075: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-31075: Id : 5, {_}: add c d =>= c [] by identity_constant
-31075: Goal:
-31075: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-31075: Order:
-31075: kbo
-31075: Leaf order:
-31075: d 1 0 0
-31075: c 2 0 0
-31075: a 2 0 2 1,1,1,2
-31075: b 3 0 3 1,2,1,1,2
-31075: negate 9 1 5 0,1,2
-31075: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-31076: Facts:
-31076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-31076: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-31076: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-31076: Id : 5, {_}: add c d =>= c [] by identity_constant
-31076: Goal:
-31076: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-31076: Order:
-31076: lpo
-31076: Leaf order:
-31076: d 1 0 0
-31076: c 2 0 0
-31076: a 2 0 2 1,1,1,2
-31076: b 3 0 3 1,2,1,1,2
-31076: negate 9 1 5 0,1,2
-31076: add 13 2 3 0,2
-% SZS status Timeout for ROB026-1.p
-NO CLASH, using fixed ground order
-32629: Facts:
-32629: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-32629: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-32629: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-32629: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-32629: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-32629: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-32629: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-32629: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-32629: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-32629: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-32629: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-32629: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-32629: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-32629: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-32629: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-32629: Goal:
-32629: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =<=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-32629: Order:
-32629: nrkbo
-32629: Leaf order:
-32629: identity 2 0 0
-32629: b 2 0 2 1,2,2
-32629: c 2 0 2 2,2,2
-32629: a 3 0 3 1,2
-32629: inverse 1 1 0
-32629: greatest_lower_bound 15 2 2 0,2,2
-32629: least_upper_bound 16 2 3 0,2
-32629: multiply 18 2 0
-NO CLASH, using fixed ground order
-32630: Facts:
-32630: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-32630: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-32630: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-32630: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-32630: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-32630: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-32630: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-32630: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-32630: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-32630: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-32630: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-32630: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-32630: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-32630: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-32630: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-32630: Goal:
-32630: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =<=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-32630: Order:
-32630: kbo
-32630: Leaf order:
-32630: identity 2 0 0
-32630: b 2 0 2 1,2,2
-32630: c 2 0 2 2,2,2
-32630: a 3 0 3 1,2
-32630: inverse 1 1 0
-32630: greatest_lower_bound 15 2 2 0,2,2
-32630: least_upper_bound 16 2 3 0,2
-32630: multiply 18 2 0
-NO CLASH, using fixed ground order
-32631: Facts:
-32631: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-32631: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-32631: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-32631: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-32631: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-32631: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-32631: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-32631: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-32631: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-32631: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-32631: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-32631: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-32631: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-32631: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-32631: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-32631: Goal:
-32631: Id : 1, {_}:
- least_upper_bound a (greatest_lower_bound b c)
- =>=
- greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
- [] by prove_distrnu
-32631: Order:
-32631: lpo
-32631: Leaf order:
-32631: identity 2 0 0
-32631: b 2 0 2 1,2,2
-32631: c 2 0 2 2,2,2
-32631: a 3 0 3 1,2
-32631: inverse 1 1 0
-32631: greatest_lower_bound 15 2 2 0,2,2
-32631: least_upper_bound 16 2 3 0,2
-32631: multiply 18 2 0
-% SZS status Timeout for GRP164-1.p
-NO CLASH, using fixed ground order
-2296: Facts:
-2296: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-2296: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-2296: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-2296: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-2296: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-2296: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-2296: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-2296: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-2296: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-2296: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-2296: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-2296: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-2296: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-2296: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-2296: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-2296: Goal:
-2296: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-2296: Order:
-2296: nrkbo
-2296: Leaf order:
-2296: identity 2 0 0
-2296: b 2 0 2 1,2,2
-2296: c 2 0 2 2,2,2
-2296: a 3 0 3 1,2
-2296: inverse 1 1 0
-2296: least_upper_bound 15 2 2 0,2,2
-2296: greatest_lower_bound 16 2 3 0,2
-2296: multiply 18 2 0
-NO CLASH, using fixed ground order
-2305: Facts:
-2305: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-2305: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-2305: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-2305: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-2305: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-2305: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-2305: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-2305: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-2305: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-2305: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-2305: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-2305: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-2305: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-2305: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-2305: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-2305: Goal:
-2305: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =<=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-2305: Order:
-2305: kbo
-2305: Leaf order:
-2305: identity 2 0 0
-2305: b 2 0 2 1,2,2
-2305: c 2 0 2 2,2,2
-2305: a 3 0 3 1,2
-2305: inverse 1 1 0
-2305: least_upper_bound 15 2 2 0,2,2
-2305: greatest_lower_bound 16 2 3 0,2
-2305: multiply 18 2 0
-NO CLASH, using fixed ground order
-2309: Facts:
-2309: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-2309: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-2309: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-2309: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-2309: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-2309: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-2309: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-2309: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-2309: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-2309: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-2309: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-2309: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-2309: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-2309: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-2309: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-2309: Goal:
-2309: Id : 1, {_}:
- greatest_lower_bound a (least_upper_bound b c)
- =>=
- least_upper_bound (greatest_lower_bound a b)
- (greatest_lower_bound a c)
- [] by prove_distrun
-2309: Order:
-2309: lpo
-2309: Leaf order:
-2309: identity 2 0 0
-2309: b 2 0 2 1,2,2
-2309: c 2 0 2 2,2,2
-2309: a 3 0 3 1,2
-2309: inverse 1 1 0
-2309: least_upper_bound 15 2 2 0,2,2
-2309: greatest_lower_bound 16 2 3 0,2
-2309: multiply 18 2 0
-% SZS status Timeout for GRP164-2.p
-NO CLASH, using fixed ground order
-4004: Facts:
-4004: Id : 2, {_}:
- multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4)
- [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
-4004: Id : 3, {_}:
- multiply ?6 (multiply ?7 (multiply ?7 ?7))
- =?=
- multiply ?7 (multiply ?7 (multiply ?7 ?6))
- [7, 6] by condition ?6 ?7
-4004: Goal:
-4004: Id : 1, {_}:
- multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a (multiply b (multiply a b))))))))))))))))
- =>=
- multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b (multiply b (multiply b b))))))))))))))))
- [] by prove_this
-4004: Order:
-4004: nrkbo
-4004: Leaf order:
-4004: a 18 0 18 1,2
-4004: b 18 0 18 1,2,2
-4004: multiply 44 2 34 0,2
-NO CLASH, using fixed ground order
-4005: Facts:
-4005: Id : 2, {_}:
- multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4)
- [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
-4005: Id : 3, {_}:
- multiply ?6 (multiply ?7 (multiply ?7 ?7))
- =?=
- multiply ?7 (multiply ?7 (multiply ?7 ?6))
- [7, 6] by condition ?6 ?7
-4005: Goal:
-4005: Id : 1, {_}:
- multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a
- (multiply b
- (multiply a (multiply b (multiply a b))))))))))))))))
- =?=
- multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply a
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b
- (multiply b (multiply b (multiply b b))))))))))))))))
- [] by prove_this
-4005: Order:
-4005: kbo
-4005: Leaf order:
-4005: a 18 0 18 1,2
-4005: b 18 0 18 1,2,2
-4005: multiply 44 2 34 0,2
-NO CLASH, using fixed ground order
-% SZS status Timeout for GRP196-1.p
-NO CLASH, using fixed ground order
-7093: Facts:
-7093: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-7093: Goal:
-7093: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-7093: Order:
-7093: nrkbo
-7093: Leaf order:
-7093: a 3 0 3 1,2
-7093: c 3 0 3 2,1,2,2
-7093: b 4 0 4 1,1,2,2
-7093: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-7104: Facts:
-7104: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-7104: Goal:
-7104: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-7104: Order:
-7104: kbo
-7104: Leaf order:
-7104: a 3 0 3 1,2
-7104: c 3 0 3 2,1,2,2
-7104: b 4 0 4 1,1,2,2
-7104: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-7109: Facts:
-7109: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
-7109: Goal:
-7109: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-7109: Order:
-7109: lpo
-7109: Leaf order:
-7109: a 3 0 3 1,2
-7109: c 3 0 3 2,1,2,2
-7109: b 4 0 4 1,1,2,2
-7109: f 18 2 8 0,2
-% SZS status Timeout for LAT070-1.p
-NO CLASH, using fixed ground order
-9646: Facts:
-9646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-9646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-9646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-9646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-9646: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-9646: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-9646: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-9646: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-9646: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-9646: Goal:
-9646: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-9646: Order:
-9646: nrkbo
-9646: Leaf order:
-9646: b 3 0 3 1,2,2
-9646: c 3 0 3 2,2,2,2
-9646: a 6 0 6 1,2
-9646: join 17 2 4 0,2,2
-9646: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-9648: Facts:
-9648: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-9648: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-9648: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-9648: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-9648: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-9648: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-9648: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-9648: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-9648: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-9648: Goal:
-9648: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-9648: Order:
-9648: kbo
-9648: Leaf order:
-9648: b 3 0 3 1,2,2
-9648: c 3 0 3 2,2,2,2
-9648: a 6 0 6 1,2
-9648: join 17 2 4 0,2,2
-9648: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-9649: Facts:
-9649: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-9649: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-9649: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-9649: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-9649: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-9649: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-9649: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-9649: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-9649: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
- [28, 27, 26] by equation_H7 ?26 ?27 ?28
-9649: Goal:
-9649: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-9649: Order:
-9649: lpo
-9649: Leaf order:
-9649: b 3 0 3 1,2,2
-9649: c 3 0 3 2,2,2,2
-9649: a 6 0 6 1,2
-9649: join 17 2 4 0,2,2
-9649: meet 21 2 6 0,2
-% SZS status Timeout for LAT138-1.p
-NO CLASH, using fixed ground order
-11119: Facts:
-11119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11119: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11119: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11119: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11119: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11119: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-11119: Goal:
-11119: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-11119: Order:
-11119: kbo
-11119: Leaf order:
-11119: a 4 0 4 1,2
-11119: b 4 0 4 1,2,2
-11119: c 4 0 4 2,2,2,2
-11119: join 17 2 4 0,2,2
-11119: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-11120: Facts:
-11120: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11120: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11120: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11120: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11120: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11120: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11120: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11120: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11120: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-11120: Goal:
-11120: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-11120: Order:
-11120: lpo
-11120: Leaf order:
-11120: a 4 0 4 1,2
-11120: b 4 0 4 1,2,2
-11120: c 4 0 4 2,2,2,2
-11120: join 17 2 4 0,2,2
-11120: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-11118: Facts:
-11118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-11118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-11118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-11118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-11118: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-11118: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-11118: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-11118: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-11118: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-11118: Goal:
-11118: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-11118: Order:
-11118: nrkbo
-11118: Leaf order:
-11118: a 4 0 4 1,2
-11118: b 4 0 4 1,2,2
-11118: c 4 0 4 2,2,2,2
-11118: join 17 2 4 0,2,2
-11118: meet 21 2 6 0,2
-% SZS status Timeout for LAT140-1.p
-NO CLASH, using fixed ground order
-12763: Facts:
-12763: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-12763: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-12763: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-12763: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-12763: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-12763: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-12763: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-12763: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-12763: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-12763: Goal:
-12763: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-12763: Order:
-12763: nrkbo
-12763: Leaf order:
-12763: b 3 0 3 1,2,2
-12763: c 3 0 3 2,2,2,2
-12763: a 6 0 6 1,2
-12763: join 16 2 4 0,2,2
-12763: meet 22 2 6 0,2
-NO CLASH, using fixed ground order
-12764: Facts:
-12764: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-12764: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-12764: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-12764: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-12764: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-12764: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-12764: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-12764: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-12764: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-12764: Goal:
-12764: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-12764: Order:
-12764: kbo
-12764: Leaf order:
-12764: b 3 0 3 1,2,2
-12764: c 3 0 3 2,2,2,2
-12764: a 6 0 6 1,2
-12764: join 16 2 4 0,2,2
-12764: meet 22 2 6 0,2
-NO CLASH, using fixed ground order
-12765: Facts:
-12765: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-12765: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-12765: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-12765: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-12765: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-12765: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-12765: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-12765: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-12765: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
- [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
-12765: Goal:
-12765: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-12765: Order:
-12765: lpo
-12765: Leaf order:
-12765: b 3 0 3 1,2,2
-12765: c 3 0 3 2,2,2,2
-12765: a 6 0 6 1,2
-12765: join 16 2 4 0,2,2
-12765: meet 22 2 6 0,2
-% SZS status Timeout for LAT145-1.p
-NO CLASH, using fixed ground order
-13612: Facts:
-13612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13612: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13612: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13612: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13612: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13612: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-13612: Goal:
-13612: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-13612: Order:
-13612: nrkbo
-13612: Leaf order:
-13612: c 2 0 2 1,2,2,2
-13612: a 3 0 3 1,2
-13612: d 3 0 3 2,2,2,2,2
-13612: b 4 0 4 1,2,2
-13612: meet 19 2 5 0,2
-13612: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-13613: Facts:
-13613: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13613: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13613: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13613: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13613: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13613: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13613: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13613: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13613: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =<=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-13613: Goal:
-13613: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-13613: Order:
-13613: kbo
-13613: Leaf order:
-13613: c 2 0 2 1,2,2,2
-13613: a 3 0 3 1,2
-13613: d 3 0 3 2,2,2,2,2
-13613: b 4 0 4 1,2,2
-13613: meet 19 2 5 0,2
-13613: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-13614: Facts:
-13614: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-13614: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-13614: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-13614: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-13614: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-13614: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-13614: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-13614: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-13614: Id : 10, {_}:
- meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
- =?=
- meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
-13614: Goal:
-13614: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (join b d)))))
- [] by prove_H43
-13614: Order:
-13614: lpo
-13614: Leaf order:
-13614: c 2 0 2 1,2,2,2
-13614: a 3 0 3 1,2
-13614: d 3 0 3 2,2,2,2,2
-13614: b 4 0 4 1,2,2
-13614: meet 19 2 5 0,2
-13614: join 19 2 5 0,2,2
-% SZS status Timeout for LAT149-1.p
-NO CLASH, using fixed ground order
-14638: Facts:
-14638: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14638: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14638: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14638: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14638: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14638: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14638: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14638: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14638: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-14638: Goal:
-14638: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-14638: Order:
-14638: nrkbo
-14638: Leaf order:
-14638: c 2 0 2 2,2,2,2
-14638: b 4 0 4 1,2,2
-14638: a 6 0 6 1,2
-14638: join 18 2 4 0,2,2
-14638: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-14639: Facts:
-14639: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14639: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14639: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14639: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14639: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14639: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14639: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14639: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14639: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-14639: Goal:
-14639: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-14639: Order:
-NO CLASH, using fixed ground order
-14640: Facts:
-14640: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-14640: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-14640: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-14640: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-14640: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-14640: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-14640: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-14640: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-14640: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
- [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
-14640: Goal:
-14640: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
- [] by prove_H7
-14640: Order:
-14640: lpo
-14640: Leaf order:
-14640: c 2 0 2 2,2,2,2
-14640: b 4 0 4 1,2,2
-14640: a 6 0 6 1,2
-14640: join 18 2 4 0,2,2
-14640: meet 20 2 6 0,2
-14639: kbo
-14639: Leaf order:
-14639: c 2 0 2 2,2,2,2
-14639: b 4 0 4 1,2,2
-14639: a 6 0 6 1,2
-14639: join 18 2 4 0,2,2
-14639: meet 20 2 6 0,2
-% SZS status Timeout for LAT153-1.p
-NO CLASH, using fixed ground order
-15430: Facts:
-15430: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15430: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15430: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15430: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15430: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15430: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15430: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15430: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15430: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-15430: Goal:
-15430: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-15430: Order:
-15430: nrkbo
-15430: Leaf order:
-15430: a 4 0 4 1,2
-15430: b 4 0 4 1,2,2
-15430: c 4 0 4 2,2,2,2
-15430: join 18 2 4 0,2,2
-15430: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-15431: Facts:
-15431: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15431: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15431: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15431: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15431: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15431: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15431: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15431: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15431: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-15431: Goal:
-15431: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-15431: Order:
-15431: kbo
-15431: Leaf order:
-15431: a 4 0 4 1,2
-15431: b 4 0 4 1,2,2
-15431: c 4 0 4 2,2,2,2
-15431: join 18 2 4 0,2,2
-15431: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-15432: Facts:
-15432: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-15432: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-15432: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-15432: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-15432: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-15432: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-15432: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-15432: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-15432: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-15432: Goal:
-15432: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
- [] by prove_H2
-15432: Order:
-15432: lpo
-15432: Leaf order:
-15432: a 4 0 4 1,2
-15432: b 4 0 4 1,2,2
-15432: c 4 0 4 2,2,2,2
-15432: join 18 2 4 0,2,2
-15432: meet 20 2 6 0,2
-% SZS status Timeout for LAT157-1.p
-NO CLASH, using fixed ground order
-16370: Facts:
-16370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-16370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-16370: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-16370: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-16370: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-16370: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-16370: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-16370: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-16370: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-16370: Goal:
-16370: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-16370: Order:
-16370: nrkbo
-16370: Leaf order:
-16370: d 2 0 2 2,2,2,2,2
-16370: b 3 0 3 1,2,2
-16370: c 3 0 3 1,2,2,2
-16370: a 4 0 4 1,2
-16370: meet 19 2 5 0,2
-16370: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-16387: Facts:
-16387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-16387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-16387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-16387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-16387: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-16387: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-16387: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-16387: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-16387: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-16387: Goal:
-16387: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-16387: Order:
-16387: kbo
-16387: Leaf order:
-16387: d 2 0 2 2,2,2,2,2
-16387: b 3 0 3 1,2,2
-16387: c 3 0 3 1,2,2,2
-16387: a 4 0 4 1,2
-16387: meet 19 2 5 0,2
-16387: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-16398: Facts:
-16398: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-16398: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-16398: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-16398: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-16398: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-16398: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-16398: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-16398: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-16398: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
- [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
-16398: Goal:
-16398: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (join (meet a c) (meet c (join b d))))
- [] by prove_H49
-16398: Order:
-16398: lpo
-16398: Leaf order:
-16398: d 2 0 2 2,2,2,2,2
-16398: b 3 0 3 1,2,2
-16398: c 3 0 3 1,2,2,2
-16398: a 4 0 4 1,2
-16398: meet 19 2 5 0,2
-16398: join 19 2 5 0,2,2
-% SZS status Timeout for LAT158-1.p
-NO CLASH, using fixed ground order
-17619: Facts:
-17619: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17619: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17619: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17619: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17619: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17619: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17619: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17619: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17619: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17619: Goal:
-17619: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-17619: Order:
-17619: nrkbo
-17619: Leaf order:
-17619: c 2 0 2 1,2,2,2,2
-17619: b 3 0 3 1,2,2
-17619: d 3 0 3 2,2,2,2,2
-17619: a 4 0 4 1,2
-17619: join 16 2 3 0,2,2
-17619: meet 21 2 7 0,2
-NO CLASH, using fixed ground order
-17620: Facts:
-17620: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17620: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17620: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17620: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17620: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17620: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17620: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17620: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17620: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17620: Goal:
-NO CLASH, using fixed ground order
-17620: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-17620: Order:
-17620: kbo
-17620: Leaf order:
-17620: c 2 0 2 1,2,2,2,2
-17620: b 3 0 3 1,2,2
-17620: d 3 0 3 2,2,2,2,2
-17620: a 4 0 4 1,2
-17620: join 16 2 3 0,2,2
-17620: meet 21 2 7 0,2
-17622: Facts:
-17622: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17622: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17622: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17622: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17622: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17622: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17622: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17622: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17622: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17622: Goal:
-17622: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-17622: Order:
-17622: lpo
-17622: Leaf order:
-17622: c 2 0 2 1,2,2,2,2
-17622: b 3 0 3 1,2,2
-17622: d 3 0 3 2,2,2,2,2
-17622: a 4 0 4 1,2
-17622: join 16 2 3 0,2,2
-17622: meet 21 2 7 0,2
-% SZS status Timeout for LAT163-1.p
-NO CLASH, using fixed ground order
-17778: Facts:
-17778: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17778: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17778: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17778: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17778: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17778: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17778: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17778: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17778: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17778: Goal:
-17778: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-17778: Order:
-17778: nrkbo
-17778: Leaf order:
-17778: d 2 0 2 2,2,2,2,2
-17778: a 3 0 3 1,2
-17778: c 3 0 3 1,2,2,2
-17778: b 4 0 4 1,2,2
-17778: join 17 2 4 0,2,2
-17778: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-17779: Facts:
-17779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17779: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17779: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17779: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17779: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17779: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17779: Goal:
-17779: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-17779: Order:
-17779: kbo
-17779: Leaf order:
-17779: d 2 0 2 2,2,2,2,2
-17779: a 3 0 3 1,2
-17779: c 3 0 3 1,2,2,2
-17779: b 4 0 4 1,2,2
-17779: join 17 2 4 0,2,2
-17779: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-17780: Facts:
-17780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-17780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-17780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-17780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-17780: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-17780: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-17780: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-17780: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-17780: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
- [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
-17780: Goal:
-17780: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-17780: Order:
-17780: lpo
-17780: Leaf order:
-17780: d 2 0 2 2,2,2,2,2
-17780: a 3 0 3 1,2
-17780: c 3 0 3 1,2,2,2
-17780: b 4 0 4 1,2,2
-17780: join 17 2 4 0,2,2
-17780: meet 20 2 6 0,2
-% SZS status Timeout for LAT165-1.p
-NO CLASH, using fixed ground order
-18025: Facts:
-18025: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18025: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18025: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18025: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18025: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18025: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18025: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18025: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18025: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-18025: Goal:
-18025: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-18025: Order:
-18025: nrkbo
-18025: Leaf order:
-18025: c 2 0 2 1,2,2,2
-18025: a 3 0 3 1,2
-18025: d 3 0 3 2,2,2,2,2
-18025: b 4 0 4 1,2,2
-18025: join 18 2 5 0,2,2
-18025: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-18026: Facts:
-18026: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18026: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18026: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18026: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18026: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18026: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18026: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18026: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18026: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-18026: Goal:
-18026: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-18026: Order:
-18026: kbo
-18026: Leaf order:
-18026: c 2 0 2 1,2,2,2
-18026: a 3 0 3 1,2
-18026: d 3 0 3 2,2,2,2,2
-18026: b 4 0 4 1,2,2
-18026: join 18 2 5 0,2,2
-18026: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-18027: Facts:
-18027: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18027: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18027: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18027: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18027: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18027: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18027: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18027: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18027: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =?=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
- [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
-18027: Goal:
-18027: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet b (join a d)))))
- [] by prove_H78
-18027: Order:
-18027: lpo
-18027: Leaf order:
-18027: c 2 0 2 1,2,2,2
-18027: a 3 0 3 1,2
-18027: d 3 0 3 2,2,2,2,2
-18027: b 4 0 4 1,2,2
-18027: join 18 2 5 0,2,2
-18027: meet 20 2 5 0,2
-% SZS status Timeout for LAT166-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-18051: Facts:
-18051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18051: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18051: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18051: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18051: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18051: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-18051: Goal:
-18051: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-18051: Order:
-18051: kbo
-18051: Leaf order:
-18051: d 2 0 2 2,2,2,2,2
-18051: a 3 0 3 1,2
-18051: c 3 0 3 1,2,2,2
-18051: b 4 0 4 1,2,2
-18051: join 18 2 4 0,2,2
-18051: meet 20 2 6 0,2
-NO CLASH, using fixed ground order
-18052: Facts:
-18052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18052: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18052: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18052: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18052: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18052: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-18052: Goal:
-18052: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-18052: Order:
-18052: lpo
-18052: Leaf order:
-18052: d 2 0 2 2,2,2,2,2
-18052: a 3 0 3 1,2
-18052: c 3 0 3 1,2,2,2
-18052: b 4 0 4 1,2,2
-18052: join 18 2 4 0,2,2
-18052: meet 20 2 6 0,2
-18050: Facts:
-18050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18050: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18050: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18050: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18050: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18050: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
- =<=
- meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
- [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
-18050: Goal:
-18050: Id : 1, {_}:
- meet a (join b (meet c (join b d)))
- =<=
- meet a (join b (meet c (join d (meet a (meet b c)))))
- [] by prove_H77
-18050: Order:
-18050: nrkbo
-18050: Leaf order:
-18050: d 2 0 2 2,2,2,2,2
-18050: a 3 0 3 1,2
-18050: c 3 0 3 1,2,2,2
-18050: b 4 0 4 1,2,2
-18050: join 18 2 4 0,2,2
-18050: meet 20 2 6 0,2
-% SZS status Timeout for LAT167-1.p
-NO CLASH, using fixed ground order
-18084: Facts:
-18084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18084: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18084: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18084: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18084: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18084: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18084: Goal:
-18084: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-18084: Order:
-18084: nrkbo
-18084: Leaf order:
-18084: c 2 0 2 1,2,2,2,2
-18084: b 3 0 3 1,2,2
-18084: d 3 0 3 2,2,2,2,2
-18084: a 4 0 4 1,2
-18084: join 17 2 3 0,2,2
-18084: meet 20 2 7 0,2
-NO CLASH, using fixed ground order
-18085: Facts:
-18085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18085: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18085: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18085: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18085: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18085: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18085: Goal:
-18085: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-18085: Order:
-18085: kbo
-18085: Leaf order:
-18085: c 2 0 2 1,2,2,2,2
-18085: b 3 0 3 1,2,2
-18085: d 3 0 3 2,2,2,2,2
-18085: a 4 0 4 1,2
-18085: join 17 2 3 0,2,2
-18085: meet 20 2 7 0,2
-NO CLASH, using fixed ground order
-18086: Facts:
-18086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18086: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18086: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18086: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18086: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18086: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18086: Goal:
-18086: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-18086: Order:
-18086: lpo
-18086: Leaf order:
-18086: c 2 0 2 1,2,2,2,2
-18086: b 3 0 3 1,2,2
-18086: d 3 0 3 2,2,2,2,2
-18086: a 4 0 4 1,2
-18086: join 17 2 3 0,2,2
-18086: meet 20 2 7 0,2
-% SZS status Timeout for LAT172-1.p
-NO CLASH, using fixed ground order
-18325: Facts:
-18325: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18325: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18325: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18325: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18325: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18325: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18325: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18325: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18325: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18325: Goal:
-18325: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-18325: Order:
-18325: nrkbo
-18325: Leaf order:
-18325: d 2 0 2 2,2,2,2,2
-18325: b 3 0 3 1,2,2
-18325: c 3 0 3 1,2,2,2
-18325: a 4 0 4 1,2
-18325: meet 18 2 5 0,2
-18325: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-18329: Facts:
-18329: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18329: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18329: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18329: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18329: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18329: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18329: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18329: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18329: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =<=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18329: Goal:
-18329: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-18329: Order:
-18329: kbo
-18329: Leaf order:
-18329: d 2 0 2 2,2,2,2,2
-18329: b 3 0 3 1,2,2
-18329: c 3 0 3 1,2,2,2
-18329: a 4 0 4 1,2
-18329: meet 18 2 5 0,2
-18329: join 19 2 5 0,2,2
-NO CLASH, using fixed ground order
-18330: Facts:
-18330: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-18330: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-18330: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-18330: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-18330: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-18330: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-18330: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-18330: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-18330: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
- =?=
- join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
- [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
-18330: Goal:
-18330: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join d (meet c (join a b)))))
- [] by prove_H40
-18330: Order:
-18330: lpo
-18330: Leaf order:
-18330: d 2 0 2 2,2,2,2,2
-18330: b 3 0 3 1,2,2
-18330: c 3 0 3 1,2,2,2
-18330: a 4 0 4 1,2
-18330: meet 18 2 5 0,2
-18330: join 19 2 5 0,2,2
-% SZS status Timeout for LAT173-1.p
-NO CLASH, using fixed ground order
-19752: Facts:
-19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19752: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19752: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19752: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-NO CLASH, using fixed ground order
-19755: Facts:
-19755: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19755: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19755: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19755: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19755: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19755: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19755: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19755: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-NO CLASH, using fixed ground order
-19757: Facts:
-19757: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-19757: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-19757: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-19757: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-19757: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-19757: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-19757: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-19757: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19757: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-19757: Goal:
-19757: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =>=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-19757: Order:
-19757: lpo
-19757: Leaf order:
-19757: c 2 0 2 1,2,2,2,2
-19757: b 3 0 3 1,2,2
-19757: d 3 0 3 2,2,2,2,2
-19757: a 4 0 4 1,2
-19757: join 18 2 3 0,2,2
-19757: meet 20 2 7 0,2
-19752: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-19752: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-19752: Goal:
-19752: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-19752: Order:
-19752: nrkbo
-19752: Leaf order:
-19752: c 2 0 2 1,2,2,2,2
-19752: b 3 0 3 1,2,2
-19752: d 3 0 3 2,2,2,2,2
-19752: a 4 0 4 1,2
-19752: join 18 2 3 0,2,2
-19752: meet 20 2 7 0,2
-19755: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-19755: Goal:
-19755: Id : 1, {_}:
- meet a (join b (meet a (meet c d)))
- =<=
- meet a (join b (meet c (join (meet a d) (meet b d))))
- [] by prove_H32
-19755: Order:
-19755: kbo
-19755: Leaf order:
-19755: c 2 0 2 1,2,2,2,2
-19755: b 3 0 3 1,2,2
-19755: d 3 0 3 2,2,2,2,2
-19755: a 4 0 4 1,2
-19755: join 18 2 3 0,2,2
-19755: meet 20 2 7 0,2
-% SZS status Timeout for LAT175-1.p
-NO CLASH, using fixed ground order
-21153: Facts:
-21153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-21153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-21153: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-21153: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-21153: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-21153: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-21153: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-21153: Goal:
-21153: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-21153: Order:
-21153: nrkbo
-21153: Leaf order:
-21153: d 2 0 2 2,2,2,2,2
-21153: b 3 0 3 1,2,2
-21153: c 3 0 3 1,2,2,2
-21153: a 4 0 4 1,2
-21153: meet 18 2 5 0,2
-21153: join 20 2 5 0,2,2
-NO CLASH, using fixed ground order
-21154: Facts:
-21154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-21154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-21154: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-21154: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-21154: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-21154: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-21154: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-21154: Goal:
-21154: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =<=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-21154: Order:
-21154: kbo
-21154: Leaf order:
-21154: d 2 0 2 2,2,2,2,2
-21154: b 3 0 3 1,2,2
-21154: c 3 0 3 1,2,2,2
-21154: a 4 0 4 1,2
-21154: meet 18 2 5 0,2
-21154: join 20 2 5 0,2,2
-NO CLASH, using fixed ground order
-21155: Facts:
-21155: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-21155: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-21155: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-21155: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-21155: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-21155: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-21155: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-21155: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-21155: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =?=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-21155: Goal:
-21155: Id : 1, {_}:
- meet a (join b (meet c (join a d)))
- =>=
- meet a (join b (meet c (join b (join d (meet a c)))))
- [] by prove_H42
-21155: Order:
-21155: lpo
-21155: Leaf order:
-21155: d 2 0 2 2,2,2,2,2
-21155: b 3 0 3 1,2,2
-21155: c 3 0 3 1,2,2,2
-21155: a 4 0 4 1,2
-21155: meet 18 2 5 0,2
-21155: join 20 2 5 0,2,2
-% SZS status Timeout for LAT176-1.p
-NO CLASH, using fixed ground order
-23137: Facts:
-23137: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23137: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23137: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-23137: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-23137: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-23137: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-23137: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-23137: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-23137: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-23137: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-23137: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-23137: Goal:
-23137: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-23137: Order:
-23137: nrkbo
-23137: Leaf order:
-23137: b 2 0 1 1,2
-23137: a 2 0 1 2,2
-23137: c 2 0 1 3
-23137: additive_identity 4 0 0
-23137: additive_inverse 2 1 0
-23137: add 14 2 0
-23137: multiply 15 2 1 0,2
-NO CLASH, using fixed ground order
-23138: Facts:
-23138: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23138: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23138: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-23138: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-23138: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-23138: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-23138: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-23138: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-23138: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-23138: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-23138: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-23138: Goal:
-23138: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-23138: Order:
-23138: kbo
-23138: Leaf order:
-23138: b 2 0 1 1,2
-23138: a 2 0 1 2,2
-23138: c 2 0 1 3
-23138: additive_identity 4 0 0
-23138: additive_inverse 2 1 0
-23138: add 14 2 0
-23138: multiply 15 2 1 0,2
-NO CLASH, using fixed ground order
-23139: Facts:
-23139: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-23139: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-23139: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-23139: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-23139: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-23139: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-23139: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-23139: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-23139: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-23139: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
- [29] by x_fourthed_is_x ?29
-23139: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-23139: Goal:
-23139: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-23139: Order:
-23139: lpo
-23139: Leaf order:
-23139: b 2 0 1 1,2
-23139: a 2 0 1 2,2
-23139: c 2 0 1 3
-23139: additive_identity 4 0 0
-23139: additive_inverse 2 1 0
-23139: add 14 2 0
-23139: multiply 15 2 1 0,2
-% SZS status Timeout for RNG035-7.p
-NO CLASH, using fixed ground order
-23161: Facts:
-NO CLASH, using fixed ground order
-23162: Facts:
-23162: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23162: Goal:
-23162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23162: Order:
-23162: kbo
-23162: Leaf order:
-23162: b 1 0 1 1,2,2
-23162: a 4 0 4 1,1,2
-23162: nand 9 2 3 0,2
-23161: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23161: Goal:
-23161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23161: Order:
-23161: nrkbo
-23161: Leaf order:
-23161: b 1 0 1 1,2,2
-23161: a 4 0 4 1,1,2
-23161: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23163: Facts:
-23163: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23163: Goal:
-23163: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23163: Order:
-23163: lpo
-23163: Leaf order:
-23163: b 1 0 1 1,2,2
-23163: a 4 0 4 1,1,2
-23163: nand 9 2 3 0,2
-% SZS status Timeout for BOO077-1.p
-NO CLASH, using fixed ground order
-23212: Facts:
-23212: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23212: Goal:
-23212: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23212: Order:
-23212: nrkbo
-23212: Leaf order:
-23212: c 2 0 2 2,2,2,2
-23212: a 3 0 3 1,2
-23212: b 3 0 3 1,2,2
-23212: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23213: Facts:
-23213: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23213: Goal:
-23213: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23213: Order:
-23213: kbo
-23213: Leaf order:
-23213: c 2 0 2 2,2,2,2
-23213: a 3 0 3 1,2
-23213: b 3 0 3 1,2,2
-23213: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23214: Facts:
-23214: Id : 2, {_}:
- nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c1 ?2 ?3 ?4
-23214: Goal:
-23214: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23214: Order:
-23214: lpo
-23214: Leaf order:
-23214: c 2 0 2 2,2,2,2
-23214: a 3 0 3 1,2
-23214: b 3 0 3 1,2,2
-23214: nand 12 2 6 0,2
-% SZS status Timeout for BOO078-1.p
-NO CLASH, using fixed ground order
-23320: Facts:
-23320: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23320: Goal:
-23320: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23320: Order:
-23320: nrkbo
-23320: Leaf order:
-23320: b 1 0 1 1,2,2
-23320: a 4 0 4 1,1,2
-23320: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23321: Facts:
-23321: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23321: Goal:
-23321: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23321: Order:
-23321: kbo
-23321: Leaf order:
-23321: b 1 0 1 1,2,2
-23321: a 4 0 4 1,1,2
-23321: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23322: Facts:
-23322: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23322: Goal:
-23322: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23322: Order:
-23322: lpo
-23322: Leaf order:
-23322: b 1 0 1 1,2,2
-23322: a 4 0 4 1,1,2
-23322: nand 9 2 3 0,2
-% SZS status Timeout for BOO079-1.p
-NO CLASH, using fixed ground order
-23351: Facts:
-23351: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23351: Goal:
-NO CLASH, using fixed ground order
-23352: Facts:
-23352: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23352: Goal:
-23352: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23352: Order:
-23352: kbo
-23352: Leaf order:
-23352: c 2 0 2 2,2,2,2
-23352: a 3 0 3 1,2
-23352: b 3 0 3 1,2,2
-23352: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23353: Facts:
-23353: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c2 ?2 ?3 ?4
-23353: Goal:
-23353: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23353: Order:
-23353: lpo
-23353: Leaf order:
-23353: c 2 0 2 2,2,2,2
-23353: a 3 0 3 1,2
-23353: b 3 0 3 1,2,2
-23353: nand 12 2 6 0,2
-23351: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23351: Order:
-23351: nrkbo
-23351: Leaf order:
-23351: c 2 0 2 2,2,2,2
-23351: a 3 0 3 1,2
-23351: b 3 0 3 1,2,2
-23351: nand 12 2 6 0,2
-% SZS status Timeout for BOO080-1.p
-NO CLASH, using fixed ground order
-23376: Facts:
-23376: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23376: Goal:
-23376: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23376: Order:
-23376: nrkbo
-23376: Leaf order:
-23376: b 1 0 1 1,2,2
-23376: a 4 0 4 1,1,2
-23376: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23377: Facts:
-23377: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23377: Goal:
-23377: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23377: Order:
-23377: kbo
-23377: Leaf order:
-23377: b 1 0 1 1,2,2
-23377: a 4 0 4 1,1,2
-23377: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23378: Facts:
-23378: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23378: Goal:
-23378: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23378: Order:
-23378: lpo
-23378: Leaf order:
-23378: b 1 0 1 1,2,2
-23378: a 4 0 4 1,1,2
-23378: nand 9 2 3 0,2
-% SZS status Timeout for BOO081-1.p
-NO CLASH, using fixed ground order
-23400: Facts:
-23400: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23400: Goal:
-23400: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23400: Order:
-23400: nrkbo
-23400: Leaf order:
-23400: c 2 0 2 2,2,2,2
-23400: a 3 0 3 1,2
-23400: b 3 0 3 1,2,2
-23400: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23401: Facts:
-23401: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23401: Goal:
-23401: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23401: Order:
-23401: kbo
-23401: Leaf order:
-23401: c 2 0 2 2,2,2,2
-23401: a 3 0 3 1,2
-23401: b 3 0 3 1,2,2
-23401: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23402: Facts:
-23402: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c3 ?2 ?3 ?4
-23402: Goal:
-23402: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23402: Order:
-23402: lpo
-23402: Leaf order:
-23402: c 2 0 2 2,2,2,2
-23402: a 3 0 3 1,2
-23402: b 3 0 3 1,2,2
-23402: nand 12 2 6 0,2
-% SZS status Timeout for BOO082-1.p
-NO CLASH, using fixed ground order
-23425: Facts:
-23425: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23425: Goal:
-23425: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23425: Order:
-23425: nrkbo
-23425: Leaf order:
-23425: b 1 0 1 1,2,2
-23425: a 4 0 4 1,1,2
-23425: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23426: Facts:
-23426: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23426: Goal:
-23426: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23426: Order:
-23426: kbo
-23426: Leaf order:
-23426: b 1 0 1 1,2,2
-23426: a 4 0 4 1,1,2
-23426: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23427: Facts:
-23427: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23427: Goal:
-23427: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23427: Order:
-23427: lpo
-23427: Leaf order:
-23427: b 1 0 1 1,2,2
-23427: a 4 0 4 1,1,2
-23427: nand 9 2 3 0,2
-% SZS status Timeout for BOO083-1.p
-NO CLASH, using fixed ground order
-23456: Facts:
-23456: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23456: Goal:
-23456: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23456: Order:
-23456: nrkbo
-23456: Leaf order:
-23456: c 2 0 2 2,2,2,2
-23456: a 3 0 3 1,2
-23456: b 3 0 3 1,2,2
-23456: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-23458: Facts:
-23458: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23458: Goal:
-23458: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23458: Order:
-23458: lpo
-23458: Leaf order:
-23458: c 2 0 2 2,2,2,2
-23458: a 3 0 3 1,2
-23458: b 3 0 3 1,2,2
-23458: nand 12 2 6 0,2
-23457: Facts:
-23457: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c4 ?2 ?3 ?4
-23457: Goal:
-23457: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23457: Order:
-23457: kbo
-23457: Leaf order:
-23457: c 2 0 2 2,2,2,2
-23457: a 3 0 3 1,2
-23457: b 3 0 3 1,2,2
-23457: nand 12 2 6 0,2
-% SZS status Timeout for BOO084-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-23485: Facts:
-23485: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23485: Goal:
-23485: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23485: Order:
-23485: kbo
-23485: Leaf order:
-23485: b 1 0 1 1,2,2
-23485: a 4 0 4 1,1,2
-23485: nand 9 2 3 0,2
-23484: Facts:
-23484: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23484: Goal:
-23484: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23484: Order:
-23484: nrkbo
-23484: Leaf order:
-23484: b 1 0 1 1,2,2
-23484: a 4 0 4 1,1,2
-23484: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23486: Facts:
-23486: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23486: Goal:
-23486: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23486: Order:
-23486: lpo
-23486: Leaf order:
-23486: b 1 0 1 1,2,2
-23486: a 4 0 4 1,1,2
-23486: nand 9 2 3 0,2
-% SZS status Timeout for BOO085-1.p
-NO CLASH, using fixed ground order
-23521: Facts:
-23521: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23521: Goal:
-23521: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23521: Order:
-23521: nrkbo
-23521: Leaf order:
-23521: c 2 0 2 2,2,2,2
-23521: a 3 0 3 1,2
-23521: b 3 0 3 1,2,2
-23521: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23522: Facts:
-23522: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23522: Goal:
-23522: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23522: Order:
-23522: kbo
-23522: Leaf order:
-23522: c 2 0 2 2,2,2,2
-23522: a 3 0 3 1,2
-23522: b 3 0 3 1,2,2
-23522: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23523: Facts:
-23523: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c5 ?2 ?3 ?4
-23523: Goal:
-23523: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23523: Order:
-23523: lpo
-23523: Leaf order:
-23523: c 2 0 2 2,2,2,2
-23523: a 3 0 3 1,2
-23523: b 3 0 3 1,2,2
-23523: nand 12 2 6 0,2
-% SZS status Timeout for BOO086-1.p
-NO CLASH, using fixed ground order
-23545: Facts:
-23545: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23545: Goal:
-23545: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23545: Order:
-23545: nrkbo
-23545: Leaf order:
-23545: b 1 0 1 1,2,2
-23545: a 4 0 4 1,1,2
-23545: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23546: Facts:
-23546: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23546: Goal:
-23546: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23546: Order:
-23546: kbo
-23546: Leaf order:
-23546: b 1 0 1 1,2,2
-23546: a 4 0 4 1,1,2
-23546: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23547: Facts:
-23547: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23547: Goal:
-23547: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23547: Order:
-23547: lpo
-23547: Leaf order:
-23547: b 1 0 1 1,2,2
-23547: a 4 0 4 1,1,2
-23547: nand 9 2 3 0,2
-% SZS status Timeout for BOO087-1.p
-NO CLASH, using fixed ground order
-23572: Facts:
-23572: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23572: Goal:
-23572: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23572: Order:
-23572: nrkbo
-23572: Leaf order:
-23572: c 2 0 2 2,2,2,2
-23572: a 3 0 3 1,2
-23572: b 3 0 3 1,2,2
-23572: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23573: Facts:
-23573: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23573: Goal:
-23573: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23573: Order:
-23573: kbo
-23573: Leaf order:
-23573: c 2 0 2 2,2,2,2
-23573: a 3 0 3 1,2
-23573: b 3 0 3 1,2,2
-23573: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23574: Facts:
-23574: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c6 ?2 ?3 ?4
-23574: Goal:
-23574: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23574: Order:
-23574: lpo
-23574: Leaf order:
-23574: c 2 0 2 2,2,2,2
-23574: a 3 0 3 1,2
-23574: b 3 0 3 1,2,2
-23574: nand 12 2 6 0,2
-% SZS status Timeout for BOO088-1.p
-NO CLASH, using fixed ground order
-23605: Facts:
-23605: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23605: Goal:
-23605: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23605: Order:
-23605: nrkbo
-23605: Leaf order:
-23605: b 1 0 1 1,2,2
-23605: a 4 0 4 1,1,2
-23605: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23606: Facts:
-23606: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23606: Goal:
-23606: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23606: Order:
-23606: kbo
-23606: Leaf order:
-23606: b 1 0 1 1,2,2
-23606: a 4 0 4 1,1,2
-23606: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23607: Facts:
-23607: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23607: Goal:
-23607: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23607: Order:
-23607: lpo
-23607: Leaf order:
-23607: b 1 0 1 1,2,2
-23607: a 4 0 4 1,1,2
-23607: nand 9 2 3 0,2
-% SZS status Timeout for BOO089-1.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-23696: Facts:
-23696: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23696: Goal:
-23696: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23696: Order:
-23696: kbo
-23696: Leaf order:
-23696: c 2 0 2 2,2,2,2
-23696: a 3 0 3 1,2
-23696: b 3 0 3 1,2,2
-23696: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23697: Facts:
-23697: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23697: Goal:
-23697: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23697: Order:
-23697: lpo
-23697: Leaf order:
-23697: c 2 0 2 2,2,2,2
-23697: a 3 0 3 1,2
-23697: b 3 0 3 1,2,2
-23697: nand 12 2 6 0,2
-23695: Facts:
-23695: Id : 2, {_}:
- nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c7 ?2 ?3 ?4
-23695: Goal:
-23695: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23695: Order:
-23695: nrkbo
-23695: Leaf order:
-23695: c 2 0 2 2,2,2,2
-23695: a 3 0 3 1,2
-23695: b 3 0 3 1,2,2
-23695: nand 12 2 6 0,2
-% SZS status Timeout for BOO090-1.p
-NO CLASH, using fixed ground order
-23723: Facts:
-23723: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23723: Goal:
-23723: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23723: Order:
-23723: nrkbo
-23723: Leaf order:
-23723: b 1 0 1 1,2,2
-23723: a 4 0 4 1,1,2
-23723: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23724: Facts:
-23724: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23724: Goal:
-23724: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23724: Order:
-23724: kbo
-23724: Leaf order:
-23724: b 1 0 1 1,2,2
-23724: a 4 0 4 1,1,2
-23724: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23725: Facts:
-23725: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23725: Goal:
-23725: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23725: Order:
-23725: lpo
-23725: Leaf order:
-23725: b 1 0 1 1,2,2
-23725: a 4 0 4 1,1,2
-23725: nand 9 2 3 0,2
-% SZS status Timeout for BOO091-1.p
-NO CLASH, using fixed ground order
-23747: Facts:
-23747: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23747: Goal:
-23747: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23747: Order:
-23747: nrkbo
-23747: Leaf order:
-23747: c 2 0 2 2,2,2,2
-23747: a 3 0 3 1,2
-23747: b 3 0 3 1,2,2
-23747: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23748: Facts:
-23748: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23748: Goal:
-23748: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23748: Order:
-23748: kbo
-23748: Leaf order:
-23748: c 2 0 2 2,2,2,2
-23748: a 3 0 3 1,2
-23748: b 3 0 3 1,2,2
-23748: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23749: Facts:
-23749: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c8 ?2 ?3 ?4
-23749: Goal:
-23749: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23749: Order:
-23749: lpo
-23749: Leaf order:
-23749: c 2 0 2 2,2,2,2
-23749: a 3 0 3 1,2
-23749: b 3 0 3 1,2,2
-23749: nand 12 2 6 0,2
-% SZS status Timeout for BOO092-1.p
-NO CLASH, using fixed ground order
-23772: Facts:
-23772: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23772: Goal:
-NO CLASH, using fixed ground order
-23773: Facts:
-23773: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23773: Goal:
-23773: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23773: Order:
-23773: kbo
-23773: Leaf order:
-23773: b 1 0 1 1,2,2
-23773: a 4 0 4 1,1,2
-23773: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23774: Facts:
-23774: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23774: Goal:
-23774: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23774: Order:
-23774: lpo
-23774: Leaf order:
-23774: b 1 0 1 1,2,2
-23774: a 4 0 4 1,1,2
-23774: nand 9 2 3 0,2
-23772: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23772: Order:
-23772: nrkbo
-23772: Leaf order:
-23772: b 1 0 1 1,2,2
-23772: a 4 0 4 1,1,2
-23772: nand 9 2 3 0,2
-% SZS status Timeout for BOO093-1.p
-NO CLASH, using fixed ground order
-23798: Facts:
-23798: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23798: Goal:
-23798: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23798: Order:
-23798: nrkbo
-23798: Leaf order:
-23798: c 2 0 2 2,2,2,2
-23798: a 3 0 3 1,2
-23798: b 3 0 3 1,2,2
-23798: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23799: Facts:
-23799: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23799: Goal:
-23799: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23799: Order:
-23799: kbo
-23799: Leaf order:
-23799: c 2 0 2 2,2,2,2
-23799: a 3 0 3 1,2
-23799: b 3 0 3 1,2,2
-23799: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23800: Facts:
-23800: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c9 ?2 ?3 ?4
-23800: Goal:
-23800: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23800: Order:
-23800: lpo
-23800: Leaf order:
-23800: c 2 0 2 2,2,2,2
-23800: a 3 0 3 1,2
-23800: b 3 0 3 1,2,2
-23800: nand 12 2 6 0,2
-% SZS status Timeout for BOO094-1.p
-NO CLASH, using fixed ground order
-23822: Facts:
-23822: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23822: Goal:
-23822: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23822: Order:
-23822: nrkbo
-23822: Leaf order:
-23822: b 1 0 1 1,2,2
-23822: a 4 0 4 1,1,2
-23822: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23823: Facts:
-23823: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23823: Goal:
-23823: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23823: Order:
-23823: kbo
-23823: Leaf order:
-23823: b 1 0 1 1,2,2
-23823: a 4 0 4 1,1,2
-23823: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23824: Facts:
-23824: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23824: Goal:
-23824: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23824: Order:
-23824: lpo
-23824: Leaf order:
-23824: b 1 0 1 1,2,2
-23824: a 4 0 4 1,1,2
-23824: nand 9 2 3 0,2
-% SZS status Timeout for BOO095-1.p
-NO CLASH, using fixed ground order
-23854: Facts:
-23854: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23854: Goal:
-23854: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23854: Order:
-23854: nrkbo
-23854: Leaf order:
-23854: c 2 0 2 2,2,2,2
-23854: a 3 0 3 1,2
-23854: b 3 0 3 1,2,2
-23854: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23855: Facts:
-23855: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23855: Goal:
-23855: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23855: Order:
-23855: kbo
-23855: Leaf order:
-23855: c 2 0 2 2,2,2,2
-23855: a 3 0 3 1,2
-23855: b 3 0 3 1,2,2
-23855: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23856: Facts:
-23856: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c10 ?2 ?3 ?4
-23856: Goal:
-23856: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23856: Order:
-23856: lpo
-23856: Leaf order:
-23856: c 2 0 2 2,2,2,2
-23856: a 3 0 3 1,2
-23856: b 3 0 3 1,2,2
-23856: nand 12 2 6 0,2
-% SZS status Timeout for BOO096-1.p
-NO CLASH, using fixed ground order
-23878: Facts:
-23878: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23878: Goal:
-23878: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23878: Order:
-23878: nrkbo
-23878: Leaf order:
-23878: b 1 0 1 1,2,2
-23878: a 4 0 4 1,1,2
-23878: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23879: Facts:
-23879: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23879: Goal:
-23879: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23879: Order:
-23879: kbo
-23879: Leaf order:
-23879: b 1 0 1 1,2,2
-23879: a 4 0 4 1,1,2
-23879: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23880: Facts:
-23880: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23880: Goal:
-23880: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23880: Order:
-23880: lpo
-23880: Leaf order:
-23880: b 1 0 1 1,2,2
-23880: a 4 0 4 1,1,2
-23880: nand 9 2 3 0,2
-% SZS status Timeout for BOO097-1.p
-NO CLASH, using fixed ground order
-23905: Facts:
-23905: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23905: Goal:
-23905: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23905: Order:
-23905: nrkbo
-23905: Leaf order:
-23905: c 2 0 2 2,2,2,2
-23905: a 3 0 3 1,2
-23905: b 3 0 3 1,2,2
-23905: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23906: Facts:
-23906: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23906: Goal:
-23906: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23906: Order:
-23906: kbo
-23906: Leaf order:
-23906: c 2 0 2 2,2,2,2
-23906: a 3 0 3 1,2
-23906: b 3 0 3 1,2,2
-23906: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23907: Facts:
-23907: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
- [4, 3, 2] by c11 ?2 ?3 ?4
-23907: Goal:
-23907: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23907: Order:
-23907: lpo
-23907: Leaf order:
-23907: c 2 0 2 2,2,2,2
-23907: a 3 0 3 1,2
-23907: b 3 0 3 1,2,2
-23907: nand 12 2 6 0,2
-% SZS status Timeout for BOO098-1.p
-NO CLASH, using fixed ground order
-23950: Facts:
-23950: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23950: Goal:
-23950: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23950: Order:
-23950: kbo
-23950: Leaf order:
-23950: b 1 0 1 1,2,2
-23950: a 4 0 4 1,1,2
-23950: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23951: Facts:
-23951: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23951: Goal:
-23951: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23951: Order:
-23951: lpo
-23951: Leaf order:
-23951: b 1 0 1 1,2,2
-23951: a 4 0 4 1,1,2
-23951: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-23949: Facts:
-23949: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23949: Goal:
-23949: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-23949: Order:
-23949: nrkbo
-23949: Leaf order:
-23949: b 1 0 1 1,2,2
-23949: a 4 0 4 1,1,2
-23949: nand 9 2 3 0,2
-% SZS status Timeout for BOO099-1.p
-NO CLASH, using fixed ground order
-23972: Facts:
-23972: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23972: Goal:
-23972: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23972: Order:
-23972: nrkbo
-23972: Leaf order:
-23972: c 2 0 2 2,2,2,2
-23972: a 3 0 3 1,2
-23972: b 3 0 3 1,2,2
-23972: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23973: Facts:
-23973: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23973: Goal:
-23973: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23973: Order:
-23973: kbo
-23973: Leaf order:
-23973: c 2 0 2 2,2,2,2
-23973: a 3 0 3 1,2
-23973: b 3 0 3 1,2,2
-23973: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-23974: Facts:
-23974: Id : 2, {_}:
- nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c12 ?2 ?3 ?4
-23974: Goal:
-23974: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-23974: Order:
-23974: lpo
-23974: Leaf order:
-23974: c 2 0 2 2,2,2,2
-23974: a 3 0 3 1,2
-23974: b 3 0 3 1,2,2
-23974: nand 12 2 6 0,2
-% SZS status Timeout for BOO100-1.p
-NO CLASH, using fixed ground order
-24933: Facts:
-24933: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24933: Goal:
-24933: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24933: Order:
-24933: nrkbo
-24933: Leaf order:
-24933: b 1 0 1 1,2,2
-24933: a 4 0 4 1,1,2
-24933: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-24934: Facts:
-24934: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24934: Goal:
-24934: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24934: Order:
-24934: kbo
-24934: Leaf order:
-24934: b 1 0 1 1,2,2
-24934: a 4 0 4 1,1,2
-24934: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-24935: Facts:
-24935: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24935: Goal:
-24935: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24935: Order:
-24935: lpo
-24935: Leaf order:
-24935: b 1 0 1 1,2,2
-24935: a 4 0 4 1,1,2
-24935: nand 9 2 3 0,2
-% SZS status Timeout for BOO101-1.p
-NO CLASH, using fixed ground order
-24957: Facts:
-NO CLASH, using fixed ground order
-24958: Facts:
-24958: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24958: Goal:
-24958: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-24958: Order:
-24958: kbo
-24958: Leaf order:
-24958: c 2 0 2 2,2,2,2
-24958: a 3 0 3 1,2
-24958: b 3 0 3 1,2,2
-24958: nand 12 2 6 0,2
-24957: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24957: Goal:
-24957: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-24957: Order:
-24957: nrkbo
-24957: Leaf order:
-24957: c 2 0 2 2,2,2,2
-24957: a 3 0 3 1,2
-24957: b 3 0 3 1,2,2
-24957: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-24959: Facts:
-24959: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c13 ?2 ?3 ?4
-24959: Goal:
-24959: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-24959: Order:
-24959: lpo
-24959: Leaf order:
-24959: c 2 0 2 2,2,2,2
-24959: a 3 0 3 1,2
-24959: b 3 0 3 1,2,2
-24959: nand 12 2 6 0,2
-% SZS status Timeout for BOO102-1.p
-NO CLASH, using fixed ground order
-24983: Facts:
-24983: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-24983: Goal:
-24983: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24983: Order:
-24983: nrkbo
-24983: Leaf order:
-24983: b 1 0 1 1,2,2
-24983: a 4 0 4 1,1,2
-24983: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-24984: Facts:
-24984: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-24984: Goal:
-24984: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24984: Order:
-24984: kbo
-24984: Leaf order:
-24984: b 1 0 1 1,2,2
-24984: a 4 0 4 1,1,2
-24984: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-24985: Facts:
-24985: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-24985: Goal:
-24985: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-24985: Order:
-24985: lpo
-24985: Leaf order:
-24985: b 1 0 1 1,2,2
-24985: a 4 0 4 1,1,2
-24985: nand 9 2 3 0,2
-% SZS status Timeout for BOO103-1.p
-NO CLASH, using fixed ground order
-25006: Facts:
-25006: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-25006: Goal:
-25006: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25006: Order:
-25006: nrkbo
-25006: Leaf order:
-25006: c 2 0 2 2,2,2,2
-25006: a 3 0 3 1,2
-25006: b 3 0 3 1,2,2
-25006: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25007: Facts:
-25007: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-25007: Goal:
-25007: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25007: Order:
-25007: kbo
-25007: Leaf order:
-25007: c 2 0 2 2,2,2,2
-25007: a 3 0 3 1,2
-25007: b 3 0 3 1,2,2
-25007: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25008: Facts:
-25008: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c14 ?2 ?3 ?4
-25008: Goal:
-25008: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25008: Order:
-25008: lpo
-25008: Leaf order:
-25008: c 2 0 2 2,2,2,2
-25008: a 3 0 3 1,2
-25008: b 3 0 3 1,2,2
-25008: nand 12 2 6 0,2
-% SZS status Timeout for BOO104-1.p
-NO CLASH, using fixed ground order
-25030: Facts:
-25030: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25030: Goal:
-25030: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25030: Order:
-25030: nrkbo
-25030: Leaf order:
-25030: b 1 0 1 1,2,2
-25030: a 4 0 4 1,1,2
-25030: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-25031: Facts:
-25031: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25031: Goal:
-25031: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25031: Order:
-25031: kbo
-25031: Leaf order:
-25031: b 1 0 1 1,2,2
-25031: a 4 0 4 1,1,2
-25031: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-25032: Facts:
-25032: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25032: Goal:
-25032: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25032: Order:
-25032: lpo
-25032: Leaf order:
-25032: b 1 0 1 1,2,2
-25032: a 4 0 4 1,1,2
-25032: nand 9 2 3 0,2
-% SZS status Timeout for BOO105-1.p
-NO CLASH, using fixed ground order
-25053: Facts:
-25053: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25053: Goal:
-25053: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25053: Order:
-25053: nrkbo
-25053: Leaf order:
-25053: c 2 0 2 2,2,2,2
-25053: a 3 0 3 1,2
-25053: b 3 0 3 1,2,2
-25053: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25054: Facts:
-25054: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25054: Goal:
-25054: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25054: Order:
-25054: kbo
-25054: Leaf order:
-25054: c 2 0 2 2,2,2,2
-25054: a 3 0 3 1,2
-25054: b 3 0 3 1,2,2
-25054: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25055: Facts:
-25055: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
- [4, 3, 2] by c15 ?2 ?3 ?4
-25055: Goal:
-25055: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25055: Order:
-25055: lpo
-25055: Leaf order:
-25055: c 2 0 2 2,2,2,2
-25055: a 3 0 3 1,2
-25055: b 3 0 3 1,2,2
-25055: nand 12 2 6 0,2
-% SZS status Timeout for BOO106-1.p
-NO CLASH, using fixed ground order
-25082: Facts:
-25082: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25082: Goal:
-25082: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25082: Order:
-25082: nrkbo
-25082: Leaf order:
-25082: b 1 0 1 1,2,2
-25082: a 4 0 4 1,1,2
-25082: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-25083: Facts:
-25083: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25083: Goal:
-25083: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25083: Order:
-25083: kbo
-25083: Leaf order:
-25083: b 1 0 1 1,2,2
-25083: a 4 0 4 1,1,2
-25083: nand 9 2 3 0,2
-NO CLASH, using fixed ground order
-25084: Facts:
-25084: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25084: Goal:
-25084: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
-25084: Order:
-25084: lpo
-25084: Leaf order:
-25084: b 1 0 1 1,2,2
-25084: a 4 0 4 1,1,2
-25084: nand 9 2 3 0,2
-% SZS status Timeout for BOO107-1.p
-NO CLASH, using fixed ground order
-25109: Facts:
-25109: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25109: Goal:
-25109: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25109: Order:
-25109: nrkbo
-25109: Leaf order:
-25109: c 2 0 2 2,2,2,2
-25109: a 3 0 3 1,2
-25109: b 3 0 3 1,2,2
-25109: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25110: Facts:
-25110: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25110: Goal:
-25110: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25110: Order:
-25110: kbo
-25110: Leaf order:
-25110: c 2 0 2 2,2,2,2
-25110: a 3 0 3 1,2
-25110: b 3 0 3 1,2,2
-25110: nand 12 2 6 0,2
-NO CLASH, using fixed ground order
-25111: Facts:
-25111: Id : 2, {_}:
- nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
- [4, 3, 2] by c16 ?2 ?3 ?4
-25111: Goal:
-25111: Id : 1, {_}:
- nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
- [] by prove_meredith_2_basis_2
-25111: Order:
-25111: lpo
-25111: Leaf order:
-25111: c 2 0 2 2,2,2,2
-25111: a 3 0 3 1,2
-25111: b 3 0 3 1,2,2
-25111: nand 12 2 6 0,2
-% SZS status Timeout for BOO108-1.p
-CLASH, statistics insufficient
-25136: Facts:
-25136: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25136: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25136: Goal:
-25136: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25136: Order:
-25136: nrkbo
-25136: Leaf order:
-25136: s 1 0 0
-25136: b 1 0 0
-25136: f 3 1 3 0,2,2
-25136: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25137: Facts:
-25137: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25137: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25137: Goal:
-25137: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25137: Order:
-25137: kbo
-25137: Leaf order:
-25137: s 1 0 0
-25137: b 1 0 0
-25137: f 3 1 3 0,2,2
-25137: apply 14 2 3 0,2
-CLASH, statistics insufficient
-25138: Facts:
-25138: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25138: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25138: Goal:
-25138: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25138: Order:
-25138: lpo
-25138: Leaf order:
-25138: s 1 0 0
-25138: b 1 0 0
-25138: f 3 1 3 0,2,2
-25138: apply 14 2 3 0,2
-% SZS status Timeout for COL067-1.p
-CLASH, statistics insufficient
-25159: Facts:
-25159: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25159: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25159: Goal:
-25159: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-25159: Order:
-25159: nrkbo
-25159: Leaf order:
-25159: s 1 0 0
-25159: b 1 0 0
-25159: combinator 1 0 1 1,3
-25159: apply 12 2 1 0,3
-CLASH, statistics insufficient
-25160: Facts:
-25160: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25160: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25160: Goal:
-25160: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-25160: Order:
-25160: kbo
-25160: Leaf order:
-25160: s 1 0 0
-25160: b 1 0 0
-25160: combinator 1 0 1 1,3
-25160: apply 12 2 1 0,3
-CLASH, statistics insufficient
-25161: Facts:
-25161: Id : 2, {_}:
- apply (apply (apply s ?3) ?4) ?5
- =?=
- apply (apply ?3 ?5) (apply ?4 ?5)
- [5, 4, 3] by s_definition ?3 ?4 ?5
-25161: Id : 3, {_}:
- apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
- [9, 8, 7] by b_definition ?7 ?8 ?9
-25161: Goal:
-25161: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
-25161: Order:
-25161: lpo
-25161: Leaf order:
-25161: s 1 0 0
-25161: b 1 0 0
-25161: combinator 1 0 1 1,3
-25161: apply 12 2 1 0,3
-% SZS status Timeout for COL068-1.p
-CLASH, statistics insufficient
-25183: Facts:
-25183: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25183: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-25183: Goal:
-25183: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25183: Order:
-25183: nrkbo
-25183: Leaf order:
-25183: b 1 0 0
-25183: l 1 0 0
-25183: f 3 1 3 0,2,2
-25183: apply 12 2 3 0,2
-CLASH, statistics insufficient
-25184: Facts:
-25184: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25184: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-25184: Goal:
-25184: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25184: Order:
-25184: kbo
-25184: Leaf order:
-25184: b 1 0 0
-25184: l 1 0 0
-25184: f 3 1 3 0,2,2
-25184: apply 12 2 3 0,2
-CLASH, statistics insufficient
-25185: Facts:
-25185: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by b_definition ?3 ?4 ?5
-25185: Id : 3, {_}:
- apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
- [8, 7] by l_definition ?7 ?8
-25185: Goal:
-25185: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by prove_fixed_point ?1
-25185: Order:
-25185: lpo
-25185: Leaf order:
-25185: b 1 0 0
-25185: l 1 0 0
-25185: f 3 1 3 0,2,2
-25185: apply 12 2 3 0,2
-% SZS status Timeout for COL069-1.p
-CLASH, statistics insufficient
-25251: Facts:
-25251: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-25251: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-25251: Goal:
-25251: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-25251: Order:
-25251: nrkbo
-25251: Leaf order:
-25251: b 1 0 0
-25251: m 1 0 0
-25251: f 3 1 3 0,2,2
-25251: apply 10 2 3 0,2
-CLASH, statistics insufficient
-25252: Facts:
-25252: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-25252: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-25252: Goal:
-25252: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-25252: Order:
-25252: kbo
-25252: Leaf order:
-25252: b 1 0 0
-25252: m 1 0 0
-25252: f 3 1 3 0,2,2
-25252: apply 10 2 3 0,2
-CLASH, statistics insufficient
-25253: Facts:
-25253: Id : 2, {_}:
- apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
- [5, 4, 3] by definition_B ?3 ?4 ?5
-25253: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
-25253: Goal:
-25253: Id : 1, {_}:
- apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
- [1] by strong_fixpoint ?1
-25253: Order:
-25253: lpo
-25253: Leaf order:
-25253: b 1 0 0
-25253: m 1 0 0
-25253: f 3 1 3 0,2,2
-25253: apply 10 2 3 0,2
-% SZS status Timeout for COL087-1.p
-NO CLASH, using fixed ground order
-25281: Facts:
-25281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25281: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25281: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25281: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25281: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =?=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25281: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =?=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25281: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25281: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25281: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25281: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25281: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25281: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25281: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25281: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-25281: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-25281: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-25281: Goal:
-25281: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-25281: Order:
-25281: nrkbo
-25281: Leaf order:
-25281: identity 5 0 0
-25281: b 5 0 3 1,2,1,2
-25281: c 5 0 3 2,2,1,2
-25281: a 7 0 5 1,1,2
-25281: inverse 1 1 0
-25281: least_upper_bound 17 2 1 0,2
-25281: greatest_lower_bound 18 2 5 0,1,2
-25281: multiply 21 2 3 0,2,1,2
-NO CLASH, using fixed ground order
-25282: Facts:
-25282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25282: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25282: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25282: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25282: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25282: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25282: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25282: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25282: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25282: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =<=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25282: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =<=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25282: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =<=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25282: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =<=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25282: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-25282: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-25282: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-25282: Goal:
-25282: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-25282: Order:
-25282: kbo
-25282: Leaf order:
-25282: identity 5 0 0
-25282: b 5 0 3 1,2,1,2
-25282: c 5 0 3 2,2,1,2
-25282: a 7 0 5 1,1,2
-25282: inverse 1 1 0
-25282: least_upper_bound 17 2 1 0,2
-25282: greatest_lower_bound 18 2 5 0,1,2
-25282: multiply 21 2 3 0,2,1,2
-NO CLASH, using fixed ground order
-25283: Facts:
-25283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
-25283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
-25283: Id : 4, {_}:
- multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
- [8, 7, 6] by associativity ?6 ?7 ?8
-25283: Id : 5, {_}:
- greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
- [11, 10] by symmetry_of_glb ?10 ?11
-25283: Id : 6, {_}:
- least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
- [14, 13] by symmetry_of_lub ?13 ?14
-25283: Id : 7, {_}:
- greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
- =<=
- greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
- [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
-25283: Id : 8, {_}:
- least_upper_bound ?20 (least_upper_bound ?21 ?22)
- =<=
- least_upper_bound (least_upper_bound ?20 ?21) ?22
- [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
-25283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
-25283: Id : 10, {_}:
- greatest_lower_bound ?26 ?26 =>= ?26
- [26] by idempotence_of_gld ?26
-25283: Id : 11, {_}:
- least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
- [29, 28] by lub_absorbtion ?28 ?29
-25283: Id : 12, {_}:
- greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
- [32, 31] by glb_absorbtion ?31 ?32
-25283: Id : 13, {_}:
- multiply ?34 (least_upper_bound ?35 ?36)
- =>=
- least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
- [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
-25283: Id : 14, {_}:
- multiply ?38 (greatest_lower_bound ?39 ?40)
- =>=
- greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
- [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
-25283: Id : 15, {_}:
- multiply (least_upper_bound ?42 ?43) ?44
- =>=
- least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
- [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
-25283: Id : 16, {_}:
- multiply (greatest_lower_bound ?46 ?47) ?48
- =>=
- greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
- [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
-25283: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
-25283: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
-25283: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
-25283: Goal:
-25283: Id : 1, {_}:
- least_upper_bound (greatest_lower_bound a (multiply b c))
- (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
- =>=
- multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
- [] by prove_p08a
-25283: Order:
-25283: lpo
-25283: Leaf order:
-25283: identity 5 0 0
-25283: b 5 0 3 1,2,1,2
-25283: c 5 0 3 2,2,1,2
-25283: a 7 0 5 1,1,2
-25283: inverse 1 1 0
-25283: least_upper_bound 17 2 1 0,2
-25283: greatest_lower_bound 18 2 5 0,1,2
-25283: multiply 21 2 3 0,2,1,2
-% SZS status Timeout for GRP177-1.p
-NO CLASH, using fixed ground order
-25304: Facts:
-25304: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-25304: Goal:
-25304: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25304: Order:
-25304: nrkbo
-25304: Leaf order:
-25304: a 3 0 3 1,2
-25304: c 3 0 3 2,1,2,2
-25304: b 4 0 4 1,1,2,2
-25304: f 17 2 8 0,2
-NO CLASH, using fixed ground order
-25305: Facts:
-25305: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-25305: Goal:
-25305: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25305: Order:
-25305: kbo
-25305: Leaf order:
-25305: a 3 0 3 1,2
-25305: c 3 0 3 2,1,2,2
-25305: b 4 0 4 1,1,2,2
-25305: f 17 2 8 0,2
-NO CLASH, using fixed ground order
-25306: Facts:
-25306: Id : 2, {_}:
- f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
- =>=
- ?3
- [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
-25306: Goal:
-25306: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25306: Order:
-25306: lpo
-25306: Leaf order:
-25306: a 3 0 3 1,2
-25306: c 3 0 3 2,1,2,2
-25306: b 4 0 4 1,1,2,2
-25306: f 17 2 8 0,2
-% SZS status Timeout for LAT071-1.p
-NO CLASH, using fixed ground order
-25332: Facts:
-25332: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-25332: Goal:
-25332: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25332: Order:
-25332: nrkbo
-25332: Leaf order:
-25332: a 3 0 3 1,2
-25332: c 3 0 3 2,1,2,2
-25332: b 4 0 4 1,1,2,2
-25332: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-25333: Facts:
-25333: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-25333: Goal:
-25333: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25333: Order:
-25333: kbo
-25333: Leaf order:
-25333: a 3 0 3 1,2
-25333: c 3 0 3 2,1,2,2
-25333: b 4 0 4 1,1,2,2
-25333: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-25334: Facts:
-25334: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
-25334: Goal:
-25334: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25334: Order:
-25334: lpo
-25334: Leaf order:
-25334: a 3 0 3 1,2
-25334: c 3 0 3 2,1,2,2
-25334: b 4 0 4 1,1,2,2
-25334: f 18 2 8 0,2
-% SZS status Timeout for LAT072-1.p
-NO CLASH, using fixed ground order
-25355: Facts:
-25355: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-25355: Goal:
-25355: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-25355: Order:
-25355: nrkbo
-25355: Leaf order:
-25355: b 3 0 3 1,2,2
-25355: c 3 0 3 1,2,2,2,2
-25355: a 4 0 4 1,2
-25355: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-25356: Facts:
-25356: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-25356: Goal:
-25356: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-25356: Order:
-25356: kbo
-25356: Leaf order:
-25356: b 3 0 3 1,2,2
-25356: c 3 0 3 1,2,2,2,2
-25356: a 4 0 4 1,2
-25356: f 18 2 8 0,2
-NO CLASH, using fixed ground order
-25357: Facts:
-25357: Id : 2, {_}:
- f (f (f ?2 (f ?3 ?2)) ?2)
- (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
- =>=
- ?3
- [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
-25357: Goal:
-25357: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-25357: Order:
-25357: lpo
-25357: Leaf order:
-25357: b 3 0 3 1,2,2
-25357: c 3 0 3 1,2,2,2,2
-25357: a 4 0 4 1,2
-25357: f 18 2 8 0,2
-% SZS status Timeout for LAT073-1.p
-NO CLASH, using fixed ground order
-25379: Facts:
-NO CLASH, using fixed ground order
-25381: Facts:
-25381: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25381: Goal:
-25381: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25381: Order:
-25381: lpo
-25381: Leaf order:
-25381: a 3 0 3 1,2
-25381: c 3 0 3 2,1,2,2
-25381: b 4 0 4 1,1,2,2
-25381: f 19 2 8 0,2
-NO CLASH, using fixed ground order
-25380: Facts:
-25380: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25380: Goal:
-25380: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25380: Order:
-25380: kbo
-25380: Leaf order:
-25380: a 3 0 3 1,2
-25380: c 3 0 3 2,1,2,2
-25380: b 4 0 4 1,1,2,2
-25380: f 19 2 8 0,2
-25379: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25379: Goal:
-25379: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25379: Order:
-25379: nrkbo
-25379: Leaf order:
-25379: a 3 0 3 1,2
-25379: c 3 0 3 2,1,2,2
-25379: b 4 0 4 1,1,2,2
-25379: f 19 2 8 0,2
-% SZS status Timeout for LAT074-1.p
-NO CLASH, using fixed ground order
-25407: Facts:
-25407: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25407: Goal:
-25407: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-25407: Order:
-25407: nrkbo
-25407: Leaf order:
-25407: b 3 0 3 1,2,2
-25407: c 3 0 3 1,2,2,2,2
-25407: a 4 0 4 1,2
-25407: f 19 2 8 0,2
-NO CLASH, using fixed ground order
-25408: Facts:
-25408: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25408: Goal:
-25408: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-25408: Order:
-25408: kbo
-25408: Leaf order:
-25408: b 3 0 3 1,2,2
-25408: c 3 0 3 1,2,2,2,2
-25408: a 4 0 4 1,2
-25408: f 19 2 8 0,2
-NO CLASH, using fixed ground order
-25409: Facts:
-25409: Id : 2, {_}:
- f (f ?2 ?3)
- (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
- =>=
- ?3
- [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
-25409: Goal:
-25409: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-25409: Order:
-25409: lpo
-25409: Leaf order:
-25409: b 3 0 3 1,2,2
-25409: c 3 0 3 1,2,2,2,2
-25409: a 4 0 4 1,2
-25409: f 19 2 8 0,2
-% SZS status Timeout for LAT075-1.p
-NO CLASH, using fixed ground order
-25460: Facts:
-25460: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25460: Goal:
-25460: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25460: Order:
-25460: nrkbo
-25460: Leaf order:
-25460: a 3 0 3 1,2
-25460: c 3 0 3 2,1,2,2
-25460: b 4 0 4 1,1,2,2
-25460: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25461: Facts:
-25461: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25461: Goal:
-25461: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25461: Order:
-25461: kbo
-25461: Leaf order:
-25461: a 3 0 3 1,2
-25461: c 3 0 3 2,1,2,2
-25461: b 4 0 4 1,1,2,2
-25461: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25462: Facts:
-25462: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25462: Goal:
-25462: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25462: Order:
-25462: lpo
-25462: Leaf order:
-25462: a 3 0 3 1,2
-25462: c 3 0 3 2,1,2,2
-25462: b 4 0 4 1,1,2,2
-25462: f 20 2 8 0,2
-% SZS status Timeout for LAT076-1.p
-NO CLASH, using fixed ground order
-25483: Facts:
-25483: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25483: Goal:
-25483: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-25483: Order:
-25483: nrkbo
-25483: Leaf order:
-25483: b 3 0 3 1,2,2
-25483: c 3 0 3 1,2,2,2,2
-25483: a 4 0 4 1,2
-25483: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25484: Facts:
-25484: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25484: Goal:
-25484: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-25484: Order:
-25484: kbo
-25484: Leaf order:
-25484: b 3 0 3 1,2,2
-25484: c 3 0 3 1,2,2,2,2
-25484: a 4 0 4 1,2
-25484: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25485: Facts:
-25485: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
- (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
-25485: Goal:
-25485: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-25485: Order:
-25485: lpo
-25485: Leaf order:
-25485: b 3 0 3 1,2,2
-25485: c 3 0 3 1,2,2,2,2
-25485: a 4 0 4 1,2
-25485: f 20 2 8 0,2
-% SZS status Timeout for LAT077-1.p
-NO CLASH, using fixed ground order
-25507: Facts:
-25507: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25507: Goal:
-25507: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25507: Order:
-25507: nrkbo
-25507: Leaf order:
-25507: a 3 0 3 1,2
-25507: c 3 0 3 2,1,2,2
-25507: b 4 0 4 1,1,2,2
-25507: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25508: Facts:
-25508: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25508: Goal:
-25508: Id : 1, {_}:
- f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
- [] by associativity
-25508: Order:
-25508: kbo
-25508: Leaf order:
-25508: a 3 0 3 1,2
-25508: c 3 0 3 2,1,2,2
-25508: b 4 0 4 1,1,2,2
-25508: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25509: Facts:
-25509: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25509: Goal:
-25509: Id : 1, {_}:
- f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
- [] by associativity
-25509: Order:
-25509: lpo
-25509: Leaf order:
-25509: a 3 0 3 1,2
-25509: c 3 0 3 2,1,2,2
-25509: b 4 0 4 1,1,2,2
-25509: f 20 2 8 0,2
-% SZS status Timeout for LAT078-1.p
-NO CLASH, using fixed ground order
-25531: Facts:
-25531: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25531: Goal:
-25531: Id : 1, {_}:
- f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
- [] by modularity
-25531: Order:
-25531: nrkbo
-25531: Leaf order:
-25531: b 3 0 3 1,2,2
-25531: c 3 0 3 1,2,2,2,2
-25531: a 4 0 4 1,2
-25531: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25532: Facts:
-25532: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25532: Goal:
-25532: Id : 1, {_}:
- f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
- [] by modularity
-25532: Order:
-25532: kbo
-25532: Leaf order:
-25532: b 3 0 3 1,2,2
-25532: c 3 0 3 1,2,2,2,2
-25532: a 4 0 4 1,2
-25532: f 20 2 8 0,2
-NO CLASH, using fixed ground order
-25533: Facts:
-25533: Id : 2, {_}:
- f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
- (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
- =>=
- ?3
- [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
-25533: Goal:
-25533: Id : 1, {_}:
- f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
- [] by modularity
-25533: Order:
-25533: lpo
-25533: Leaf order:
-25533: b 3 0 3 1,2,2
-25533: c 3 0 3 1,2,2,2,2
-25533: a 4 0 4 1,2
-25533: f 20 2 8 0,2
-% SZS status Timeout for LAT079-1.p
-NO CLASH, using fixed ground order
-25631: Facts:
-25631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25631: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25631: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25631: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25631: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25631: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-25631: Goal:
-25631: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-25631: Order:
-25631: nrkbo
-25631: Leaf order:
-25631: b 3 0 3 1,2,2
-25631: c 3 0 3 2,2,2,2
-25631: a 4 0 4 1,2
-25631: join 16 2 3 0,2,2
-25631: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-25633: Facts:
-25633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25633: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25633: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25633: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25633: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25633: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =?=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-25633: Goal:
-25633: Id : 1, {_}:
- meet a (join b (meet a c))
- =>=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-25633: Order:
-25633: lpo
-25633: Leaf order:
-25633: b 3 0 3 1,2,2
-25633: c 3 0 3 2,2,2,2
-25633: a 4 0 4 1,2
-25633: join 16 2 3 0,2,2
-25633: meet 20 2 5 0,2
-NO CLASH, using fixed ground order
-25632: Facts:
-25632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25632: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25632: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25632: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25632: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25632: Id : 10, {_}:
- meet ?26 (join ?27 (meet ?26 ?28))
- =<=
- meet ?26
- (join ?27
- (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
- [28, 27, 26] by equation_H11 ?26 ?27 ?28
-25632: Goal:
-25632: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join b (meet c (join a (meet b c))))
- [] by prove_H10
-25632: Order:
-25632: kbo
-25632: Leaf order:
-25632: b 3 0 3 1,2,2
-25632: c 3 0 3 2,2,2,2
-25632: a 4 0 4 1,2
-25632: join 16 2 3 0,2,2
-25632: meet 20 2 5 0,2
-% SZS status Timeout for LAT139-1.p
-NO CLASH, using fixed ground order
-25659: Facts:
-25659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25659: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25659: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25659: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25659: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25659: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25659: Goal:
-25659: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25659: Order:
-25659: nrkbo
-25659: Leaf order:
-25659: b 3 0 3 1,2,2
-25659: c 3 0 3 2,2,2,2
-25659: a 6 0 6 1,2
-25659: join 17 2 4 0,2,2
-25659: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-25660: Facts:
-25660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25660: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25660: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25660: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25660: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25660: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25660: Goal:
-25660: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25660: Order:
-25660: kbo
-25660: Leaf order:
-25660: b 3 0 3 1,2,2
-25660: c 3 0 3 2,2,2,2
-25660: a 6 0 6 1,2
-25660: join 17 2 4 0,2,2
-25660: meet 21 2 6 0,2
-NO CLASH, using fixed ground order
-25661: Facts:
-25661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25661: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25661: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25661: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25661: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25661: Id : 10, {_}:
- join (meet ?26 ?27) (meet ?26 ?28)
- =<=
- meet ?26
- (join (meet ?27 (join ?26 (meet ?27 ?28)))
- (meet ?28 (join ?26 ?27)))
- [28, 27, 26] by equation_H21 ?26 ?27 ?28
-25661: Goal:
-25661: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25661: Order:
-25661: lpo
-25661: Leaf order:
-25661: b 3 0 3 1,2,2
-25661: c 3 0 3 2,2,2,2
-25661: a 6 0 6 1,2
-25661: join 17 2 4 0,2,2
-25661: meet 21 2 6 0,2
-% SZS status Timeout for LAT141-1.p
-NO CLASH, using fixed ground order
-25683: Facts:
-25683: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25683: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25683: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25683: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25683: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25683: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25683: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25683: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25683: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-25683: Goal:
-25683: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-25683: Order:
-25683: nrkbo
-25683: Leaf order:
-25683: c 2 0 2 2,1,2,2
-25683: d 2 0 2 2,2,2,2
-25683: a 3 0 3 1,2
-25683: b 5 0 5 1,1,2,2
-25683: join 18 2 5 0,1,2,2
-25683: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-25684: Facts:
-25684: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25684: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25684: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25684: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25684: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25684: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25684: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25684: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25684: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-25684: Goal:
-25684: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-25684: Order:
-25684: kbo
-25684: Leaf order:
-25684: c 2 0 2 2,1,2,2
-25684: d 2 0 2 2,2,2,2
-25684: a 3 0 3 1,2
-25684: b 5 0 5 1,1,2,2
-25684: join 18 2 5 0,1,2,2
-25684: meet 18 2 5 0,2
-NO CLASH, using fixed ground order
-25685: Facts:
-25685: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25685: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25685: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25685: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25685: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25685: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25685: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25685: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25685: Id : 10, {_}:
- meet ?26 (join ?27 ?28)
- =<=
- meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
- [28, 27, 26] by equation_H58 ?26 ?27 ?28
-25685: Goal:
-25685: Id : 1, {_}:
- meet a (meet (join b c) (join b d))
- =<=
- meet a (join b (meet (join b d) (join c (meet a b))))
- [] by prove_H59
-25685: Order:
-25685: lpo
-25685: Leaf order:
-25685: c 2 0 2 2,1,2,2
-25685: d 2 0 2 2,2,2,2
-25685: a 3 0 3 1,2
-25685: b 5 0 5 1,1,2,2
-25685: join 18 2 5 0,1,2,2
-25685: meet 18 2 5 0,2
-% SZS status Timeout for LAT161-1.p
-NO CLASH, using fixed ground order
-25706: Facts:
-25706: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25706: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25706: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25706: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25706: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25706: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25706: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25706: Id : 9, {_}:
- join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-NO CLASH, using fixed ground order
-25707: Facts:
-25707: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25707: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25707: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25707: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25707: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25707: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25707: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25707: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25707: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-25707: Goal:
-25707: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25707: Order:
-25707: kbo
-25707: Leaf order:
-25707: b 3 0 3 1,2,2
-25707: c 3 0 3 2,2,2,2
-25707: a 6 0 6 1,2
-25707: join 19 2 4 0,2,2
-25707: meet 19 2 6 0,2
-NO CLASH, using fixed ground order
-25708: Facts:
-25708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
-25708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
-25708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
-25708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
-25708: Id : 6, {_}:
- meet ?12 ?13 =?= meet ?13 ?12
- [13, 12] by commutativity_of_meet ?12 ?13
-25708: Id : 7, {_}:
- join ?15 ?16 =?= join ?16 ?15
- [16, 15] by commutativity_of_join ?15 ?16
-25708: Id : 8, {_}:
- meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
- [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
-25708: Id : 9, {_}:
- join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
- [24, 23, 22] by associativity_of_join ?22 ?23 ?24
-25708: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-25708: Goal:
-25708: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25708: Order:
-25708: lpo
-25708: Leaf order:
-25708: b 3 0 3 1,2,2
-25708: c 3 0 3 2,2,2,2
-25708: a 6 0 6 1,2
-25708: join 19 2 4 0,2,2
-25708: meet 19 2 6 0,2
-25706: Id : 10, {_}:
- join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
- =<=
- join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
- [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
-25706: Goal:
-25706: Id : 1, {_}:
- meet a (join b (meet a c))
- =<=
- meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
- [] by prove_H6
-25706: Order:
-25706: nrkbo
-25706: Leaf order:
-25706: b 3 0 3 1,2,2
-25706: c 3 0 3 2,2,2,2
-25706: a 6 0 6 1,2
-25706: join 19 2 4 0,2,2
-25706: meet 19 2 6 0,2
-% SZS status Timeout for LAT177-1.p
-NO CLASH, using fixed ground order
-25759: Facts:
-25759: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-25759: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-25759: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-25759: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-25759: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-25759: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-25759: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-25759: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-25759: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =<=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-25759: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-25759: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-25759: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-25759: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-25759: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =>=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-25759: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =>=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-25759: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =<=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-25759: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =<=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-25759: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-25759: Id : 20, {_}:
- associator ?50 ?51 ?52
- =<=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-25759: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-25759: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-25759: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-25759: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =<=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-25759: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =?=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-25759: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =?=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-25759: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =?=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-25759: Goal:
-25759: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25759: Order:
-25759: nrkbo
-25759: Leaf order:
-25759: a 2 0 2 1,2
-25759: b 2 0 2 2,2
-25759: c 2 0 2 3,2
-25759: d 2 0 2 4,2
-25759: additive_identity 11 0 0
-25759: additive_inverse 20 1 1 0,3
-25759: commutator 1 2 0
-25759: add 22 2 0
-25759: multiply 51 2 0
-25759: associator 6 3 0
-25759: s 3 4 2 0,2
-NO CLASH, using fixed ground order
-25760: Facts:
-25760: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-25760: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-25760: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-25760: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-25760: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-25760: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-25760: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-25760: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-25760: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =<=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-25760: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-25760: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-25760: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-25760: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-25760: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =>=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-25760: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =>=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-25760: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =<=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-25760: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =<=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-25760: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-25760: Id : 20, {_}:
- associator ?50 ?51 ?52
- =<=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-25760: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-25760: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-25760: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-25760: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =<=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-25760: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =<=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-25760: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =>=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-25760: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =<=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-25760: Goal:
-25760: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25760: Order:
-25760: kbo
-25760: Leaf order:
-25760: a 2 0 2 1,2
-25760: b 2 0 2 2,2
-25760: c 2 0 2 3,2
-25760: d 2 0 2 4,2
-25760: additive_identity 11 0 0
-25760: additive_inverse 20 1 1 0,3
-25760: commutator 1 2 0
-25760: add 22 2 0
-25760: multiply 51 2 0
-25760: associator 6 3 0
-25760: s 3 4 2 0,2
-NO CLASH, using fixed ground order
-25761: Facts:
-25761: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
-25761: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associative_addition ?5 ?6 ?7
-25761: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
-25761: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
-25761: Id : 6, {_}:
- add ?13 (additive_inverse ?13) =>= additive_identity
- [13] by right_additive_inverse ?13
-25761: Id : 7, {_}:
- add (additive_inverse ?15) ?15 =>= additive_identity
- [15] by left_additive_inverse ?15
-25761: Id : 8, {_}:
- additive_inverse additive_identity =>= additive_identity
- [] by additive_inverse_identity
-25761: Id : 9, {_}:
- add ?18 (add (additive_inverse ?18) ?19) =>= ?19
- [19, 18] by property_of_inverse_and_add ?18 ?19
-25761: Id : 10, {_}:
- additive_inverse (add ?21 ?22)
- =<=
- add (additive_inverse ?21) (additive_inverse ?22)
- [22, 21] by distribute_additive_inverse ?21 ?22
-25761: Id : 11, {_}:
- additive_inverse (additive_inverse ?24) =>= ?24
- [24] by additive_inverse_additive_inverse ?24
-25761: Id : 12, {_}:
- multiply ?26 additive_identity =>= additive_identity
- [26] by multiply_additive_id1 ?26
-25761: Id : 13, {_}:
- multiply additive_identity ?28 =>= additive_identity
- [28] by multiply_additive_id2 ?28
-25761: Id : 14, {_}:
- multiply (additive_inverse ?30) (additive_inverse ?31)
- =>=
- multiply ?30 ?31
- [31, 30] by product_of_inverse ?30 ?31
-25761: Id : 15, {_}:
- multiply ?33 (additive_inverse ?34)
- =>=
- additive_inverse (multiply ?33 ?34)
- [34, 33] by multiply_additive_inverse1 ?33 ?34
-25761: Id : 16, {_}:
- multiply (additive_inverse ?36) ?37
- =>=
- additive_inverse (multiply ?36 ?37)
- [37, 36] by multiply_additive_inverse2 ?36 ?37
-25761: Id : 17, {_}:
- multiply ?39 (add ?40 ?41)
- =>=
- add (multiply ?39 ?40) (multiply ?39 ?41)
- [41, 40, 39] by distribute1 ?39 ?40 ?41
-25761: Id : 18, {_}:
- multiply (add ?43 ?44) ?45
- =>=
- add (multiply ?43 ?45) (multiply ?44 ?45)
- [45, 44, 43] by distribute2 ?43 ?44 ?45
-25761: Id : 19, {_}:
- multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
- [48, 47] by right_alternative ?47 ?48
-25761: Id : 20, {_}:
- associator ?50 ?51 ?52
- =>=
- add (multiply (multiply ?50 ?51) ?52)
- (additive_inverse (multiply ?50 (multiply ?51 ?52)))
- [52, 51, 50] by associator ?50 ?51 ?52
-25761: Id : 21, {_}:
- commutator ?54 ?55
- =<=
- add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
- [55, 54] by commutator ?54 ?55
-25761: Id : 22, {_}:
- multiply (multiply (associator ?57 ?57 ?58) ?57)
- (associator ?57 ?57 ?58)
- =>=
- additive_identity
- [58, 57] by middle_associator ?57 ?58
-25761: Id : 23, {_}:
- multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
- [61, 60] by left_alternative ?60 ?61
-25761: Id : 24, {_}:
- s ?63 ?64 ?65 ?66
- =>=
- add
- (add (associator (multiply ?63 ?64) ?65 ?66)
- (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
- (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
- [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
-25761: Id : 25, {_}:
- multiply ?68 (multiply ?69 (multiply ?70 ?69))
- =<=
- multiply (multiply (multiply ?68 ?69) ?70) ?69
- [70, 69, 68] by right_moufang ?68 ?69 ?70
-25761: Id : 26, {_}:
- multiply (multiply ?72 (multiply ?73 ?72)) ?74
- =>=
- multiply ?72 (multiply ?73 (multiply ?72 ?74))
- [74, 73, 72] by left_moufang ?72 ?73 ?74
-25761: Id : 27, {_}:
- multiply (multiply ?76 ?77) (multiply ?78 ?76)
- =<=
- multiply (multiply ?76 (multiply ?77 ?78)) ?76
- [78, 77, 76] by middle_moufang ?76 ?77 ?78
-25761: Goal:
-25761: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25761: Order:
-25761: lpo
-25761: Leaf order:
-25761: a 2 0 2 1,2
-25761: b 2 0 2 2,2
-25761: c 2 0 2 3,2
-25761: d 2 0 2 4,2
-25761: additive_identity 11 0 0
-25761: additive_inverse 20 1 1 0,3
-25761: commutator 1 2 0
-25761: add 22 2 0
-25761: multiply 51 2 0
-25761: associator 6 3 0
-25761: s 3 4 2 0,2
-% SZS status Timeout for RNG010-5.p
-NO CLASH, using fixed ground order
-25787: Facts:
-25787: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25787: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25787: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25787: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25787: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25787: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25787: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25787: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25787: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25787: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25787: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25787: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25787: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25787: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25787: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25787: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =<=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-25787: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =?=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-25787: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =?=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-25787: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =?=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-25787: Goal:
-25787: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25787: Order:
-25787: nrkbo
-25787: Leaf order:
-25787: a 2 0 2 1,2
-25787: b 2 0 2 2,2
-25787: c 2 0 2 3,2
-25787: d 2 0 2 4,2
-25787: additive_identity 8 0 0
-25787: additive_inverse 9 1 1 0,3
-25787: commutator 1 2 0
-25787: add 18 2 0
-25787: multiply 43 2 0
-25787: associator 4 3 0
-25787: s 3 4 2 0,2
-NO CLASH, using fixed ground order
-25788: Facts:
-25788: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25788: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25788: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25788: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25788: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25788: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25788: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25788: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25788: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25788: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25788: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25788: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25788: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25788: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25788: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25788: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =<=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-25788: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =<=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-25788: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =>=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-25788: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =<=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-25788: Goal:
-25788: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25788: Order:
-25788: kbo
-25788: Leaf order:
-25788: a 2 0 2 1,2
-25788: b 2 0 2 2,2
-25788: c 2 0 2 3,2
-25788: d 2 0 2 4,2
-25788: additive_identity 8 0 0
-25788: additive_inverse 9 1 1 0,3
-25788: commutator 1 2 0
-25788: add 18 2 0
-25788: multiply 43 2 0
-25788: associator 4 3 0
-25788: s 3 4 2 0,2
-NO CLASH, using fixed ground order
-25789: Facts:
-25789: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25789: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25789: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25789: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25789: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25789: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25789: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25789: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25789: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25789: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25789: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25789: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25789: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25789: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25789: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25789: Id : 17, {_}:
- s ?44 ?45 ?46 ?47
- =>=
- add
- (add (associator (multiply ?44 ?45) ?46 ?47)
- (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
- (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
- [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
-25789: Id : 18, {_}:
- multiply ?49 (multiply ?50 (multiply ?51 ?50))
- =<=
- multiply (multiply (multiply ?49 ?50) ?51) ?50
- [51, 50, 49] by right_moufang ?49 ?50 ?51
-25789: Id : 19, {_}:
- multiply (multiply ?53 (multiply ?54 ?53)) ?55
- =>=
- multiply ?53 (multiply ?54 (multiply ?53 ?55))
- [55, 54, 53] by left_moufang ?53 ?54 ?55
-25789: Id : 20, {_}:
- multiply (multiply ?57 ?58) (multiply ?59 ?57)
- =<=
- multiply (multiply ?57 (multiply ?58 ?59)) ?57
- [59, 58, 57] by middle_moufang ?57 ?58 ?59
-25789: Goal:
-25789: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25789: Order:
-25789: lpo
-25789: Leaf order:
-25789: a 2 0 2 1,2
-25789: b 2 0 2 2,2
-25789: c 2 0 2 3,2
-25789: d 2 0 2 4,2
-25789: additive_identity 8 0 0
-25789: additive_inverse 9 1 1 0,3
-25789: commutator 1 2 0
-25789: add 18 2 0
-25789: multiply 43 2 0
-25789: associator 4 3 0
-25789: s 3 4 2 0,2
-% SZS status Timeout for RNG010-6.p
-NO CLASH, using fixed ground order
-25814: Facts:
-25814: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25814: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25814: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25814: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25814: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25814: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25814: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25814: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25814: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25814: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25814: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25814: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25814: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25814: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25814: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25814: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25814: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25814: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25814: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25814: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25814: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25814: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25814: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =<=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-25814: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =?=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-25814: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =?=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-25814: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =?=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-25814: Goal:
-25814: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25814: Order:
-25814: nrkbo
-25814: Leaf order:
-25814: a 2 0 2 1,2
-25814: b 2 0 2 2,2
-25814: c 2 0 2 3,2
-25814: d 2 0 2 4,2
-25814: additive_identity 8 0 0
-25814: additive_inverse 25 1 1 0,3
-25814: commutator 1 2 0
-25814: add 26 2 0
-25814: multiply 61 2 0
-25814: associator 4 3 0
-25814: s 3 4 2 0,2
-NO CLASH, using fixed ground order
-25815: Facts:
-NO CLASH, using fixed ground order
-25816: Facts:
-25816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25816: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25816: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25816: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25816: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25816: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25816: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25816: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25816: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25816: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25816: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25816: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25816: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25816: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25816: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25816: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25816: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25816: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25816: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25816: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25816: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25816: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25816: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =>=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-25816: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =<=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-25816: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =>=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-25816: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =<=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-25816: Goal:
-25816: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25816: Order:
-25816: lpo
-25816: Leaf order:
-25816: a 2 0 2 1,2
-25816: b 2 0 2 2,2
-25816: c 2 0 2 3,2
-25816: d 2 0 2 4,2
-25816: additive_identity 8 0 0
-25816: additive_inverse 25 1 1 0,3
-25816: commutator 1 2 0
-25816: add 26 2 0
-25816: multiply 61 2 0
-25816: associator 4 3 0
-25816: s 3 4 2 0,2
-25815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-25815: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-25815: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-25815: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-25815: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-25815: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-25815: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-25815: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-25815: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-25815: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-25815: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-25815: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25815: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-25815: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-25815: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-25815: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-25815: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-25815: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-25815: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-25815: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-25815: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-25815: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-25815: Id : 24, {_}:
- s ?69 ?70 ?71 ?72
- =<=
- add
- (add (associator (multiply ?69 ?70) ?71 ?72)
- (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
- (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
- [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
-25815: Id : 25, {_}:
- multiply ?74 (multiply ?75 (multiply ?76 ?75))
- =<=
- multiply (multiply (multiply ?74 ?75) ?76) ?75
- [76, 75, 74] by right_moufang ?74 ?75 ?76
-25815: Id : 26, {_}:
- multiply (multiply ?78 (multiply ?79 ?78)) ?80
- =>=
- multiply ?78 (multiply ?79 (multiply ?78 ?80))
- [80, 79, 78] by left_moufang ?78 ?79 ?80
-25815: Id : 27, {_}:
- multiply (multiply ?82 ?83) (multiply ?84 ?82)
- =<=
- multiply (multiply ?82 (multiply ?83 ?84)) ?82
- [84, 83, 82] by middle_moufang ?82 ?83 ?84
-25815: Goal:
-25815: Id : 1, {_}:
- s a b c d =<= additive_inverse (s b a c d)
- [] by prove_skew_symmetry
-25815: Order:
-25815: kbo
-25815: Leaf order:
-25815: a 2 0 2 1,2
-25815: b 2 0 2 2,2
-25815: c 2 0 2 3,2
-25815: d 2 0 2 4,2
-25815: additive_identity 8 0 0
-25815: additive_inverse 25 1 1 0,3
-25815: commutator 1 2 0
-25815: add 26 2 0
-25815: multiply 61 2 0
-25815: associator 4 3 0
-25815: s 3 4 2 0,2
-% SZS status Timeout for RNG010-7.p
-NO CLASH, using fixed ground order
-25837: Facts:
-25837: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25837: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25837: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25837: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25837: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25837: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25837: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25837: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25837: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25837: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25837: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25837: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25837: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25837: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25837: Goal:
-25837: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25837: Order:
-25837: nrkbo
-25837: Leaf order:
-25837: y 6 0 6 3,1,1,2
-25837: additive_identity 9 0 1 3
-25837: x 12 0 12 1,1,1,2
-25837: additive_inverse 6 1 0
-25837: commutator 1 2 0
-25837: add 17 2 1 0,2
-25837: multiply 22 2 4 0,1,2
-25837: associator 7 3 6 0,1,1,2
-NO CLASH, using fixed ground order
-25838: Facts:
-25838: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25838: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25838: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25838: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25838: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25838: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25838: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25838: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25838: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25838: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25838: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25838: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25838: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25838: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25838: Goal:
-25838: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25838: Order:
-25838: kbo
-25838: Leaf order:
-25838: y 6 0 6 3,1,1,2
-25838: additive_identity 9 0 1 3
-25838: x 12 0 12 1,1,1,2
-25838: additive_inverse 6 1 0
-25838: commutator 1 2 0
-25838: add 17 2 1 0,2
-25838: multiply 22 2 4 0,1,2
-25838: associator 7 3 6 0,1,1,2
-NO CLASH, using fixed ground order
-25839: Facts:
-25839: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25839: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25839: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25839: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25839: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25839: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25839: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25839: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25839: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25839: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25839: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25839: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25839: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25839: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25839: Goal:
-25839: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25839: Order:
-25839: lpo
-25839: Leaf order:
-25839: y 6 0 6 3,1,1,2
-25839: additive_identity 9 0 1 3
-25839: x 12 0 12 1,1,1,2
-25839: additive_inverse 6 1 0
-25839: commutator 1 2 0
-25839: add 17 2 1 0,2
-25839: multiply 22 2 4 0,1,2
-25839: associator 7 3 6 0,1,1,2
-% SZS status Timeout for RNG030-6.p
-NO CLASH, using fixed ground order
-25861: Facts:
-25861: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25861: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25861: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25861: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25861: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25861: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25861: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25861: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25861: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25861: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25861: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25861: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25861: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25861: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25861: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25861: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25861: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25861: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25861: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25861: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25861: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25861: Goal:
-25861: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25861: Order:
-25861: nrkbo
-25861: Leaf order:
-25861: y 6 0 6 3,1,1,2
-25861: additive_identity 9 0 1 3
-25861: x 12 0 12 1,1,1,2
-25861: additive_inverse 22 1 0
-25861: commutator 1 2 0
-25861: add 25 2 1 0,2
-25861: multiply 40 2 4 0,1,2add
-25861: associator 7 3 6 0,1,1,2
-NO CLASH, using fixed ground order
-25862: Facts:
-NO CLASH, using fixed ground order
-25863: Facts:
-25863: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25863: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25863: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25863: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25863: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25863: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25863: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25863: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25863: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25863: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25863: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25863: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25863: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25863: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25863: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25863: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25863: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25863: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25863: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25863: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25863: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25863: Goal:
-25863: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25863: Order:
-25863: lpo
-25863: Leaf order:
-25863: y 6 0 6 3,1,1,2
-25863: additive_identity 9 0 1 3
-25863: x 12 0 12 1,1,1,2
-25863: additive_inverse 22 1 0
-25863: commutator 1 2 0
-25863: add 25 2 1 0,2
-25863: multiply 40 2 4 0,1,2add
-25863: associator 7 3 6 0,1,1,2
-25862: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25862: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25862: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25862: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25862: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25862: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25862: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25862: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25862: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25862: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25862: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25862: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25862: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25862: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25862: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25862: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25862: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25862: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25862: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25862: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25862: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25862: Goal:
-25862: Id : 1, {_}:
- add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_1
-25862: Order:
-25862: kbo
-25862: Leaf order:
-25862: y 6 0 6 3,1,1,2
-25862: additive_identity 9 0 1 3
-25862: x 12 0 12 1,1,1,2
-25862: additive_inverse 22 1 0
-25862: commutator 1 2 0
-25862: add 25 2 1 0,2
-25862: multiply 40 2 4 0,1,2add
-25862: associator 7 3 6 0,1,1,2
-% SZS status Timeout for RNG030-7.p
-NO CLASH, using fixed ground order
-25886: Facts:
-25886: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25886: Id : 3, {_}:
- add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25886: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25886: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25886: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25886: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25886: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25886: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25886: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25886: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25886: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25886: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25886: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25886: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25886: Goal:
-25886: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25886: Order:
-25886: nrkbo
-25886: Leaf order:
-25886: additive_identity 9 0 1 3
-25886: y 18 0 18 3,1,1,1,1,1,1,2
-25886: x 36 0 36 1,1,1,1,1,1,1,2
-25886: additive_inverse 6 1 0
-25886: commutator 1 2 0
-25886: add 21 2 5 0,2
-25886: multiply 30 2 12 0,1,1,1,1,1,2
-25886: associator 19 3 18 0,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-25887: Facts:
-25887: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25887: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25887: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25887: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25887: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25887: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25887: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25887: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25887: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25887: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25887: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25887: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25887: Id : 14, {_}:
- associator ?34 ?35 ?36
- =<=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25887: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25887: Goal:
-25887: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25887: Order:
-25887: kbo
-25887: Leaf order:
-25887: additive_identity 9 0 1 3
-25887: y 18 0 18 3,1,1,1,1,1,1,2
-25887: x 36 0 36 1,1,1,1,1,1,1,2
-25887: additive_inverse 6 1 0
-25887: commutator 1 2 0
-25887: add 21 2 5 0,2
-25887: multiply 30 2 12 0,1,1,1,1,1,2
-25887: associator 19 3 18 0,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-25888: Facts:
-25888: Id : 2, {_}:
- add ?2 ?3 =?= add ?3 ?2
- [3, 2] by commutativity_for_addition ?2 ?3
-25888: Id : 3, {_}:
- add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
- [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
-25888: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
-25888: Id : 5, {_}:
- add ?11 additive_identity =>= ?11
- [11] by right_additive_identity ?11
-25888: Id : 6, {_}:
- multiply additive_identity ?13 =>= additive_identity
- [13] by left_multiplicative_zero ?13
-25888: Id : 7, {_}:
- multiply ?15 additive_identity =>= additive_identity
- [15] by right_multiplicative_zero ?15
-25888: Id : 8, {_}:
- add (additive_inverse ?17) ?17 =>= additive_identity
- [17] by left_additive_inverse ?17
-25888: Id : 9, {_}:
- add ?19 (additive_inverse ?19) =>= additive_identity
- [19] by right_additive_inverse ?19
-25888: Id : 10, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-25888: Id : 11, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-25888: Id : 12, {_}:
- additive_inverse (additive_inverse ?29) =>= ?29
- [29] by additive_inverse_additive_inverse ?29
-25888: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-25888: Id : 14, {_}:
- associator ?34 ?35 ?36
- =>=
- add (multiply (multiply ?34 ?35) ?36)
- (additive_inverse (multiply ?34 (multiply ?35 ?36)))
- [36, 35, 34] by associator ?34 ?35 ?36
-25888: Id : 15, {_}:
- commutator ?38 ?39
- =<=
- add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
- [39, 38] by commutator ?38 ?39
-25888: Goal:
-25888: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25888: Order:
-25888: lpo
-25888: Leaf order:
-25888: additive_identity 9 0 1 3
-25888: y 18 0 18 3,1,1,1,1,1,1,2
-25888: x 36 0 36 1,1,1,1,1,1,1,2
-25888: additive_inverse 6 1 0
-25888: commutator 1 2 0
-25888: add 21 2 5 0,2
-25888: multiply 30 2 12 0,1,1,1,1,1,2
-25888: associator 19 3 18 0,1,1,1,1,1,1,2
-% SZS status Timeout for RNG032-6.p
-NO CLASH, using fixed ground order
-25915: Facts:
-25915: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25915: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25915: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25915: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25915: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25915: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25915: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25915: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25915: Id : 10, {_}:
- add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25915: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25915: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25915: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25915: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25915: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25915: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25915: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25915: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25915: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25915: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25915: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25915: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25915: Goal:
-25915: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25915: Order:
-25915: nrkbo
-25915: Leaf order:
-25915: additive_identity 9 0 1 3
-25915: y 18 0 18 3,1,1,1,1,1,1,2
-25915: x 36 0 36 1,1,1,1,1,1,1,2
-25915: additive_inverse 22 1 0
-25915: commutator 1 2 0
-25915: add 29 2 5 0,2
-25915: multiply 48 2 12 0,1,1,1,1,1,2add
-25915: associator 19 3 18 0,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-25916: Facts:
-25916: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25916: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25916: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25916: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =<=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25916: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =<=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25916: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =<=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25916: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =<=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25916: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25916: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25916: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25916: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25916: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25916: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25916: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25916: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25916: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =<=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25916: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =<=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25916: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25916: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25916: Id : 21, {_}:
- associator ?59 ?60 ?61
- =<=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25916: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25916: Goal:
-25916: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25916: Order:
-25916: kbo
-25916: Leaf order:
-25916: additive_identity 9 0 1 3
-25916: y 18 0 18 3,1,1,1,1,1,1,2
-25916: x 36 0 36 1,1,1,1,1,1,1,2
-25916: additive_inverse 22 1 0
-25916: commutator 1 2 0
-25916: add 29 2 5 0,2
-25916: multiply 48 2 12 0,1,1,1,1,1,2add
-25916: associator 19 3 18 0,1,1,1,1,1,1,2
-NO CLASH, using fixed ground order
-25917: Facts:
-25917: Id : 2, {_}:
- multiply (additive_inverse ?2) (additive_inverse ?3)
- =>=
- multiply ?2 ?3
- [3, 2] by product_of_inverses ?2 ?3
-25917: Id : 3, {_}:
- multiply (additive_inverse ?5) ?6
- =>=
- additive_inverse (multiply ?5 ?6)
- [6, 5] by inverse_product1 ?5 ?6
-25917: Id : 4, {_}:
- multiply ?8 (additive_inverse ?9)
- =>=
- additive_inverse (multiply ?8 ?9)
- [9, 8] by inverse_product2 ?8 ?9
-25917: Id : 5, {_}:
- multiply ?11 (add ?12 (additive_inverse ?13))
- =>=
- add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
- [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
-25917: Id : 6, {_}:
- multiply (add ?15 (additive_inverse ?16)) ?17
- =>=
- add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
- [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
-25917: Id : 7, {_}:
- multiply (additive_inverse ?19) (add ?20 ?21)
- =>=
- add (additive_inverse (multiply ?19 ?20))
- (additive_inverse (multiply ?19 ?21))
- [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
-25917: Id : 8, {_}:
- multiply (add ?23 ?24) (additive_inverse ?25)
- =>=
- add (additive_inverse (multiply ?23 ?25))
- (additive_inverse (multiply ?24 ?25))
- [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
-25917: Id : 9, {_}:
- add ?27 ?28 =?= add ?28 ?27
- [28, 27] by commutativity_for_addition ?27 ?28
-25917: Id : 10, {_}:
- add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
- [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
-25917: Id : 11, {_}:
- add additive_identity ?34 =>= ?34
- [34] by left_additive_identity ?34
-25917: Id : 12, {_}:
- add ?36 additive_identity =>= ?36
- [36] by right_additive_identity ?36
-25917: Id : 13, {_}:
- multiply additive_identity ?38 =>= additive_identity
- [38] by left_multiplicative_zero ?38
-25917: Id : 14, {_}:
- multiply ?40 additive_identity =>= additive_identity
- [40] by right_multiplicative_zero ?40
-25917: Id : 15, {_}:
- add (additive_inverse ?42) ?42 =>= additive_identity
- [42] by left_additive_inverse ?42
-25917: Id : 16, {_}:
- add ?44 (additive_inverse ?44) =>= additive_identity
- [44] by right_additive_inverse ?44
-25917: Id : 17, {_}:
- multiply ?46 (add ?47 ?48)
- =>=
- add (multiply ?46 ?47) (multiply ?46 ?48)
- [48, 47, 46] by distribute1 ?46 ?47 ?48
-25917: Id : 18, {_}:
- multiply (add ?50 ?51) ?52
- =>=
- add (multiply ?50 ?52) (multiply ?51 ?52)
- [52, 51, 50] by distribute2 ?50 ?51 ?52
-25917: Id : 19, {_}:
- additive_inverse (additive_inverse ?54) =>= ?54
- [54] by additive_inverse_additive_inverse ?54
-25917: Id : 20, {_}:
- multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
- [57, 56] by right_alternative ?56 ?57
-25917: Id : 21, {_}:
- associator ?59 ?60 ?61
- =>=
- add (multiply (multiply ?59 ?60) ?61)
- (additive_inverse (multiply ?59 (multiply ?60 ?61)))
- [61, 60, 59] by associator ?59 ?60 ?61
-25917: Id : 22, {_}:
- commutator ?63 ?64
- =<=
- add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
- [64, 63] by commutator ?63 ?64
-25917: Goal:
-25917: Id : 1, {_}:
- add
- (add
- (add
- (add
- (add
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y))))
- (multiply (associator x x y)
- (multiply (associator x x y) (associator x x y)))
- =>=
- additive_identity
- [] by prove_conjecture_3
-25917: Order:
-25917: lpo
-25917: Leaf order:
-25917: additive_identity 9 0 1 3
-25917: y 18 0 18 3,1,1,1,1,1,1,2
-25917: x 36 0 36 1,1,1,1,1,1,1,2
-25917: additive_inverse 22 1 0
-25917: commutator 1 2 0
-25917: add 29 2 5 0,2
-25917: multiply 48 2 12 0,1,1,1,1,1,2add
-25917: associator 19 3 18 0,1,1,1,1,1,1,2
-% SZS status Timeout for RNG032-7.p
-NO CLASH, using fixed ground order
-26009: Facts:
-26009: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26009: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26009: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26009: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26009: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26009: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26009: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26009: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26009: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26009: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26009: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-NO CLASH, using fixed ground order
-26010: Facts:
-26010: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26010: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26010: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26010: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26010: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26010: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26010: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26010: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26010: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26010: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26010: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26010: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26010: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26010: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26010: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26010: Goal:
-26010: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26010: Order:
-26010: lpo
-26010: Leaf order:
-26010: x 4 0 4 1,1,1,2
-26010: y 4 0 4 2,1,1,2
-26010: z 4 0 4 2,1,2
-26010: w 4 0 4 3,1,2
-26010: additive_identity 8 0 0
-26010: additive_inverse 6 1 0
-26010: commutator 2 2 1 0,3,2,2
-26010: add 18 2 2 0,2
-26010: multiply 25 2 3 0,1,1,2
-26010: associator 5 3 4 0,1,2
-26009: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26009: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26009: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26009: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26009: Goal:
-26009: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26009: Order:
-26009: kbo
-26009: Leaf order:
-26009: x 4 0 4 1,1,1,2
-26009: y 4 0 4 2,1,1,2
-26009: z 4 0 4 2,1,2
-26009: w 4 0 4 3,1,2
-26009: additive_identity 8 0 0
-26009: additive_inverse 6 1 0
-26009: commutator 2 2 1 0,3,2,2
-26009: add 18 2 2 0,2
-26009: multiply 25 2 3 0,1,1,2
-26009: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26008: Facts:
-26008: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26008: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26008: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26008: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26008: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26008: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26008: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26008: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26008: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26008: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26008: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26008: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26008: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26008: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26008: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26008: Goal:
-26008: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26008: Order:
-26008: nrkbo
-26008: Leaf order:
-26008: x 4 0 4 1,1,1,2
-26008: y 4 0 4 2,1,1,2
-26008: z 4 0 4 2,1,2
-26008: w 4 0 4 3,1,2
-26008: additive_identity 8 0 0
-26008: additive_inverse 6 1 0
-26008: commutator 2 2 1 0,3,2,2
-26008: add 18 2 2 0,2
-26008: multiply 25 2 3 0,1,1,2
-26008: associator 5 3 4 0,1,2
-% SZS status Timeout for RNG033-6.p
-NO CLASH, using fixed ground order
-26035: Facts:
-26035: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26035: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26035: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26035: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26035: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26035: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26035: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26035: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26035: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26035: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26035: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26035: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26035: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26035: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26035: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26035: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26035: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26035: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26035: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26035: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26035: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26035: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26035: Goal:
-26035: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26035: Order:
-26035: nrkbo
-26035: Leaf order:
-26035: x 4 0 4 1,1,1,2
-26035: y 4 0 4 2,1,1,2
-26035: z 4 0 4 2,1,2
-26035: w 4 0 4 3,1,2
-26035: additive_identity 8 0 0
-26035: additive_inverse 22 1 0
-26035: commutator 2 2 1 0,3,2,2
-26035: add 26 2 2 0,2
-26035: multiply 43 2 3 0,1,1,2
-26035: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26036: Facts:
-26036: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26036: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26036: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26036: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26036: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26036: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26036: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26036: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26036: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26036: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26036: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26036: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26036: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26036: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26036: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26036: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26036: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26036: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26036: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26036: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26036: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26036: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26036: Goal:
-26036: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26036: Order:
-26036: kbo
-26036: Leaf order:
-26036: x 4 0 4 1,1,1,2
-26036: y 4 0 4 2,1,1,2
-26036: z 4 0 4 2,1,2
-26036: w 4 0 4 3,1,2
-26036: additive_identity 8 0 0
-26036: additive_inverse 22 1 0
-26036: commutator 2 2 1 0,3,2,2
-26036: add 26 2 2 0,2
-26036: multiply 43 2 3 0,1,1,2
-26036: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26037: Facts:
-26037: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26037: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26037: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26037: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26037: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26037: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26037: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26037: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26037: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26037: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26037: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26037: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26037: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26037: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26037: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26037: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26037: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26037: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26037: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26037: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26037: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26037: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26037: Goal:
-26037: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26037: Order:
-26037: lpo
-26037: Leaf order:
-26037: x 4 0 4 1,1,1,2
-26037: y 4 0 4 2,1,1,2
-26037: z 4 0 4 2,1,2
-26037: w 4 0 4 3,1,2
-26037: additive_identity 8 0 0
-26037: additive_inverse 22 1 0
-26037: commutator 2 2 1 0,3,2,2
-26037: add 26 2 2 0,2
-26037: multiply 43 2 3 0,1,1,2
-26037: associator 5 3 4 0,1,2
-% SZS status Timeout for RNG033-7.p
-NO CLASH, using fixed ground order
-26058: Facts:
-26058: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26058: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26058: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26058: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26058: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26058: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26058: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26058: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26058: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26058: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26058: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26058: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26058: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26058: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26058: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26058: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =?=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-26058: Goal:
-26058: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26058: Order:
-26058: nrkbo
-26058: Leaf order:
-26058: x 4 0 4 1,1,1,2
-26058: y 4 0 4 2,1,1,2
-26058: z 4 0 4 2,1,2
-26058: w 4 0 4 3,1,2
-26058: additive_identity 8 0 0
-26058: additive_inverse 6 1 0
-26058: commutator 2 2 1 0,3,2,2
-26058: add 18 2 2 0,2
-26058: multiply 31 2 3 0,1,1,2
-26058: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26059: Facts:
-26059: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26059: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26059: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26059: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26059: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26059: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26059: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26059: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26059: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26059: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26059: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26059: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26059: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26059: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26059: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26059: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =<=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-26059: Goal:
-26059: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26059: Order:
-26059: kbo
-26059: Leaf order:
-26059: x 4 0 4 1,1,1,2
-26059: y 4 0 4 2,1,1,2
-26059: z 4 0 4 2,1,2
-26059: w 4 0 4 3,1,2
-26059: additive_identity 8 0 0
-26059: additive_inverse 6 1 0
-26059: commutator 2 2 1 0,3,2,2
-26059: add 18 2 2 0,2
-26059: multiply 31 2 3 0,1,1,2
-26059: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26060: Facts:
-26060: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26060: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26060: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26060: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26060: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26060: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26060: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26060: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26060: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26060: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26060: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26060: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26060: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26060: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26060: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26060: Id : 17, {_}:
- multiply ?44 (multiply ?45 (multiply ?46 ?45))
- =<=
- multiply (multiply (multiply ?44 ?45) ?46) ?45
- [46, 45, 44] by right_moufang ?44 ?45 ?46
-26060: Goal:
-26060: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26060: Order:
-26060: lpo
-26060: Leaf order:
-26060: x 4 0 4 1,1,1,2
-26060: y 4 0 4 2,1,1,2
-26060: z 4 0 4 2,1,2
-26060: w 4 0 4 3,1,2
-26060: additive_identity 8 0 0
-26060: additive_inverse 6 1 0
-26060: commutator 2 2 1 0,3,2,2
-26060: add 18 2 2 0,2
-26060: multiply 31 2 3 0,1,1,2
-26060: associator 5 3 4 0,1,2
-% SZS status Timeout for RNG033-8.p
-NO CLASH, using fixed ground order
-26087: Facts:
-26087: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26087: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26087: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26087: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26087: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26087: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26087: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26087: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26087: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26087: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26087: Id : 12, {_}:
- add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26087: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26087: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26087: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26087: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26087: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26087: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26087: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26087: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26087: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26087: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26087: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26087: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =?=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-26087: Goal:
-26087: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26087: Order:
-26087: nrkbo
-26087: Leaf order:
-26087: x 4 0 4 1,1,1,2
-26087: y 4 0 4 2,1,1,2
-26087: z 4 0 4 2,1,2
-26087: w 4 0 4 3,1,2
-26087: additive_identity 8 0 0
-26087: additive_inverse 22 1 0
-26087: commutator 2 2 1 0,3,2,2
-26087: add 26 2 2 0,2
-26087: multiply 49 2 3 0,1,1,2
-26087: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26089: Facts:
-26089: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26089: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26089: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26089: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26089: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26089: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26089: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26089: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =>=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26089: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =>=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26089: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26089: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26089: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26089: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26089: Id : 15, {_}:
- associator ?37 ?38 ?39
- =>=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26089: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26089: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26089: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26089: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26089: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =>=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26089: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =>=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26089: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =>=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26089: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =>=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26089: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =<=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-26089: Goal:
-26089: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26089: Order:
-26089: lpo
-26089: Leaf order:
-26089: x 4 0 4 1,1,1,2
-26089: y 4 0 4 2,1,1,2
-26089: z 4 0 4 2,1,2
-26089: w 4 0 4 3,1,2
-26089: additive_identity 8 0 0
-26089: additive_inverse 22 1 0
-26089: commutator 2 2 1 0,3,2,2
-26089: add 26 2 2 0,2
-26089: multiply 49 2 3 0,1,1,2
-26089: associator 5 3 4 0,1,2
-NO CLASH, using fixed ground order
-26088: Facts:
-26088: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26088: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26088: Id : 4, {_}:
- multiply additive_identity ?6 =>= additive_identity
- [6] by left_multiplicative_zero ?6
-26088: Id : 5, {_}:
- multiply ?8 additive_identity =>= additive_identity
- [8] by right_multiplicative_zero ?8
-26088: Id : 6, {_}:
- add (additive_inverse ?10) ?10 =>= additive_identity
- [10] by left_additive_inverse ?10
-26088: Id : 7, {_}:
- add ?12 (additive_inverse ?12) =>= additive_identity
- [12] by right_additive_inverse ?12
-26088: Id : 8, {_}:
- additive_inverse (additive_inverse ?14) =>= ?14
- [14] by additive_inverse_additive_inverse ?14
-26088: Id : 9, {_}:
- multiply ?16 (add ?17 ?18)
- =<=
- add (multiply ?16 ?17) (multiply ?16 ?18)
- [18, 17, 16] by distribute1 ?16 ?17 ?18
-26088: Id : 10, {_}:
- multiply (add ?20 ?21) ?22
- =<=
- add (multiply ?20 ?22) (multiply ?21 ?22)
- [22, 21, 20] by distribute2 ?20 ?21 ?22
-26088: Id : 11, {_}:
- add ?24 ?25 =?= add ?25 ?24
- [25, 24] by commutativity_for_addition ?24 ?25
-26088: Id : 12, {_}:
- add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
- [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
-26088: Id : 13, {_}:
- multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
- [32, 31] by right_alternative ?31 ?32
-26088: Id : 14, {_}:
- multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
- [35, 34] by left_alternative ?34 ?35
-26088: Id : 15, {_}:
- associator ?37 ?38 ?39
- =<=
- add (multiply (multiply ?37 ?38) ?39)
- (additive_inverse (multiply ?37 (multiply ?38 ?39)))
- [39, 38, 37] by associator ?37 ?38 ?39
-26088: Id : 16, {_}:
- commutator ?41 ?42
- =<=
- add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
- [42, 41] by commutator ?41 ?42
-26088: Id : 17, {_}:
- multiply (additive_inverse ?44) (additive_inverse ?45)
- =>=
- multiply ?44 ?45
- [45, 44] by product_of_inverses ?44 ?45
-26088: Id : 18, {_}:
- multiply (additive_inverse ?47) ?48
- =>=
- additive_inverse (multiply ?47 ?48)
- [48, 47] by inverse_product1 ?47 ?48
-26088: Id : 19, {_}:
- multiply ?50 (additive_inverse ?51)
- =>=
- additive_inverse (multiply ?50 ?51)
- [51, 50] by inverse_product2 ?50 ?51
-26088: Id : 20, {_}:
- multiply ?53 (add ?54 (additive_inverse ?55))
- =<=
- add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
- [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
-26088: Id : 21, {_}:
- multiply (add ?57 (additive_inverse ?58)) ?59
- =<=
- add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
- [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
-26088: Id : 22, {_}:
- multiply (additive_inverse ?61) (add ?62 ?63)
- =<=
- add (additive_inverse (multiply ?61 ?62))
- (additive_inverse (multiply ?61 ?63))
- [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
-26088: Id : 23, {_}:
- multiply (add ?65 ?66) (additive_inverse ?67)
- =<=
- add (additive_inverse (multiply ?65 ?67))
- (additive_inverse (multiply ?66 ?67))
- [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
-26088: Id : 24, {_}:
- multiply ?69 (multiply ?70 (multiply ?71 ?70))
- =<=
- multiply (multiply (multiply ?69 ?70) ?71) ?70
- [71, 70, 69] by right_moufang ?69 ?70 ?71
-26088: Goal:
-26088: Id : 1, {_}:
- add (associator (multiply x y) z w) (associator x y (commutator z w))
- =>=
- add (multiply x (associator y z w)) (multiply (associator x z w) y)
- [] by prove_challenge
-26088: Order:
-26088: kbo
-26088: Leaf order:
-26088: x 4 0 4 1,1,1,2
-26088: y 4 0 4 2,1,1,2
-26088: z 4 0 4 2,1,2
-26088: w 4 0 4 3,1,2
-26088: additive_identity 8 0 0
-26088: additive_inverse 22 1 0
-26088: commutator 2 2 1 0,3,2,2
-26088: add 26 2 2 0,2
-26088: multiply 49 2 3 0,1,1,2
-26088: associator 5 3 4 0,1,2
-% SZS status Timeout for RNG033-9.p
-NO CLASH, using fixed ground order
-NO CLASH, using fixed ground order
-26115: Facts:
-26115: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26116: Facts:
-26116: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26116: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26116: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-26116: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-26116: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-26116: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-26116: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-26116: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-26115: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26116: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-26115: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-26115: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-26115: Id : 6, {_}:
- add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-26115: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-26115: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-26115: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =<=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-26115: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =<=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-26115: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-26115: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-26115: Goal:
-NO CLASH, using fixed ground order
-26117: Facts:
-26117: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
-26117: Id : 3, {_}:
- add ?4 additive_identity =>= ?4
- [4] by right_additive_identity ?4
-26117: Id : 4, {_}:
- add (additive_inverse ?6) ?6 =>= additive_identity
- [6] by left_additive_inverse ?6
-26117: Id : 5, {_}:
- add ?8 (additive_inverse ?8) =>= additive_identity
- [8] by right_additive_inverse ?8
-26117: Id : 6, {_}:
- add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
- [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
-26117: Id : 7, {_}:
- add ?14 ?15 =?= add ?15 ?14
- [15, 14] by commutativity_for_addition ?14 ?15
-26117: Id : 8, {_}:
- multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
- [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
-26117: Id : 9, {_}:
- multiply ?21 (add ?22 ?23)
- =>=
- add (multiply ?21 ?22) (multiply ?21 ?23)
- [23, 22, 21] by distribute1 ?21 ?22 ?23
-26117: Id : 10, {_}:
- multiply (add ?25 ?26) ?27
- =>=
- add (multiply ?25 ?27) (multiply ?26 ?27)
- [27, 26, 25] by distribute2 ?25 ?26 ?27
-26117: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-26117: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-26117: Goal:
-26117: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-26117: Order:
-26117: lpo
-26117: Leaf order:
-26117: b 2 0 1 1,2
-26117: a 2 0 1 2,2
-26117: c 2 0 1 3
-26117: additive_identity 4 0 0
-26117: additive_inverse 2 1 0
-26117: add 14 2 0
-26117: multiply 16 2 1 0,2
-26116: Id : 11, {_}:
- multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
- [29] by x_fifthed_is_x ?29
-26116: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
-26116: Goal:
-26116: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-26116: Order:
-26116: kbo
-26116: Leaf order:
-26116: b 2 0 1 1,2
-26116: a 2 0 1 2,2
-26116: c 2 0 1 3
-26116: additive_identity 4 0 0
-26116: additive_inverse 2 1 0
-26116: add 14 2 0
-26116: multiply 16 2 1 0,2
-26115: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
-26115: Order:
-26115: nrkbo
-26115: Leaf order:
-26115: b 2 0 1 1,2
-26115: a 2 0 1 2,2
-26115: c 2 0 1 3
-26115: additive_identity 4 0 0
-26115: additive_inverse 2 1 0
-26115: add 14 2 0
-26115: multiply 16 2 1 0,2
-% SZS status Timeout for RNG036-7.p
-NO CLASH, using fixed ground order
-26159: Facts:
-26159: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26159: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26159: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26159: Goal:
-26159: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26159: Order:
-26159: nrkbo
-26159: Leaf order:
-26159: a 2 0 2 1,1,1,2
-26159: b 3 0 3 1,2,1,1,2
-26159: negate 9 1 5 0,1,2
-26159: add 12 2 3 0,2
-NO CLASH, using fixed ground order
-26160: Facts:
-26160: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26160: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26160: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26160: Goal:
-26160: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26160: Order:
-26160: kbo
-26160: Leaf order:
-26160: a 2 0 2 1,1,1,2
-26160: b 3 0 3 1,2,1,1,2
-26160: negate 9 1 5 0,1,2
-26160: add 12 2 3 0,2
-NO CLASH, using fixed ground order
-26161: Facts:
-26161: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26161: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26161: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26161: Goal:
-26161: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26161: Order:
-26161: lpo
-26161: Leaf order:
-26161: a 2 0 2 1,1,1,2
-26161: b 3 0 3 1,2,1,1,2
-26161: negate 9 1 5 0,1,2
-26161: add 12 2 3 0,2
-% SZS status Timeout for ROB001-1.p
-NO CLASH, using fixed ground order
-26183: Facts:
-26183: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26183: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26183: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26183: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26183: Goal:
-26183: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26183: Order:
-26183: nrkbo
-26183: Leaf order:
-26183: a 3 0 2 1,1,1,2
-26183: b 5 0 3 1,2,1,1,2
-26183: negate 11 1 5 0,1,2
-26183: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-26184: Facts:
-26184: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26184: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26184: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26184: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26184: Goal:
-26184: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26184: Order:
-26184: kbo
-26184: Leaf order:
-26184: a 3 0 2 1,1,1,2
-26184: b 5 0 3 1,2,1,1,2
-26184: negate 11 1 5 0,1,2
-26184: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-26185: Facts:
-26185: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26185: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26185: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26185: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26185: Goal:
-26185: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26185: Order:
-26185: lpo
-26185: Leaf order:
-26185: a 3 0 2 1,1,1,2
-26185: b 5 0 3 1,2,1,1,2
-26185: negate 11 1 5 0,1,2
-26185: add 13 2 3 0,2
-% SZS status Timeout for ROB007-1.p
-NO CLASH, using fixed ground order
-26215: Facts:
-26215: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26215: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26215: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26215: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26215: Goal:
-26215: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26215: Order:
-26215: nrkbo
-26215: Leaf order:
-26215: a 1 0 0
-26215: b 2 0 0
-26215: negate 6 1 0
-26215: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-26216: Facts:
-26216: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26216: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26216: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26216: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26216: Goal:
-26216: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26216: Order:
-26216: kbo
-26216: Leaf order:
-26216: a 1 0 0
-26216: b 2 0 0
-26216: negate 6 1 0
-26216: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-26217: Facts:
-26217: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26217: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26217: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26217: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
-26217: Goal:
-26217: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26217: Order:
-26217: lpo
-26217: Leaf order:
-26217: a 1 0 0
-26217: b 2 0 0
-26217: negate 6 1 0
-26217: add 11 2 1 0,2
-% SZS status Timeout for ROB007-2.p
-NO CLASH, using fixed ground order
-26249: Facts:
-26249: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26249: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26249: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26249: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26249: Goal:
-26249: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26249: Order:
-26249: nrkbo
-26249: Leaf order:
-26249: a 3 0 2 1,1,1,2
-26249: b 5 0 3 1,2,1,1,2
-26249: negate 11 1 5 0,1,2
-26249: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-26250: Facts:
-26250: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26250: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26250: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26250: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26250: Goal:
-26250: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26250: Order:
-26250: kbo
-26250: Leaf order:
-26250: a 3 0 2 1,1,1,2
-26250: b 5 0 3 1,2,1,1,2
-26250: negate 11 1 5 0,1,2
-26250: add 13 2 3 0,2
-NO CLASH, using fixed ground order
-26251: Facts:
-26251: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26251: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26251: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26251: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26251: Goal:
-26251: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26251: Order:
-26251: lpo
-26251: Leaf order:
-26251: a 3 0 2 1,1,1,2
-26251: b 5 0 3 1,2,1,1,2
-26251: negate 11 1 5 0,1,2
-26251: add 13 2 3 0,2
-% SZS status Timeout for ROB020-1.p
-NO CLASH, using fixed ground order
-26275: Facts:
-26275: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26275: Id : 3, {_}:
- add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26275: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26275: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26275: Goal:
-26275: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26275: Order:
-26275: nrkbo
-26275: Leaf order:
-26275: a 1 0 0
-26275: b 2 0 0
-26275: negate 6 1 0
-26275: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-26276: Facts:
-26276: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26276: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26276: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26276: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26276: Goal:
-26276: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26276: Order:
-26276: kbo
-26276: Leaf order:
-26276: a 1 0 0
-26276: b 2 0 0
-26276: negate 6 1 0
-26276: add 11 2 1 0,2
-NO CLASH, using fixed ground order
-26277: Facts:
-26277: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
-26277: Id : 3, {_}:
- add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
- [8, 7, 6] by associativity_of_add ?6 ?7 ?8
-26277: Id : 4, {_}:
- negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
- =>=
- ?10
- [11, 10] by robbins_axiom ?10 ?11
-26277: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
-26277: Goal:
-26277: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
-26277: Order:
-26277: lpo
-26277: Leaf order:
-26277: a 1 0 0
-26277: b 2 0 0
-26277: negate 6 1 0
-26277: add 11 2 1 0,2
-% SZS status Timeout for ROB020-2.p
-NO CLASH, using fixed ground order
-26303: Facts:
-26303: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26303: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26303: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26303: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-26303: Goal:
-26303: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26303: Order:
-26303: nrkbo
-26303: Leaf order:
-26303: b 5 0 3 1,2,1,1,2
-26303: a 6 0 2 1,1,1,2
-26303: negate 13 1 5 0,1,2
-26303: add 16 2 3 0,2
-NO CLASH, using fixed ground order
-26304: Facts:
-26304: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26304: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26304: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26304: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-26304: Goal:
-26304: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26304: Order:
-26304: kbo
-26304: Leaf order:
-26304: b 5 0 3 1,2,1,1,2
-26304: a 6 0 2 1,1,1,2
-26304: negate 13 1 5 0,1,2
-26304: add 16 2 3 0,2
-NO CLASH, using fixed ground order
-26305: Facts:
-26305: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26305: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26305: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26305: Id : 5, {_}:
- negate (add (negate (add a (add a b))) (negate (add a (negate b))))
- =>=
- a
- [] by the_condition
-26305: Goal:
-26305: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26305: Order:
-26305: lpo
-26305: Leaf order:
-26305: b 5 0 3 1,2,1,1,2
-26305: a 6 0 2 1,1,1,2
-26305: negate 13 1 5 0,1,2
-26305: add 16 2 3 0,2
-% SZS status Timeout for ROB024-1.p
-NO CLASH, using fixed ground order
-26392: Facts:
-26392: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26392: Id : 3, {_}:
- add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26392: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26392: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-26392: Goal:
-26392: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26392: Order:
-26392: nrkbo
-26392: Leaf order:
-26392: c 2 0 0
-26392: a 2 0 2 1,1,1,2
-26392: b 3 0 3 1,2,1,1,2
-26392: negate 11 1 5 0,1,2
-26392: add 12 2 3 0,2
-NO CLASH, using fixed ground order
-26393: Facts:
-26393: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26393: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26393: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26393: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-26393: Goal:
-26393: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26393: Order:
-26393: kbo
-26393: Leaf order:
-26393: c 2 0 0
-26393: a 2 0 2 1,1,1,2
-26393: b 3 0 3 1,2,1,1,2
-26393: negate 11 1 5 0,1,2
-26393: add 12 2 3 0,2
-NO CLASH, using fixed ground order
-26394: Facts:
-26394: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
-26394: Id : 3, {_}:
- add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
- [7, 6, 5] by associativity_of_add ?5 ?6 ?7
-26394: Id : 4, {_}:
- negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
- =>=
- ?9
- [10, 9] by robbins_axiom ?9 ?10
-26394: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
-26394: Goal:
-26394: Id : 1, {_}:
- add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
- =>=
- b
- [] by prove_huntingtons_axiom
-26394: Order:
-26394: lpo
-26394: Leaf order:
-26394: c 2 0 0
-26394: a 2 0 2 1,1,1,2
-26394: b 3 0 3 1,2,1,1,2
-26394: negate 11 1 5 0,1,2
-26394: add 12 2 3 0,2
-% SZS status Timeout for ROB027-1.p
-NO CLASH, using fixed ground order
-26415: Facts:
-26415: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26415: Id : 3, {_}:
- add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26415: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26415: Goal:
-26415: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-26415: Order:
-26415: nrkbo
-26415: Leaf order:
-26415: negate 6 1 2 0,2
-26415: add 10 2 1 0,1,2
-NO CLASH, using fixed ground order
-26416: Facts:
-26416: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26416: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26416: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26416: Goal:
-26416: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-26416: Order:
-26416: kbo
-26416: Leaf order:
-26416: negate 6 1 2 0,2
-26416: add 10 2 1 0,1,2
-NO CLASH, using fixed ground order
-26417: Facts:
-26417: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26417: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26417: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26417: Goal:
-26417: Id : 1, {_}:
- negate (add ?1 ?2) =>= negate ?2
- [2, 1] by prove_absorption_within_negation ?1 ?2
-26417: Order:
-26417: lpo
-26417: Leaf order:
-26417: negate 6 1 2 0,2
-26417: add 10 2 1 0,1,2
-% SZS status Timeout for ROB031-1.p
-NO CLASH, using fixed ground order
-26440: Facts:
-26440: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26440: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26440: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26440: Goal:
-26440: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-26440: Order:
-26440: kbo
-26440: Leaf order:
-26440: negate 4 1 0
-26440: add 10 2 1 0,2
-NO CLASH, using fixed ground order
-26441: Facts:
-26441: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26441: Id : 3, {_}:
- add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26441: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26441: Goal:
-26441: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-26441: Order:
-26441: lpo
-26441: Leaf order:
-26441: negate 4 1 0
-26441: add 10 2 1 0,2
-NO CLASH, using fixed ground order
-26439: Facts:
-26439: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
-26439: Id : 3, {_}:
- add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
- [9, 8, 7] by associativity_of_add ?7 ?8 ?9
-26439: Id : 4, {_}:
- negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
- =>=
- ?11
- [12, 11] by robbins_axiom ?11 ?12
-26439: Goal:
-26439: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
-26439: Order:
-26439: nrkbo
-26439: Leaf order:
-26439: negate 4 1 0
-26439: add 10 2 1 0,2
-% SZS status Timeout for ROB032-1.p
projects / helm.git / commitdiff